LMFDB - Embedded newform 1323.2.f.e.883.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (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			883.5
Root			$-1.02682 + 1.77851i$ of defining polynomial
Character	$\chi$	$=$	1323.883
Dual form			1323.2.f.e.442.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} +(-0.0731228 - 0.126652i) q^{5} -0.446582 q^{8} +O(q^{10})$	\(q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} +(-0.0731228 - 0.126652i) q^{5} -0.446582 q^{8} -0.300337 q^{10} +(0.832020 - 1.44110i) q^{11} +(0.0999454 + 0.173111i) q^{13} +(1.75890 - 3.04650i) q^{16} +6.27110 q^{17} -6.91758 q^{19} +(-0.162147 + 0.280847i) q^{20} +(-1.70867 - 2.95951i) q^{22} +(-3.09092 - 5.35363i) q^{23} +(2.48931 - 4.31160i) q^{25} +0.410505 q^{26} +(2.46757 - 4.27396i) q^{29} +(1.25890 + 2.18047i) q^{31} +(-4.05873 - 7.02993i) q^{32} +(6.43931 - 11.1532i) q^{34} +7.00046 q^{37} +(-7.10312 + 12.3030i) q^{38} +(0.0326554 + 0.0565608i) q^{40} +(-1.15895 - 2.00736i) q^{41} +(-0.940993 + 1.62985i) q^{43} -3.68994 q^{44} -12.6953 q^{46} +(-0.905887 + 1.56904i) q^{47} +(-5.11215 - 8.85451i) q^{50} +(0.221625 - 0.383865i) q^{52} -5.34614 q^{53} -0.243359 q^{55} +(-5.06752 - 8.77720i) q^{58} +(-2.28549 - 3.95859i) q^{59} +(0.339138 - 0.587404i) q^{61} +5.17066 q^{62} -9.63481 q^{64} +(0.0146166 - 0.0253167i) q^{65} +(3.09342 + 5.35796i) q^{67} +(-6.95296 - 12.0429i) q^{68} -1.27749 q^{71} +1.55721 q^{73} +(7.18823 - 12.4504i) q^{74} +(7.66972 + 13.2843i) q^{76} +(-6.39787 + 11.0814i) q^{79} -0.514462 q^{80} -4.76015 q^{82} +(-3.75687 + 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(1.93247 + 3.34713i) q^{86} +(-0.371566 + 0.643571i) q^{88} +9.06788 q^{89} +(-6.85398 + 11.8714i) q^{92} +(1.86037 + 3.22226i) q^{94} +(0.505833 + 0.876128i) q^{95} +(-3.98514 + 6.90246i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^8	$ 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8} + 14 q^{10} - 4 q^{11} - 8 q^{13} + 2 q^{16} + 24 q^{17} - 2 q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 22 q^{26} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} - 20 q^{44} - 6 q^{46} - 27 q^{47} - 19 q^{50} - 10 q^{52} - 42 q^{53} + 4 q^{55} - 10 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 27 q^{68} + 6 q^{71} - 30 q^{73} + 36 q^{74} + 5 q^{76} - 4 q^{79} + 40 q^{80} + 10 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} + 56 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 - 4 * q^5 + 6 * q^8 + 14 * q^10 - 4 * q^11 - 8 * q^13 + 2 * q^16 + 24 * q^17 - 2 * q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 + 22 * q^26 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 - 20 * q^44 - 6 * q^46 - 27 * q^47 - 19 * q^50 - 10 * q^52 - 42 * q^53 + 4 * q^55 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 + 6 * q^71 - 30 * q^73 + 36 * q^74 + 5 * q^76 - 4 * q^79 + 40 * q^80 + 10 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 + 56 * 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 $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	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
$5$	−0.0731228	−	0.126652i	−0.0327015	−	0.0566407i	0.849211	−	0.528053i	$-0.177078\pi$
$5$	−0.0731228	−	0.126652i	−0.0327015	−	0.0566407i	−0.881913	+	0.471412i	$0.843744\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−0.446582			−0.157891
$9$		0			0
$10$	−0.300337			−0.0949748
$11$	0.832020	−	1.44110i	0.250864	−	0.434508i	−0.712900	−	0.701265i	$-0.752619\pi$
$11$	0.832020	−	1.44110i	0.250864	−	0.434508i	0.963764	+	0.266757i	$0.0859521\pi$
$12$		0			0
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	0.879553	−	0.475802i	$-0.157842\pi$
$13$	0.0999454	+	0.173111i	0.0277199	+	0.0480122i	−0.851833	+	0.523814i	$0.824509\pi$
$14$		0			0
$15$		0			0
$16$	1.75890	−	3.04650i	0.439724	−	0.761625i
$17$	6.27110			1.52097			0.760483	−	0.649358i	$-0.224962\pi$
$17$	6.27110			1.52097			0.760483	+	0.649358i	$0.224962\pi$
$18$		0			0
$19$	−6.91758			−1.58700			−0.793500	−	0.608570i	$-0.791744\pi$
$19$	−6.91758			−1.58700			−0.793500	+	0.608570i	$0.791744\pi$
$20$	−0.162147	+	0.280847i	−0.0362571	+	0.0627992i
$21$		0			0
$22$	−1.70867	−	2.95951i	−0.364291	−	0.630970i
$23$	−3.09092	−	5.35363i	−0.644501	−	1.11631i	−0.984417	−	0.175852i	$-0.943732\pi$
$23$	−3.09092	−	5.35363i	−0.644501	−	1.11631i	0.339916	−	0.940456i	$-0.389601\pi$
$24$		0			0
$25$	2.48931	−	4.31160i	0.497861	−	0.862321i
$26$	0.410505			0.0805066
$27$		0			0
$28$		0			0
$29$	2.46757	−	4.27396i	0.458217	−	0.793655i	−0.540650	−	0.841248i	$-0.681822\pi$
$29$	2.46757	−	4.27396i	0.458217	−	0.793655i	0.998867	+	0.0475930i	$0.0151551\pi$
$30$		0			0
$31$	1.25890	+	2.18047i	0.226105	+	0.391625i	0.956650	−	0.291239i	$-0.0940675\pi$
$31$	1.25890	+	2.18047i	0.226105	+	0.391625i	−0.730546	+	0.682864i	$0.760734\pi$
$32$	−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
$37$	7.00046			1.15087			0.575434	−	0.817848i	$-0.304833\pi$
$37$	7.00046			1.15087			0.575434	+	0.817848i	$0.304833\pi$
$38$	−7.10312	+	12.3030i	−1.15228	+	1.99581i
$39$		0			0
$40$	0.0326554	+	0.0565608i	0.00516327	+	0.00894304i
$41$	−1.15895	−	2.00736i	−0.180998	−	0.313498i	0.761223	−	0.648491i	$-0.224599\pi$
$41$	−1.15895	−	2.00736i	−0.180998	−	0.313498i	−0.942221	+	0.334993i	$0.891266\pi$
$42$		0			0
$43$	−0.940993	+	1.62985i	−0.143500	+	0.248550i	−0.928812	−	0.370550i	$-0.879169\pi$
$43$	−0.940993	+	1.62985i	−0.143500	+	0.248550i	0.785312	+	0.619100i	$0.212502\pi$
$44$	−3.68994			−0.556280
$45$		0			0
$46$	−12.6953			−1.87182
$47$	−0.905887	+	1.56904i	−0.132137	+	0.228868i	−0.924500	−	0.381181i	$-0.875517\pi$
$47$	−0.905887	+	1.56904i	−0.132137	+	0.228868i	0.792363	+	0.610050i	$0.208851\pi$
$48$		0			0
$49$		0			0
$50$	−5.11215	−	8.85451i	−0.722967	−	1.25222i
$51$		0			0
$52$	0.221625	−	0.383865i	0.0307338	−	0.0532325i
$53$	−5.34614			−0.734348			−0.367174	−	0.930152i	$-0.619675\pi$
$53$	−5.34614			−0.734348			−0.367174	+	0.930152i	$0.619675\pi$
$54$		0			0
$55$	−0.243359			−0.0328145
$56$		0			0
$57$		0			0
$58$	−5.06752	−	8.77720i	−0.665398	−	1.15250i
$59$	−2.28549	−	3.95859i	−0.297546	−	0.515364i	0.678028	−	0.735036i	$-0.262835\pi$
$59$	−2.28549	−	3.95859i	−0.297546	−	0.515364i	−0.975574	+	0.219672i	$0.929501\pi$
$60$		0			0
$61$	0.339138	−	0.587404i	0.0434221	−	0.0752094i	−0.843498	−	0.537133i	$-0.819507\pi$
$61$	0.339138	−	0.587404i	0.0434221	−	0.0752094i	0.886920	+	0.461924i	$0.152841\pi$
$62$	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	$0.709972\pi$
$68$	−6.95296	−	12.0429i	−0.843170	−	1.46041i
$69$		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
$73$	1.55721			0.182257			0.0911286	−	0.995839i	$-0.470953\pi$
$73$	1.55721			0.182257			0.0911286	+	0.995839i	$0.470953\pi$
$74$	7.18823	−	12.4504i	0.835614	−	1.44733i
$75$		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	$0.910892\pi$
$80$	−0.514462			−0.0575186
$81$		0			0
$82$	−4.76015			−0.525671
$83$	−3.75687	+	6.50709i	−0.412370	+	0.714246i	−0.995148	−	0.0983854i	$-0.968632\pi$
$83$	−3.75687	+	6.50709i	−0.412370	+	0.714246i	0.582778	+	0.812631i	$0.301966\pi$
$84$		0			0
$85$	−0.458561	−	0.794251i	−0.0497379	−	0.0861486i
$86$	1.93247	+	3.34713i	0.208383	+	0.360930i
$87$		0			0
$88$	−0.371566	+	0.643571i	−0.0396090	+	0.0686048i
$89$	9.06788			0.961193			0.480597	−	0.876942i	$-0.340420\pi$
$89$	9.06788			0.961193			0.480597	+	0.876942i	$0.340420\pi$
$90$		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	$-0.965933\pi$
$97$	−3.98514	+	6.90246i	−0.404630	+	0.700839i	0.589649	+	0.807660i	$0.299266\pi$
$98$		0			0
$99$		0			0
$100$	−11.0399			−1.10399
$101$	7.42150	−	12.8544i	0.738467	−	1.27906i	−0.214719	−	0.976676i	$-0.568883\pi$
$101$	7.42150	−	12.8544i	0.738467	−	1.27906i	0.953186	−	0.302386i	$-0.0977832\pi$
$102$		0			0
$103$	0.101974	+	0.176624i	0.0100478	+	0.0174033i	0.871006	−	0.491273i	$-0.163468\pi$
$103$	0.101974	+	0.176624i	0.0100478	+	0.0174033i	−0.860958	+	0.508676i	$0.830135\pi$
$104$	−0.0446339	−	0.0773081i	−0.00437671	−	0.00758068i
$105$		0			0
$106$	−5.48953	+	9.50815i	−0.533191	+	0.923513i
$107$	6.96889			0.673708			0.336854	−	0.941557i	$-0.390637\pi$
$107$	6.96889			0.673708			0.336854	+	0.941557i	$0.390637\pi$
$108$		0			0
$109$	−6.66116			−0.638024			−0.319012	−	0.947751i	$-0.603351\pi$
$109$	−6.66116			−0.638024			−0.319012	+	0.947751i	$0.603351\pi$
$110$	−0.249886	+	0.432816i	−0.0238257	+	0.0412674i
$111$		0			0
$112$		0			0
$113$	0.0193234	+	0.0334691i	0.00181779	+	0.00314851i	0.866933	−	0.498425i	$-0.166088\pi$
$113$	0.0193234	+	0.0334691i	0.00181779	+	0.00314851i	−0.865115	+	0.501573i	$0.832755\pi$
$114$		0			0
$115$	−0.452033	+	0.782945i	−0.0421523	+	0.0730100i
$116$	−10.9435			−1.01608
$117$		0			0
$118$	−9.38718			−0.864160
$119$		0			0
$120$		0			0
$121$	4.11548	+	7.12823i	0.374135	+	0.648021i
$122$	−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
$131$	−9.91665	−	17.1761i	−0.866422	−	1.50069i	−0.865628	−	0.500687i	$-0.833081\pi$
$131$	−9.91665	−	17.1761i	−0.866422	−	1.50069i	−0.000793988	−	1.00000i	$-0.500253\pi$
$132$		0			0
$133$		0			0
$134$	12.7056			1.09759
$135$		0			0
$136$	−2.80056			−0.240146
$137$	−3.22255	+	5.58162i	−0.275321	+	0.476870i	−0.970216	−	0.242241i	$-0.922117\pi$
$137$	−3.22255	+	5.58162i	−0.275321	+	0.476870i	0.694895	+	0.719111i	$0.255451\pi$
$138$		0			0
$139$	6.26527	+	10.8518i	0.531413	+	0.920435i	0.999328	+	0.0366611i	$0.0116722\pi$
$139$	6.26527	+	10.8518i	0.531413	+	0.920435i	−0.467914	+	0.883774i	$0.654994\pi$
$140$		0			0
$141$		0			0
$142$	−1.31176	+	2.27203i	−0.110080	+	0.190665i
$143$	0.332626			0.0278156
$144$		0			0
$145$	−0.721743			−0.0599375
$146$	1.59897	−	2.76950i	0.132332	−	0.229206i
$147$		0			0
$148$	−7.76161	−	13.4435i	−0.638000	−	1.10505i
$149$	8.88364	+	15.3869i	0.727776	+	1.26054i	0.957821	+	0.287365i	$0.0927792\pi$
$149$	8.88364	+	15.3869i	0.727776	+	1.26054i	−0.230045	+	0.973180i	$0.573887\pi$
$150$		0			0
$151$	−4.23300	+	7.33177i	−0.344476	+	0.596651i	−0.985259	−	0.171072i	$-0.945277\pi$
$151$	−4.23300	+	7.33177i	−0.344476	+	0.596651i	0.640782	+	0.767723i	$0.278610\pi$
$152$	3.08927			0.250573
$153$		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	0.729616	−	0.683857i	$-0.239699\pi$
$157$	−2.84968	−	4.93579i	−0.227429	−	0.393919i	−0.957045	+	0.289938i	$0.906365\pi$
$158$	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
$163$	2.12535			0.166470			0.0832349	−	0.996530i	$-0.473475\pi$
$163$	2.12535			0.166470			0.0832349	+	0.996530i	$0.473475\pi$
$164$	−2.56993	+	4.45125i	−0.200678	+	0.347584i
$165$		0			0
$166$	7.71528	+	13.3632i	0.598821	+	1.03719i
$167$	5.78723	+	10.0238i	0.447829	+	0.775663i	0.998244	−	0.0592278i	$-0.0188638\pi$
$167$	5.78723	+	10.0238i	0.447829	+	0.775663i	−0.550415	+	0.834891i	$0.685530\pi$
$168$		0			0
$169$	6.48002	−	11.2237i	0.498463	−	0.863364i
$170$	−1.88344			−0.144453
$171$		0			0
$172$	4.17323			0.318206
$173$	−7.95546	+	13.7793i	−0.604842	+	1.04762i	0.387234	+	0.921981i	$0.373430\pi$
$173$	−7.95546	+	13.7793i	−0.604842	+	1.04762i	−0.992076	+	0.125636i	$0.959903\pi$
$174$		0			0
$175$		0			0
$176$	−2.92688	−	5.06950i	−0.220622	−	0.382128i
$177$		0			0
$178$	9.31110	−	16.1273i	0.697897	−	1.20879i
$179$	7.75331			0.579509			0.289755	−	0.957101i	$-0.406426\pi$
$179$	7.75331			0.579509			0.289755	+	0.957101i	$0.406426\pi$
$180$		0			0
$181$	−12.1618			−0.903982			−0.451991	−	0.892022i	$-0.649286\pi$
$181$	−12.1618			−0.903982			−0.451991	+	0.892022i	$0.649286\pi$
$182$		0			0
$183$		0			0
$184$	1.38035	+	2.39084i	0.101761	+	0.176255i
$185$	−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	$0.653109\pi$
$194$	8.18406	+	14.1752i	0.587581	+	1.01772i
$195$		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
$199$	19.9442			1.41380			0.706902	−	0.707311i	$-0.250092\pi$
$199$	19.9442			1.41380			0.706902	+	0.707311i	$0.250092\pi$
$200$	−1.11168	+	1.92549i	−0.0786077	+	0.136152i
$201$		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
$206$	0.418838			0.0291818
$207$		0			0
$208$	0.703175			0.0487564
$209$	−5.75556	+	9.96893i	−0.398121	+	0.689565i
$210$		0			0
$211$	11.7569	+	20.3636i	0.809381	+	1.40189i	0.913293	+	0.407303i	$0.133531\pi$
$211$	11.7569	+	20.3636i	0.809381	+	1.40189i	−0.103912	+	0.994587i	$0.533136\pi$
$212$	5.92742	+	10.2666i	0.407097	+	0.705112i
$213$		0			0
$214$	7.15581	−	12.3942i	0.489161	−	0.847252i
$215$	0.275232			0.0187707
$216$		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	$-0.789917\pi$
$223$	2.03052	−	3.51696i	0.135974	−	0.235513i	0.925969	+	0.377600i	$0.123250\pi$
$224$		0			0
$225$		0			0
$226$	0.0793667			0.00527940
$227$	−1.92643	+	3.33667i	−0.127861	+	0.221462i	−0.922848	−	0.385165i	$-0.874145\pi$
$227$	−1.92643	+	3.33667i	−0.127861	+	0.221462i	0.794986	+	0.606627i	$0.207478\pi$
$228$		0			0
$229$	−6.55812	−	11.3590i	−0.433373	−	0.750624i	0.563788	−	0.825919i	$-0.309343\pi$
$229$	−6.55812	−	11.3590i	−0.433373	−	0.750624i	−0.997161	+	0.0752952i	$0.976010\pi$
$230$	0.928316	+	1.60789i	0.0612113	+	0.106021i
$231$		0			0
$232$	−1.10197	+	1.90868i	−0.0723481	+	0.125311i
$233$	−17.5023			−1.14661			−0.573307	−	0.819340i	$-0.694340\pi$
$233$	−17.5023			−1.14661			−0.573307	+	0.819340i	$0.694340\pi$
$234$		0			0
$235$	0.264964			0.0172844
$236$	−5.06798	+	8.77801i	−0.329898	+	0.571400i
$237$		0			0
$238$		0			0
$239$	−3.65857	−	6.33683i	−0.236653	−	0.409895i	0.723099	−	0.690745i	$-0.242717\pi$
$239$	−3.65857	−	6.33683i	−0.236653	−	0.409895i	−0.959752	+	0.280849i	$0.909384\pi$
$240$		0			0
$241$	−3.11553	+	5.39626i	−0.200689	+	0.347604i	−0.948751	−	0.316026i	$-0.897651\pi$
$241$	−3.11553	+	5.39626i	−0.200689	+	0.347604i	0.748062	+	0.663629i	$0.230985\pi$
$242$	16.9035			1.08660
$243$		0			0
$244$	−1.50405			−0.0962868
$245$		0			0
$246$		0			0
$247$	−0.691380	−	1.19751i	−0.0439915	−	0.0761954i
$248$	−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	$-0.557093\pi$
$251$	−5.65283			−0.356803			−0.178402	+	0.983958i	$0.557093\pi$
$252$		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
$257$	5.90082	+	10.2205i	0.368083	+	0.637539i	0.989266	−	0.146127i	$-0.0466808\pi$
$257$	5.90082	+	10.2205i	0.368083	+	0.637539i	−0.621183	+	0.783666i	$0.713347\pi$
$258$		0			0
$259$		0			0
$260$	−0.0648233			−0.00402017
$261$		0			0
$262$	−40.7306			−2.51634
$263$	−11.1200	+	19.2605i	−0.685691	+	1.18765i	0.287528	+	0.957772i	$0.407166\pi$
$263$	−11.1200	+	19.2605i	−0.685691	+	1.18765i	−0.973219	+	0.229879i	$0.926167\pi$
$264$		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
$269$	−2.38884			−0.145650			−0.0728251	−	0.997345i	$-0.523201\pi$
$269$	−2.38884			−0.145650			−0.0728251	+	0.997345i	$0.523201\pi$
$270$		0			0
$271$	23.2258			1.41087			0.705435	−	0.708775i	$-0.250752\pi$
$271$	23.2258			1.41087			0.705435	+	0.708775i	$0.250752\pi$
$272$	11.0302	−	19.1049i	0.668806	−	1.15841i
$273$		0			0
$274$	6.61797	+	11.4627i	0.399806	+	0.692484i
$275$	−4.14231	−	7.17469i	−0.249790	−	0.432650i
$276$		0			0
$277$	2.30900	−	3.99931i	0.138734	−	0.240295i	−0.788283	−	0.615312i	$-0.789030\pi$
$277$	2.30900	−	3.99931i	0.138734	−	0.240295i	0.927018	+	0.375017i	$0.122363\pi$
$278$	25.7333			1.54338
$279$		0			0
$280$		0			0
$281$	−5.90841	+	10.2337i	−0.352466	+	0.610489i	−0.986681	−	0.162668i	$-0.947990\pi$
$281$	−5.90841	+	10.2337i	−0.352466	+	0.610489i	0.634215	+	0.773157i	$0.281324\pi$
$282$		0			0
$283$	−7.92483	−	13.7262i	−0.471082	−	0.815939i	0.528370	−	0.849014i	$-0.322803\pi$
$283$	−7.92483	−	13.7262i	−0.471082	−	0.815939i	−0.999453	+	0.0330753i	$0.989470\pi$
$284$	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
$289$	22.3267			1.31334
$290$	−0.741102	+	1.28363i	−0.0435190	+	0.0753772i
$291$		0			0
$292$	−1.72652	−	2.99042i	−0.101037	−	0.175001i
$293$	−7.04804	−	12.2076i	−0.411751	−	0.713173i	0.583330	−	0.812235i	$-0.301749\pi$
$293$	−7.04804	−	12.2076i	−0.411751	−	0.713173i	−0.995081	+	0.0990615i	$0.968416\pi$
$294$		0			0
$295$	−0.334243	+	0.578927i	−0.0194604	+	0.0337064i
$296$	−3.12628			−0.181711
$297$		0			0
$298$	36.4877			2.11367
$299$	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
$304$	−12.1673	+	21.0744i	−0.697843	+	1.20870i
$305$	−0.0991949			−0.00567988
$306$		0			0
$307$	27.3916			1.56332			0.781660	−	0.623704i	$-0.214373\pi$
$307$	27.3916			1.56332			0.781660	+	0.623704i	$0.214373\pi$
$308$		0			0
$309$		0			0
$310$	−0.378093	−	0.654877i	−0.0214742	−	0.0371945i
$311$	−7.02785	−	12.1726i	−0.398513	−	0.690244i	0.595030	−	0.803704i	$-0.297140\pi$
$311$	−7.02785	−	12.1726i	−0.398513	−	0.690244i	−0.993543	+	0.113459i	$0.963807\pi$
$312$		0			0
$313$	−10.8723	+	18.8314i	−0.614540	+	1.06441i	0.375925	+	0.926650i	$0.377325\pi$
$313$	−10.8723	+	18.8314i	−0.614540	+	1.06441i	−0.990465	+	0.137764i	$0.956008\pi$
$314$	−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
$320$	0.704524	+	1.22027i	0.0393841	+	0.0682153i
$321$		0			0
$322$		0			0
$323$	−43.3808			−2.41377
$324$		0			0
$325$	0.995179			0.0552026
$326$	2.18235	−	3.77995i	0.120869	−	0.209352i
$327$		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	$0.263022\pi$
$332$	16.6614			0.914413
$333$		0			0
$334$	23.7698			1.30063
$335$	0.452399	−	0.783578i	0.0247172	−	0.0428114i
$336$		0			0
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	0.908014	−	0.418940i	$-0.137598\pi$
$337$	1.67411	+	2.89964i	0.0911945	+	0.157954i	−0.816819	+	0.576893i	$0.804265\pi$
$338$	−13.3077	−	23.0496i	−0.723842	−	1.25373i
$339$		0			0
$340$	−1.01684	+	1.76122i	−0.0551459	+	0.0955154i
$341$	4.18971			0.226886
$342$		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	$-0.909877\pi$
$349$	−4.44917	+	7.70619i	−0.238159	+	0.412503i	0.722027	+	0.691865i	$0.243211\pi$
$350$		0			0
$351$		0			0
$352$	−13.5078			−0.719968
$353$	−1.32349	+	2.29236i	−0.0704424	+	0.122010i	−0.899095	−	0.437753i	$-0.855774\pi$
$353$	−1.32349	+	2.29236i	−0.0704424	+	0.122010i	0.828653	+	0.559763i	$0.189108\pi$
$354$		0			0
$355$	0.0934139	+	0.161798i	0.00495790	+	0.00858733i
$356$	−10.0538	−	17.4137i	−0.532852	−	0.922926i
$357$		0			0
$358$	7.96127	−	13.7893i	0.420766	−	0.728789i
$359$	−25.9671			−1.37049			−0.685245	−	0.728312i	$-0.740305\pi$
$359$	−25.9671			−1.37049			−0.685245	+	0.728312i	$0.740305\pi$
$360$		0			0
$361$	28.8529			1.51857
$362$	−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
$367$	−8.79371	+	15.2312i	−0.459028	+	0.795060i	−0.998910	−	0.0466808i	$-0.985136\pi$
$367$	−8.79371	+	15.2312i	−0.459028	+	0.795060i	0.539882	+	0.841741i	$0.318469\pi$
$368$	−21.7464			−1.13361
$369$		0			0
$370$	−2.10249			−0.109303
$371$		0			0
$372$		0			0
$373$	−0.407538	−	0.705876i	−0.0211015	−	0.0365489i	0.855282	−	0.518163i	$-0.173384\pi$
$373$	−0.407538	−	0.705876i	−0.0211015	−	0.0365489i	−0.876383	+	0.481614i	$0.840051\pi$
$374$	−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
$383$	8.94638	+	15.4956i	0.457139	+	0.791788i	0.998808	−	0.0488039i	$-0.0155409\pi$
$383$	8.94638	+	15.4956i	0.457139	+	0.791788i	−0.541670	+	0.840591i	$0.682208\pi$
$384$		0			0
$385$		0			0
$386$	30.6084			1.55793
$387$		0			0
$388$	17.6738			0.897249
$389$	7.81392	−	13.5341i	0.396181	−	0.686206i	−0.597070	−	0.802189i	$-0.703669\pi$
$389$	7.81392	−	13.5341i	0.396181	−	0.686206i	0.993251	+	0.115983i	$0.0370018\pi$
$390$		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
$395$	1.87132			0.0941564
$396$		0			0
$397$	−19.2613			−0.966696			−0.483348	−	0.875428i	$-0.660579\pi$
$397$	−19.2613			−0.966696			−0.483348	+	0.875428i	$0.660579\pi$
$398$	20.4791	−	35.4709i	1.02653	−	1.77799i
$399$		0			0
$400$	−8.75687	−	15.1673i	−0.437843	−	0.758367i
$401$	7.15064	+	12.3853i	0.357086	+	0.618491i	0.987473	−	0.157790i	$-0.0504370\pi$
$401$	7.15064	+	12.3853i	0.357086	+	0.618491i	−0.630387	+	0.776281i	$0.717104\pi$
$402$		0			0
$403$	−0.251642	+	0.435857i	−0.0125352	+	0.0217116i
$404$	−32.9137			−1.63752
$405$		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	$-0.877932\pi$
$409$	−15.9305	−	27.5924i	−0.787712	−	1.36436i	0.139654	−	0.990200i	$-0.455401\pi$
$410$	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
$415$	1.09885			0.0539405
$416$	0.811304	−	1.40522i	0.0397774	−	0.0688965i
$417$		0			0
$418$	11.8199	+	20.4726i	0.578130	+	1.00135i
$419$	−11.9480	−	20.6945i	−0.583697	−	1.01099i	−0.995036	−	0.0995110i	$-0.968272\pi$
$419$	−11.9480	−	20.6945i	−0.583697	−	1.01099i	0.411339	−	0.911482i	$-0.365061\pi$
$420$		0			0
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	−0.894278	−	0.447513i	$-0.852310\pi$
$421$	−1.22251	+	2.11744i	−0.0595813	+	0.103198i	0.834696	+	0.550711i	$0.185643\pi$
$422$	48.2892			2.35068
$423$		0			0
$424$	2.38749			0.115947
$425$	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
$430$	0.282615	−	0.489503i	0.0136289	−	0.0236059i
$431$	4.92764			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$431$	4.92764			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$432$		0			0
$433$	30.8539			1.48274			0.741371	−	0.671095i	$-0.234176\pi$
$433$	30.8539			1.48274			0.741371	+	0.671095i	$0.234176\pi$
$434$		0			0
$435$		0			0
$436$	7.38543	+	12.7919i	0.353698	+	0.612622i
$437$	21.3817	+	37.0341i	1.02282	+	1.77158i
$438$		0			0
$439$	−1.22411	+	2.12022i	−0.0584235	+	0.101192i	−0.893758	−	0.448550i	$-0.851941\pi$
$439$	−1.22411	+	2.12022i	−0.0584235	+	0.101192i	0.835334	+	0.549742i	$0.185274\pi$
$440$	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
$446$	−4.16996	−	7.22259i	−0.197453	−	0.341999i
$447$		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
$451$	−3.85709			−0.181623
$452$	0.0428488	−	0.0742163i	0.00201544	−	0.00349084i
$453$		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	$0.0979754\pi$
$458$	−26.9361			−1.25864
$459$		0			0
$460$	2.00473			0.0934710
$461$	−14.6152	+	25.3143i	−0.680698	+	1.17900i	0.294070	+	0.955784i	$0.404990\pi$
$461$	−14.6152	+	25.3143i	−0.680698	+	1.17900i	−0.974768	+	0.223220i	$0.928343\pi$
$462$		0			0
$463$	−8.21031	−	14.2207i	−0.381565	−	0.660891i	0.609721	−	0.792616i	$-0.291282\pi$
$463$	−8.21031	−	14.2207i	−0.381565	−	0.660891i	−0.991286	+	0.131726i	$0.957948\pi$
$464$	−8.68041	−	15.0349i	−0.402978	−	0.697978i
$465$		0			0
$466$	−17.9718	+	31.1280i	−0.832526	+	1.44198i
$467$	15.3726			0.711361			0.355680	−	0.934608i	$-0.384249\pi$
$467$	15.3726			0.711361			0.355680	+	0.934608i	$0.384249\pi$
$468$		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
$478$	−15.0268			−0.687310
$479$	−18.9646	+	32.8476i	−0.866513	+	1.50084i	−0.000975329		1.00000i	$0.500310\pi$
$479$	−18.9646	+	32.8476i	−0.866513	+	1.50084i	−0.865537	+	0.500844i	$0.833023\pi$
$480$		0			0
$481$	0.699663	+	1.21185i	0.0319019	+	0.0552557i
$482$	6.39820	+	11.0820i	0.291430	+	0.504772i
$483$		0			0
$484$	9.12591	−	15.8065i	0.414814	−	0.718479i
$485$	1.16562			0.0529280
$486$		0			0
$487$	−4.60495			−0.208670			−0.104335	−	0.994542i	$-0.533271\pi$
$487$	−4.60495			−0.208670			−0.104335	+	0.994542i	$0.533271\pi$
$488$	−0.151453	+	0.262324i	−0.00685595	+	0.0118749i
$489$		0			0
$490$		0			0
$491$	15.1876	+	26.3056i	0.685405	+	1.18716i	0.973309	+	0.229497i	$0.0737082\pi$
$491$	15.1876	+	26.3056i	0.685405	+	1.18716i	−0.287904	+	0.957659i	$0.592958\pi$
$492$		0			0
$493$	15.4744	−	26.8024i	0.696932	−	1.20712i
$494$	−2.83970			−0.127764
$495$		0			0
$496$	8.85709			0.397695
$497$		0			0
$498$		0			0
$499$	−4.63436	−	8.02694i	−0.207462	−	0.359335i	0.743452	−	0.668789i	$-0.233187\pi$
$499$	−4.63436	−	8.02694i	−0.207462	−	0.359335i	−0.950914	+	0.309454i	$0.899854\pi$
$500$	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	$-0.333372\pi$
$503$	22.4230			0.999791			0.499896	+	0.866086i	$0.333372\pi$
$504$		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
$509$	−18.8207	−	32.5984i	−0.834213	−	1.44490i	−0.894670	−	0.446728i	$-0.852589\pi$
$509$	−18.8207	−	32.5984i	−0.834213	−	1.44490i	0.0604572	−	0.998171i	$-0.480744\pi$
$510$		0			0
$511$		0			0
$512$	−31.6976			−1.40085
$513$		0			0
$514$	24.2364			1.06902
$515$	0.0149133	−	0.0258306i	0.000657158	−	0.00113823i
$516$		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
$521$	34.9283			1.53023			0.765117	−	0.643891i	$-0.222681\pi$
$521$	34.9283			1.53023			0.765117	+	0.643891i	$0.222681\pi$
$522$		0			0
$523$	23.7471			1.03839			0.519194	−	0.854656i	$-0.326232\pi$
$523$	23.7471			1.03839			0.519194	+	0.854656i	$0.326232\pi$
$524$	−21.9898	+	38.0874i	−0.960628	+	1.66386i
$525$		0			0
$526$	22.8366	+	39.5542i	0.995723	+	1.72464i
$527$	7.89468	+	13.6740i	0.343898	+	0.595648i
$528$		0			0
$529$	−7.60755	+	13.1767i	−0.330763	+	0.572898i
$530$	1.60564			0.0697446
$531$		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
$541$	−17.1708			−0.738232			−0.369116	−	0.929383i	$-0.620340\pi$
$541$	−17.1708			−0.738232			−0.369116	+	0.929383i	$0.620340\pi$
$542$	23.8488	−	41.3074i	1.02439	−	1.77430i
$543$		0			0
$544$	−25.4527	−	44.0854i	−1.09128	−	1.89015i
$545$	0.487083	+	0.843653i	0.0208643	+	0.0361381i
$546$		0			0
$547$	−10.0046	+	17.3284i	−0.427765	+	0.740910i	−0.996674	−	0.0814901i	$-0.974032\pi$
$547$	−10.0046	+	17.3284i	−0.427765	+	0.740910i	0.568910	+	0.822400i	$0.307365\pi$
$548$	14.2917			0.610512
$549$		0			0
$550$	−17.0137			−0.725465
$551$	−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
$556$	13.8930	−	24.0633i	0.589193	−	1.02051i
$557$	−0.245481			−0.0104014			−0.00520068	−	0.999986i	$-0.501655\pi$
$557$	−0.245481			−0.0104014			−0.00520068	+	0.999986i	$0.501655\pi$
$558$		0			0
$559$	−0.376192			−0.0159112
$560$		0			0
$561$		0			0
$562$	12.1338	+	21.0163i	0.511833	+	0.886520i
$563$	−22.1255	−	38.3224i	−0.932477	−	1.61510i	−0.779073	−	0.626934i	$-0.784310\pi$
$563$	−22.1255	−	38.3224i	−0.932477	−	1.61510i	−0.153404	−	0.988164i	$-0.549024\pi$
$564$		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	$0.805966\pi$
$572$	−0.368793	−	0.638768i	−0.0154200	−	0.0267082i
$573$		0			0
$574$		0			0
$575$	−30.7770			−1.28349
$576$		0			0
$577$	5.64550			0.235025			0.117513	−	0.993071i	$-0.462508\pi$
$577$	5.64550			0.235025			0.117513	+	0.993071i	$0.462508\pi$
$578$	22.9256	−	39.7083i	0.953579	−	1.65165i
$579$		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
$584$	−0.695420			−0.0287767
$585$		0			0
$586$	−28.9483			−1.19585
$587$	−9.36644	+	16.2232i	−0.386595	+	0.669601i	−0.991989	−	0.126324i	$-0.959682\pi$
$587$	−9.36644	+	16.2232i	−0.386595	+	0.669601i	0.605394	+	0.795926i	$0.293015\pi$
$588$		0			0
$589$	−8.70852	−	15.0836i	−0.358828	−	0.621509i
$590$	0.686417	+	1.18891i	0.0282594	+	0.0489466i
$591$		0			0
$592$	12.3131	−	21.3269i	0.506065	−	0.876530i
$593$	−18.8703			−0.774912			−0.387456	−	0.921888i	$-0.626646\pi$
$593$	−18.8703			−0.774912			−0.387456	+	0.921888i	$0.626646\pi$
$594$		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	$-0.920196\pi$
$601$	−6.60716	+	11.4439i	−0.269511	+	0.466808i	0.699224	+	0.714902i	$0.253529\pi$
$602$		0			0
$603$		0			0
$604$	18.7730			0.763862
$605$	0.601872	−	1.04247i	0.0244696	−	0.0423825i
$606$		0			0
$607$	−12.9026	−	22.3480i	−0.523701	−	0.907076i	−0.999619	−	0.0275869i	$-0.991218\pi$
$607$	−12.9026	−	22.3480i	−0.523701	−	0.907076i	0.475919	−	0.879489i	$-0.342116\pi$
$608$	28.0766	+	48.6301i	1.13866	+	1.97221i
$609$		0			0
$610$	−0.101856	+	0.176419i	−0.00412401	+	0.00714299i
$611$	−0.362157			−0.0146513
$612$		0			0
$613$	−26.9533			−1.08863			−0.544316	−	0.838880i	$-0.683211\pi$
$613$	−26.9533			−1.08863			−0.544316	+	0.838880i	$0.683211\pi$
$614$	28.1263	−	48.7162i	1.13509	−	1.96603i
$615$		0			0
$616$		0			0
$617$	4.76588	+	8.25474i	0.191867	+	0.332323i	0.945869	−	0.324549i	$-0.105212\pi$
$617$	4.76588	+	8.25474i	0.191867	+	0.332323i	−0.754002	+	0.656872i	$0.771879\pi$
$618$		0			0
$619$	−17.3536	+	30.0573i	−0.697499	+	1.20810i	0.271832	+	0.962345i	$0.412370\pi$
$619$	−17.3536	+	30.0573i	−0.697499	+	1.20810i	−0.969331	+	0.245759i	$0.920963\pi$
$620$	−0.816505			−0.0327916
$621$		0			0
$622$	−28.8654			−1.15740
$623$		0			0
$624$		0			0
$625$	−12.3398	−	21.3732i	−0.493593	−	0.854928i
$626$	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
$635$	−0.985611	−	1.70713i	−0.0391128	−	0.0677453i
$636$		0			0
$637$		0			0
$638$	−16.8651			−0.667696
$639$		0			0
$640$	0.519397			0.0205310
$641$	−22.0922	+	38.2648i	−0.872590	+	1.51137i	−0.0132813	+	0.999912i	$0.504228\pi$
$641$	−22.0922	+	38.2648i	−0.872590	+	1.51137i	−0.859308	+	0.511458i	$0.829106\pi$
$642$		0			0
$643$	7.24065	+	12.5412i	0.285543	+	0.494575i	0.972741	−	0.231895i	$-0.0744926\pi$
$643$	7.24065	+	12.5412i	0.285543	+	0.494575i	−0.687197	+	0.726471i	$0.741159\pi$
$644$		0			0
$645$		0			0
$646$	−44.5444	+	77.1532i	−1.75258	+	3.03555i
$647$	−33.3071			−1.30944			−0.654719	−	0.755872i	$-0.727213\pi$
$647$	−33.3071			−1.30944			−0.654719	+	0.755872i	$0.727213\pi$
$648$		0			0
$649$	−7.60631			−0.298574
$650$	1.02187	−	1.76993i	0.0400811	−	0.0694225i
$651$		0			0
$652$	−2.35643	−	4.08146i	−0.0922850	−	0.159842i
$653$	−4.53322	−	7.85176i	−0.177398	−	0.307263i	0.763590	−	0.645701i	$-0.223435\pi$
$653$	−4.53322	−	7.85176i	−0.177398	−	0.307263i	−0.940989	+	0.338438i	$0.890101\pi$
$654$		0			0
$655$	−1.45027	+	2.51194i	−0.0566666	+	0.0981495i
$656$	−8.15391			−0.318357
$657$		0			0
$658$		0			0
$659$	−16.1806	+	28.0256i	−0.630305	+	1.09172i	0.357184	+	0.934034i	$0.383737\pi$
$659$	−16.1806	+	28.0256i	−0.630305	+	1.09172i	−0.987489	+	0.157686i	$0.949596\pi$
$660$		0			0
$661$	4.32958	+	7.49905i	0.168401	+	0.291679i	0.937858	−	0.347020i	$-0.112806\pi$
$661$	4.32958	+	7.49905i	0.168401	+	0.291679i	−0.769457	+	0.638699i	$0.779473\pi$
$662$	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
$667$	−30.5083			−1.18128
$668$	12.8329	−	22.2273i	0.496522	−	0.860001i
$669$		0			0
$670$	−0.929067	−	1.60919i	−0.0358930	−	0.0621685i
$671$	−0.564339	−	0.977464i	−0.0217861	−	0.0377346i
$672$		0			0
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	−0.691831	−	0.722059i	$-0.743196\pi$
$673$	7.24842	−	12.5546i	0.279406	−	0.483946i	0.971237	+	0.238114i	$0.0765291\pi$
$674$	6.87605			0.264856
$675$		0			0
$676$	−28.7384			−1.10532
$677$	19.1657	−	33.1960i	0.736600	−	1.27583i	−0.217418	−	0.976078i	$-0.569764\pi$
$677$	19.1657	−	33.1960i	0.736600	−	1.27583i	0.954018	−	0.299749i	$-0.0969030\pi$
$678$		0			0
$679$		0			0
$680$	0.204785	+	0.354698i	0.00785315	+	0.0136021i
$681$		0			0
$682$	4.30209	−	7.45144i	0.164736	−	0.285330i
$683$	−6.63318			−0.253812			−0.126906	−	0.991915i	$-0.540505\pi$
$683$	−6.63318			−0.253812			−0.126906	+	0.991915i	$0.540505\pi$
$684$		0			0
$685$	0.942567			0.0360136
$686$		0			0
$687$		0			0
$688$	3.31022	+	5.73347i	0.126201	+	0.218587i
$689$	−0.534322	−	0.925472i	−0.0203560	−	0.0352577i
$690$		0			0
$691$	11.6938	−	20.2542i	0.444852	−	0.770506i	−0.553190	−	0.833055i	$-0.686590\pi$
$691$	11.6938	−	20.2542i	0.444852	−	0.770506i	0.998042	+	0.0625490i	$0.0199230\pi$
$692$	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
$698$	9.13702	+	15.8258i	0.345841	+	0.599015i
$699$		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
$703$	−48.4262			−1.82643
$704$	−8.01636	+	13.8847i	−0.302128	+	0.523301i
$705$		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	$0.252802\pi$
$710$	0.383678			0.0143992
$711$		0			0
$712$	−4.04956			−0.151763
$713$	7.78230	−	13.4793i	0.291449	−	0.504805i
$714$		0			0
$715$	−0.0243226	−	0.0421280i	−0.000909613	−	0.00157550i
$716$	−8.59632	−	14.8893i	−0.321260	−	0.556438i
$717$		0			0
$718$	−26.6636	+	46.1827i	−0.995077	+	1.72352i
$719$	13.8570			0.516777			0.258389	−	0.966041i	$-0.416808\pi$
$719$	13.8570			0.516777			0.258389	+	0.966041i	$0.416808\pi$
$720$		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	−0.412928	−	0.910764i	$-0.635494\pi$
$727$	15.7000	−	27.1932i	0.582280	−	1.00854i	0.995208	−	0.0977755i	$-0.0311727\pi$
$728$		0			0
$729$		0			0
$730$	−0.467686			−0.0173098
$731$	−5.90107	+	10.2209i	−0.218259	+	0.378035i
$732$		0			0
$733$	13.3003	+	23.0368i	0.491257	+	0.850883i	0.999949	−	0.0100658i	$-0.00320409\pi$
$733$	13.3003	+	23.0368i	0.491257	+	0.850883i	−0.508692	+	0.860949i	$0.669871\pi$
$734$	18.0592	+	31.2794i	0.666576	+	1.15454i
$735$		0			0
$736$	−25.0904	+	43.4579i	−0.924845	+	1.60188i
$737$	10.2951			0.379227
$738$		0			0
$739$	−33.0039			−1.21407			−0.607034	−	0.794676i	$-0.707641\pi$
$739$	−33.0039			−1.21407			−0.607034	+	0.794676i	$0.707641\pi$
$740$	−1.13510	+	1.96605i	−0.0417272	+	0.0722736i
$741$		0			0
$742$		0			0
$743$	−19.3008	−	33.4299i	−0.708076	−	1.22642i	−0.965570	−	0.260144i	$-0.916230\pi$
$743$	−19.3008	−	33.4299i	−0.708076	−	1.22642i	0.257493	−	0.966280i	$-0.417103\pi$
$744$		0			0
$745$	1.29919	−	2.25027i	0.0475988	−	0.0824435i
$746$	−1.67388			−0.0612849
$747$		0			0
$748$	−23.1400			−0.846082
$749$		0			0
$750$		0			0
$751$	18.9498	+	32.8220i	0.691487	+	1.19769i	0.971351	+	0.237651i	$0.0763776\pi$
$751$	18.9498	+	32.8220i	0.691487	+	1.19769i	−0.279863	+	0.960040i	$0.590289\pi$
$752$	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
$761$	13.8735	+	24.0296i	0.502913	+	0.871072i	0.999994	+	0.00336738i	$0.00107187\pi$
$761$	13.8735	+	24.0296i	0.502913	+	0.871072i	−0.497081	+	0.867704i	$0.665595\pi$
$762$		0			0
$763$		0			0
$764$	11.0156			0.398529
$765$		0			0
$766$	36.7454			1.32766
$767$	0.456849	−	0.791286i	0.0164959	−	0.0285717i
$768$		0			0
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	0.735412	−	0.677621i	$-0.236989\pi$
$769$	−6.07668	−	10.5251i	−0.219131	−	0.379546i	−0.954542	+	0.298075i	$0.903655\pi$
$770$		0			0
$771$		0			0
$772$	16.5250	−	28.6221i	0.594747	−	1.03013i
$773$	−41.5591			−1.49478			−0.747388	−	0.664388i	$-0.768692\pi$
$773$	−41.5591			−1.49478			−0.747388	+	0.664388i	$0.768692\pi$
$774$		0			0
$775$	12.5351			0.450275
$776$	1.77969	−	3.08252i	0.0638873	−	0.110656i
$777$		0			0
$778$	−16.0470	−	27.7942i	−0.575313	−	0.996472i
$779$	8.01714	+	13.8861i	0.287244	+	0.497521i
$780$		0			0
$781$	−1.06290	+	1.84100i	−0.0380336	+	0.0658761i
$782$	−79.6135			−2.84697
$783$		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	0.989941	−	0.141479i	$-0.0451857\pi$
$787$	10.4484	+	18.0972i	0.372446	+	0.645096i	−0.617495	+	0.786575i	$0.711852\pi$
$788$	−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
$793$	0.135581			0.00481462
$794$	−19.7779	+	34.2564i	−0.701892	+	1.21571i
$795$		0			0
$796$	−22.1127	−	38.3003i	−0.783763	−	1.35752i
$797$	0.319383	+	0.553188i	0.0113131	+	0.0195949i	0.871627	−	0.490171i	$-0.163066\pi$
$797$	0.319383	+	0.553188i	0.0113131	+	0.0195949i	−0.860313	+	0.509765i	$0.829732\pi$
$798$		0			0
$799$	−5.68091	+	9.83963i	−0.200976	+	0.348101i
$800$	−40.4137			−1.42884
$801$		0			0
$802$	29.3698			1.03708
$803$	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
$808$	−3.31431	+	5.74055i	−0.116597	+	0.201952i
$809$	50.5592			1.77757			0.888783	−	0.458327i	$-0.151551\pi$
$809$	50.5592			1.77757			0.888783	+	0.458327i	$0.151551\pi$
$810$		0			0
$811$	−0.784071			−0.0275325			−0.0137662	−	0.999905i	$-0.504382\pi$
$811$	−0.784071			−0.0275325			−0.0137662	+	0.999905i	$0.504382\pi$
$812$		0			0
$813$		0			0
$814$	−11.9615	−	20.7179i	−0.419250	−	0.726163i
$815$	−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	$0.855350\pi$
$824$	−0.0455399	−	0.0788774i	−0.00158646	−	0.00274782i
$825$		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
$829$	35.0427			1.21708			0.608541	−	0.793522i	$-0.291755\pi$
$829$	35.0427			1.21708			0.608541	+	0.793522i	$0.291755\pi$
$830$	1.12833	−	1.95432i	0.0391648	−	0.0678353i
$831$		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
$836$	25.5255			0.882816
$837$		0			0
$838$	−49.0738			−1.69523
$839$	18.7921	−	32.5489i	0.648777	−	1.12371i	−0.334639	−	0.942347i	$-0.608614\pi$
$839$	18.7921	−	32.5489i	0.648777	−	1.12371i	0.983415	−	0.181368i	$-0.0580524\pi$
$840$		0			0
$841$	2.32218	+	4.02213i	0.0800750	+	0.138694i
$842$	2.51060	+	4.34848i	0.0865208	+	0.149858i
$843$		0			0
$844$	26.0705	−	45.1555i	0.897385	−	1.55432i
$845$	−1.89535			−0.0652020
$846$		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	−0.436400	−	0.899753i	$-0.643747\pi$
$853$	16.3849	−	28.3795i	0.561009	−	0.971696i	0.997409	−	0.0719434i	$-0.0229201\pi$
$854$		0			0
$855$		0			0
$856$	−3.11218			−0.106372
$857$	13.7673	−	23.8457i	0.470283	−	0.814554i	−0.529139	−	0.848535i	$-0.677485\pi$
$857$	13.7673	−	23.8457i	0.470283	−	0.814554i	0.999422	+	0.0339808i	$0.0108185\pi$
$858$		0			0
$859$	23.2550	+	40.2789i	0.793451	+	1.37430i	0.923818	+	0.382832i	$0.125051\pi$
$859$	23.2550	+	40.2789i	0.793451	+	1.37430i	−0.130366	+	0.991466i	$0.541615\pi$
$860$	−0.305158	−	0.528549i	−0.0104058	−	0.0180234i
$861$		0			0
$862$	5.05981	−	8.76384i	0.172338	−	0.298498i
$863$	4.88014			0.166122			0.0830610	−	0.996544i	$-0.473530\pi$
$863$	4.88014			0.166122			0.0830610	+	0.996544i	$0.473530\pi$
$864$		0			0
$865$	2.32690			0.0791170
$866$	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
$871$	−0.618346	+	1.07101i	−0.0209518	+	0.0362897i
$872$	2.97476			0.100738
$873$		0			0
$874$	87.8207			2.97058
$875$		0			0
$876$		0			0
$877$	−19.6446	−	34.0255i	−0.663352	−	1.14896i	−0.979729	−	0.200326i	$-0.935800\pi$
$877$	−19.6446	−	34.0255i	−0.663352	−	1.14896i	0.316378	−	0.948633i	$-0.397533\pi$
$878$	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	$-0.794103\pi$
$881$	−47.3713			−1.59598			−0.797990	+	0.602670i	$0.794103\pi$
$882$		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
$887$	−11.4800	−	19.8840i	−0.385461	−	0.667638i	0.606372	−	0.795181i	$-0.292624\pi$
$887$	−11.4800	−	19.8840i	−0.385461	−	0.667638i	−0.991833	+	0.127543i	$0.959291\pi$
$888$		0			0
$889$		0			0
$890$	−2.72342			−0.0912891
$891$		0			0
$892$	−9.00518			−0.301516
$893$	6.26655	−	10.8540i	0.209702	−	0.363214i
$894$		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
$899$	12.4257			0.414420
$900$		0			0
$901$	−33.5262			−1.11692
$902$	−3.96054	+	6.85986i	−0.131872	+	0.228408i
$903$		0			0
$904$	−0.00862948	−	0.0149467i	−0.000287012	−	0.000497120i
$905$	0.889308	+	1.54033i	0.0295616	+	0.0512022i
$906$		0			0
$907$	13.9491	−	24.1606i	0.463173	−	0.802238i	−0.535944	−	0.844253i	$-0.680044\pi$
$907$	13.9491	−	24.1606i	0.463173	−	0.802238i	0.999117	+	0.0420148i	$0.0133777\pi$
$908$	8.54354			0.283527
$909$		0			0
$910$		0			0
$911$	18.7381	−	32.4553i	0.620820	−	1.07529i	−0.368513	−	0.929623i	$-0.620133\pi$
$911$	18.7381	−	32.4553i	0.620820	−	1.07529i	0.989333	−	0.145670i	$-0.0465337\pi$
$912$		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
$919$	30.2147			0.996691			0.498345	−	0.866979i	$-0.333941\pi$
$919$	30.2147			0.996691			0.498345	+	0.866979i	$0.333941\pi$
$920$	0.201870	−	0.349649i	0.00665546	−	0.0115276i
$921$		0			0
$922$	30.0145	+	51.9866i	0.988474	+	1.71209i
$923$	−0.127680	−	0.221147i	−0.00420262	−	0.00727916i
$924$		0			0
$925$	17.4263	−	30.1832i	0.572972	−	0.992417i
$926$	−33.7221			−1.10818
$927$		0			0
$928$	−40.0609			−1.31506
$929$	−22.9675	+	39.7809i	−0.753540	+	1.30517i	0.192556	+	0.981286i	$0.438322\pi$
$929$	−22.9675	+	39.7809i	−0.753540	+	1.30517i	−0.946097	+	0.323884i	$0.895011\pi$
$930$		0			0
$931$		0			0
$932$	19.4053	+	33.6110i	0.635642	+	1.10096i
$933$		0			0
$934$	15.7850	−	27.3404i	0.516500	−	0.894604i
$935$	−1.52613			−0.0499097
$936$		0			0
$937$	−45.3797			−1.48249			−0.741245	−	0.671235i	$-0.765764\pi$
$937$	−45.3797			−1.48249			−0.741245	+	0.671235i	$0.765764\pi$
$938$		0			0
$939$		0			0
$940$	−0.293774	−	0.508831i	−0.00958184	−	0.0165962i
$941$	24.7002	+	42.7819i	0.805202	+	1.39465i	0.916154	+	0.400825i	$0.131277\pi$
$941$	24.7002	+	42.7819i	0.805202	+	1.39465i	−0.110952	+	0.993826i	$0.535390\pi$
$942$		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
$950$	35.3637	+	61.2517i	1.14735	+	1.98727i
$951$		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
$955$	0.726498			0.0235089
$956$	−8.11273	+	14.0517i	−0.262384	+	0.454463i
$957$		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
$962$	2.87372			0.0926525
$963$		0			0
$964$	13.8171			0.445020
$965$	1.08985	−	1.88768i	0.0350836	−	0.0607666i
$966$		0			0
$967$	4.98525	+	8.63470i	0.160315	+	0.277673i	0.934982	−	0.354696i	$-0.115416\pi$
$967$	4.98525	+	8.63470i	0.160315	+	0.277673i	−0.774667	+	0.632370i	$0.782082\pi$
$968$	−1.83790	−	3.18334i	−0.0590724	−	0.102316i
$969$		0			0
$970$	1.19688	−	2.07306i	0.0384296	−	0.0665621i
$971$	1.04511			0.0335391			0.0167695	−	0.999859i	$-0.494662\pi$
$971$	1.04511			0.0335391			0.0167695	+	0.999859i	$0.494662\pi$
$972$		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
$982$	62.3797			1.99062
$983$	1.14446	−	1.98226i	0.0365025	−	0.0632242i	−0.847197	−	0.531279i	$-0.821712\pi$
$983$	1.14446	−	1.98226i	0.0365025	−	0.0632242i	0.883700	+	0.468055i	$0.155045\pi$
$984$		0			0
$985$	−1.55465	−	2.69274i	−0.0495353	−	0.0857977i
$986$	−31.7789	−	55.0427i	−1.01205	−	1.75292i
$987$		0			0
$988$	−1.53311	+	2.65542i	−0.0487746	+	0.0844801i
$989$	11.6341			0.369944
$990$		0			0
$991$	19.0698			0.605773			0.302886	−	0.953027i	$-0.402050\pi$
$991$	19.0698			0.605773			0.302886	+	0.953027i	$0.402050\pi$
$992$	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
$997$	−18.5075	+	32.0560i	−0.586139	+	1.01522i	0.408593	+	0.912717i	$0.366020\pi$
$997$	−18.5075	+	32.0560i	−0.586139	+	1.01522i	−0.994732	+	0.102507i	$0.967314\pi$
$998$	−19.0346			−0.602531
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.1	✓	10	63.23	odd	6
63.2.g.b.16.1	yes	10	21.11	odd	6
63.2.h.b.25.5	yes	10	21.2	odd	6
63.2.h.b.58.5	yes	10	63.32	odd	6
189.2.g.b.100.5		10	7.4	even	3
189.2.g.b.172.5		10	63.58	even	3
189.2.h.b.37.1		10	63.4	even	3
189.2.h.b.46.1		10	7.2	even	3
441.2.f.e.148.1		10	9.5	odd	6
441.2.f.e.295.1		10	3.2	odd	2
441.2.f.f.148.1		10	63.41	even	6
441.2.f.f.295.1		10	21.20	even	2
441.2.g.f.67.1		10	63.5	even	6
441.2.g.f.79.1		10	21.17	even	6
441.2.h.f.214.5		10	21.5	even	6
441.2.h.f.373.5		10	63.59	even	6
567.2.e.e.163.5		10	63.25	even	3
567.2.e.e.487.5		10	63.16	even	3
567.2.e.f.163.1		10	63.11	odd	6
567.2.e.f.487.1		10	63.2	odd	6
1008.2.q.i.529.5		10	84.23	even	6
1008.2.q.i.625.5		10	252.95	even	6
1008.2.t.i.193.2		10	252.23	even	6
1008.2.t.i.961.2		10	84.11	even	6
1323.2.f.e.442.5		10	9.4	even	3	inner
1323.2.f.e.883.5		10	1.1	even	1	trivial
1323.2.f.f.442.5		10	63.13	odd	6
1323.2.f.f.883.5		10	7.6	odd	2
1323.2.g.f.361.5		10	63.40	odd	6
1323.2.g.f.667.5		10	7.3	odd	6
1323.2.h.f.226.1		10	63.31	odd	6
1323.2.h.f.802.1		10	7.5	odd	6
3024.2.q.i.2305.3		10	252.67	odd	6
3024.2.q.i.2881.3		10	28.23	odd	6
3024.2.t.i.289.3		10	28.11	odd	6
3024.2.t.i.1873.3		10	252.247	odd	6
3969.2.a.z.1.5		5	9.2	odd	6
3969.2.a.ba.1.5		5	63.20	even	6
3969.2.a.bb.1.1		5	63.34	odd	6
3969.2.a.bc.1.1		5	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} +(-0.0731228 - 0.126652i) q^{5} -0.446582 q^{8} +O(q^{10})\)	\(q+(1.02682 - 1.77851i) q^{2} +(-1.10873 - 1.92038i) q^{4} +(-0.0731228 - 0.126652i) q^{5} -0.446582 q^{8} -0.300337 q^{10} +(0.832020 - 1.44110i) q^{11} +(0.0999454 + 0.173111i) q^{13} +(1.75890 - 3.04650i) q^{16} +6.27110 q^{17} -6.91758 q^{19} +(-0.162147 + 0.280847i) q^{20} +(-1.70867 - 2.95951i) q^{22} +(-3.09092 - 5.35363i) q^{23} +(2.48931 - 4.31160i) q^{25} +0.410505 q^{26} +(2.46757 - 4.27396i) q^{29} +(1.25890 + 2.18047i) q^{31} +(-4.05873 - 7.02993i) q^{32} +(6.43931 - 11.1532i) q^{34} +7.00046 q^{37} +(-7.10312 + 12.3030i) q^{38} +(0.0326554 + 0.0565608i) q^{40} +(-1.15895 - 2.00736i) q^{41} +(-0.940993 + 1.62985i) q^{43} -3.68994 q^{44} -12.6953 q^{46} +(-0.905887 + 1.56904i) q^{47} +(-5.11215 - 8.85451i) q^{50} +(0.221625 - 0.383865i) q^{52} -5.34614 q^{53} -0.243359 q^{55} +(-5.06752 - 8.77720i) q^{58} +(-2.28549 - 3.95859i) q^{59} +(0.339138 - 0.587404i) q^{61} +5.17066 q^{62} -9.63481 q^{64} +(0.0146166 - 0.0253167i) q^{65} +(3.09342 + 5.35796i) q^{67} +(-6.95296 - 12.0429i) q^{68} -1.27749 q^{71} +1.55721 q^{73} +(7.18823 - 12.4504i) q^{74} +(7.66972 + 13.2843i) q^{76} +(-6.39787 + 11.0814i) q^{79} -0.514462 q^{80} -4.76015 q^{82} +(-3.75687 + 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(1.93247 + 3.34713i) q^{86} +(-0.371566 + 0.643571i) q^{88} +9.06788 q^{89} +(-6.85398 + 11.8714i) q^{92} +(1.86037 + 3.22226i) q^{94} +(0.505833 + 0.876128i) q^{95} +(-3.98514 + 6.90246i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^8	\( 10 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 6 q^{8} + 14 q^{10} - 4 q^{11} - 8 q^{13} + 2 q^{16} + 24 q^{17} - 2 q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 22 q^{26} - 7 q^{29} - 3 q^{31} + 2 q^{32} + 3 q^{34} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} - 20 q^{44} - 6 q^{46} - 27 q^{47} - 19 q^{50} - 10 q^{52} - 42 q^{53} + 4 q^{55} - 10 q^{58} - 30 q^{59} - 14 q^{61} + 12 q^{62} - 50 q^{64} + 11 q^{65} - 2 q^{67} - 27 q^{68} + 6 q^{71} - 30 q^{73} + 36 q^{74} + 5 q^{76} - 4 q^{79} + 40 q^{80} + 10 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} + 56 q^{89} - 27 q^{92} - 3 q^{94} + 14 q^{95} - 12 q^{97}+O(q^{100}) \) 10 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 6 * q^8 + 14 * q^10 - 4 * q^11 - 8 * q^13 + 2 * q^16 + 24 * q^17 - 2 * q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 + 22 * q^26 - 7 * q^29 - 3 * q^31 + 2 * q^32 + 3 * q^34 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 - 20 * q^44 - 6 * q^46 - 27 * q^47 - 19 * q^50 - 10 * q^52 - 42 * q^53 + 4 * q^55 - 10 * q^58 - 30 * q^59 - 14 * q^61 + 12 * q^62 - 50 * q^64 + 11 * q^65 - 2 * q^67 - 27 * q^68 + 6 * q^71 - 30 * q^73 + 36 * q^74 + 5 * q^76 - 4 * q^79 + 40 * q^80 + 10 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 + 56 * q^89 - 27 * q^92 - 3 * q^94 + 14 * q^95 - 12 * q^97

Introduction

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