LMFDB - Embedded newform 441.2.w.a.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(62,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 11]))

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

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

chi := DirichletCharacter("441.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (of order $14$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.2
Character	$\chi$	$=$	441.251
Dual form			441.2.w.a.188.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.12540 - 1.69495i) q^{2} +(1.19944 + 5.25507i) q^{4} +(2.70367 + 1.30202i) q^{5} +(-0.967619 + 2.46246i) q^{7} +(3.99879 - 8.30358i) q^{8} +O(q^{10})$	\(q+(-2.12540 - 1.69495i) q^{2} +(1.19944 + 5.25507i) q^{4} +(2.70367 + 1.30202i) q^{5} +(-0.967619 + 2.46246i) q^{7} +(3.99879 - 8.30358i) q^{8} +(-3.53953 - 7.34991i) q^{10} +(-1.87132 - 1.49233i) q^{11} +(1.93441 + 1.54264i) q^{13} +(6.23034 - 3.59366i) q^{14} +(-12.8604 + 6.19325i) q^{16} +(-1.15098 + 5.04278i) q^{17} +0.270871i q^{19} +(-3.59932 + 15.7697i) q^{20} +(1.44789 + 6.34361i) q^{22} +(-8.11148 + 1.85139i) q^{23} +(2.49713 + 3.13130i) q^{25} +(-1.49670 - 6.55747i) q^{26} +(-14.1010 - 2.13134i) q^{28} +(2.64195 + 0.603008i) q^{29} +8.55709i q^{31} +(19.8604 + 4.53301i) q^{32} +(10.9936 - 8.76709i) q^{34} +(-5.82229 + 5.39782i) q^{35} +(1.31758 - 5.77270i) q^{37} +(0.459113 - 0.575710i) q^{38} +(21.6228 - 17.2436i) q^{40} +(-0.862545 - 0.415380i) q^{41} +(5.37639 - 2.58913i) q^{43} +(5.59777 - 11.6239i) q^{44} +(20.3782 + 9.81363i) q^{46} +(-5.40670 + 6.77979i) q^{47} +(-5.12743 - 4.76545i) q^{49} -10.8878i q^{50} +(-5.78648 + 12.0158i) q^{52} +(1.39025 - 0.317315i) q^{53} +(-3.11640 - 6.47127i) q^{55} +(16.5779 + 17.8816i) q^{56} +(-4.59314 - 5.75962i) q^{58} +(5.63248 - 2.71246i) q^{59} +(12.1109 + 2.76423i) q^{61} +(14.5039 - 18.1873i) q^{62} +(-16.7288 - 20.9773i) q^{64} +(3.22146 + 6.68943i) q^{65} -9.18698 q^{67} -27.8807 q^{68} +(21.5238 - 1.60405i) q^{70} +(3.43876 - 0.784875i) q^{71} +(-6.58618 + 5.25231i) q^{73} +(-12.5848 + 10.0361i) q^{74} +(-1.42344 + 0.324892i) q^{76} +(5.48553 - 3.16405i) q^{77} +8.56875 q^{79} -42.8340 q^{80} +(1.12921 + 2.34483i) q^{82} +(0.701261 + 0.879353i) q^{83} +(-9.67767 + 12.1354i) q^{85} +(-15.8155 - 3.60978i) q^{86} +(-19.8747 + 9.57116i) q^{88} +(10.3983 + 13.0391i) q^{89} +(-5.67046 + 3.27072i) q^{91} +(-19.4584 - 40.4058i) q^{92} +(22.9829 - 5.24569i) q^{94} +(-0.352678 + 0.732344i) q^{95} +1.73671i q^{97} +(2.82065 + 18.8193i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4}+O(q^{10}) $ 120 * q + 24 * q^4	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$-1$

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 $

$2$	−2.12540	−	1.69495i	−1.50289	−	1.19851i	−0.923581	−	0.383404i	$-0.874752\pi$
$2$	−2.12540	−	1.69495i	−1.50289	−	1.19851i	−0.579307	−	0.815109i	$-0.696677\pi$
$3$		0			0
$3$		0			0
$4$	1.19944	+	5.25507i	0.599718	+	2.62753i
$5$	2.70367	+	1.30202i	1.20912	+	0.582280i	0.926261	−	0.376882i	$-0.123004\pi$
$5$	2.70367	+	1.30202i	1.20912	+	0.582280i	0.282856	+	0.959162i	$0.408718\pi$
$6$		0			0
$7$	−0.967619	+	2.46246i	−0.365725	+	0.930723i
$7$	−0.967619	+	2.46246i	−0.365725	+	0.930723i
$8$	3.99879	−	8.30358i	1.41379	−	2.93576i
$9$		0			0
$10$	−3.53953	−	7.34991i	−1.11930	−	2.32425i
$11$	−1.87132	−	1.49233i	−0.564225	−	0.449955i	0.299372	−	0.954136i	$-0.403223\pi$
$11$	−1.87132	−	1.49233i	−0.564225	−	0.449955i	−0.863598	+	0.504182i	$0.831794\pi$
$12$		0			0
$13$	1.93441	+	1.54264i	0.536509	+	0.427851i	0.853895	−	0.520445i	$-0.174234\pi$
$13$	1.93441	+	1.54264i	0.536509	+	0.427851i	−0.317387	+	0.948296i	$0.602805\pi$
$14$	6.23034	−	3.59366i	1.66513	−	0.960445i
$15$		0			0
$16$	−12.8604	+	6.19325i	−3.21510	+	1.54831i
$17$	−1.15098	+	5.04278i	−0.279154	+	1.22305i	0.619711	+	0.784830i	$0.287250\pi$
$17$	−1.15098	+	5.04278i	−0.279154	+	1.22305i	−0.898866	+	0.438225i	$0.855607\pi$
$18$		0			0
$19$			0.270871i			0.0621420i	0.999517	+	0.0310710i	$0.00989179\pi$
$19$			0.270871i			0.0621420i	−0.999517	+	0.0310710i	$0.990108\pi$
$20$	−3.59932	+	15.7697i	−0.804833	+	3.52620i
$21$		0			0
$22$	1.44789	+	6.34361i	0.308691	+	1.35246i
$23$	−8.11148	+	1.85139i	−1.69136	+	0.386042i	−0.956398	−	0.292066i	$-0.905657\pi$
$23$	−8.11148	+	1.85139i	−1.69136	+	0.386042i	−0.734963	+	0.678108i	$0.762800\pi$
$24$		0			0
$25$	2.49713	+	3.13130i	0.499425	+	0.626260i
$26$	−1.49670	−	6.55747i	−0.293527	−	1.28603i
$27$		0			0
$28$	−14.1010	−	2.13134i	−2.66484	−	0.402785i
$29$	2.64195	+	0.603008i	0.490598	+	0.111976i	0.460661	−	0.887576i	$-0.347612\pi$
$29$	2.64195	+	0.603008i	0.490598	+	0.111976i	0.0299365	+	0.999552i	$0.490469\pi$
$30$		0			0
$31$			8.55709i			1.53690i	0.639911	+	0.768449i	$0.278971\pi$
$31$			8.55709i			1.53690i	−0.639911	+	0.768449i	$0.721029\pi$
$32$	19.8604	+	4.53301i	3.51086	+	0.801331i
$33$		0			0
$34$	10.9936	−	8.76709i	1.88538	−	1.50354i
$35$	−5.82229	+	5.39782i	−0.984147	+	0.912399i
$36$		0			0
$37$	1.31758	−	5.77270i	0.216609	−	0.949026i	−0.743354	−	0.668898i	$-0.766766\pi$
$37$	1.31758	−	5.77270i	0.216609	−	0.949026i	0.959963	−	0.280127i	$-0.0903767\pi$
$38$	0.459113	−	0.575710i	0.0744780	−	0.0933924i
$39$		0			0
$40$	21.6228	−	17.2436i	3.41887	−	2.72646i
$41$	−0.862545	−	0.415380i	−0.134707	−	0.0648715i	0.365316	−	0.930884i	$-0.380961\pi$
$41$	−0.862545	−	0.415380i	−0.134707	−	0.0648715i	−0.500023	+	0.866012i	$0.666675\pi$
$42$		0			0
$43$	5.37639	−	2.58913i	0.819892	−	0.394839i	0.0235776	−	0.999722i	$-0.492494\pi$
$43$	5.37639	−	2.58913i	0.819892	−	0.394839i	0.796315	+	0.604883i	$0.206780\pi$
$44$	5.59777	−	11.6239i	0.843895	−	1.75237i
$45$		0			0
$46$	20.3782	+	9.81363i	3.00460	+	1.44694i
$47$	−5.40670	+	6.77979i	−0.788648	+	0.988934i	0.211285	+	0.977424i	$0.432235\pi$
$47$	−5.40670	+	6.77979i	−0.788648	+	0.988934i	−0.999934	+	0.0115095i	$0.996336\pi$
$48$		0			0
$49$	−5.12743	−	4.76545i	−0.732490	−	0.680778i
$50$		−	10.8878i		−	1.53977i
$51$		0			0
$52$	−5.78648	+	12.0158i	−0.802441	+	1.66629i
$53$	1.39025	−	0.317315i	0.190965	−	0.0435866i	−0.125968	−	0.992034i	$-0.540204\pi$
$53$	1.39025	−	0.317315i	0.190965	−	0.0435866i	0.316934	+	0.948448i	$0.397347\pi$
$54$		0			0
$55$	−3.11640	−	6.47127i	−0.420215	−	0.872585i
$56$	16.5779	+	17.8816i	2.21532	+	2.38953i
$57$		0			0
$58$	−4.59314	−	5.75962i	−0.603109	−	0.756275i
$59$	5.63248	−	2.71246i	0.733286	−	0.353132i	−0.0296897	−	0.999559i	$-0.509452\pi$
$59$	5.63248	−	2.71246i	0.733286	−	0.353132i	0.762976	+	0.646427i	$0.223738\pi$
$60$		0			0
$61$	12.1109	+	2.76423i	1.55064	+	0.353923i	0.910227	−	0.414109i	$-0.135907\pi$
$61$	12.1109	+	2.76423i	1.55064	+	0.353923i	0.640411	+	0.768032i	$0.278764\pi$
$62$	14.5039	−	18.1873i	1.84199	−	2.30979i
$63$		0			0
$64$	−16.7288	−	20.9773i	−2.09110	−	2.62216i
$65$	3.22146	+	6.68943i	0.399573	+	0.829721i
$66$		0			0
$67$	−9.18698			−1.12237			−0.561184	−	0.827691i	$-0.689654\pi$
$67$	−9.18698			−1.12237			−0.561184	+	0.827691i	$0.689654\pi$
$68$	−27.8807			−3.38103
$69$		0			0
$70$	21.5238	−	1.60405i	2.57258	−	0.191720i
$71$	3.43876	−	0.784875i	0.408106	−	0.0931475i	−0.0135394	−	0.999908i	$-0.504310\pi$
$71$	3.43876	−	0.784875i	0.408106	−	0.0931475i	0.421645	+	0.906761i	$0.361453\pi$
$72$		0			0
$73$	−6.58618	+	5.25231i	−0.770854	+	0.614736i	−0.927889	−	0.372857i	$-0.878378\pi$
$73$	−6.58618	+	5.25231i	−0.770854	+	0.614736i	0.157034	+	0.987593i	$0.449807\pi$
$74$	−12.5848	+	10.0361i	−1.46296	+	1.16667i
$75$		0			0
$76$	−1.42344	+	0.324892i	−0.163280	+	0.0372676i
$77$	5.48553	−	3.16405i	0.625134	−	0.360577i
$78$		0			0
$79$	8.56875			0.964059			0.482030	−	0.876155i	$-0.339900\pi$
$79$	8.56875			0.964059			0.482030	+	0.876155i	$0.339900\pi$
$80$	−42.8340			−4.78899
$81$		0			0
$82$	1.12921	+	2.34483i	0.124700	+	0.258943i
$83$	0.701261	+	0.879353i	0.0769734	+	0.0965216i	0.818827	−	0.574040i	$-0.194625\pi$
$83$	0.701261	+	0.879353i	0.0769734	+	0.0965216i	−0.741854	+	0.670562i	$0.766053\pi$
$84$		0			0
$85$	−9.67767	+	12.1354i	−1.04969	+	1.31627i
$86$	−15.8155	−	3.60978i	−1.70543	−	0.389252i
$87$		0			0
$88$	−19.8747	+	9.57116i	−2.11865	+	1.02029i
$89$	10.3983	+	13.0391i	1.10222	+	1.38214i	0.916736	+	0.399494i	$0.130814\pi$
$89$	10.3983	+	13.0391i	1.10222	+	1.38214i	0.185485	+	0.982647i	$0.440615\pi$
$90$		0			0
$91$	−5.67046	+	3.27072i	−0.594426	+	0.342865i
$92$	−19.4584	−	40.4058i	−2.02868	−	4.21259i
$93$		0			0
$94$	22.9829	−	5.24569i	2.37050	−	0.541051i
$95$	−0.352678	+	0.732344i	−0.0361840	+	0.0751369i
$96$		0			0
$97$			1.73671i			0.176336i	0.996106	+	0.0881680i	$0.0281012\pi$
$97$			1.73671i			0.176336i	−0.996106	+	0.0881680i	$0.971899\pi$
$98$	2.82065	+	18.8193i	0.284929	+	1.90103i
$99$		0			0
$100$	−13.4600	+	16.8784i	−1.34600	+	1.68784i
$101$	6.02148	+	2.89979i	0.599160	+	0.288540i	0.708776	−	0.705434i	$-0.249248\pi$
$101$	6.02148	+	2.89979i	0.599160	+	0.288540i	−0.109616	+	0.993974i	$0.534962\pi$
$102$		0			0
$103$	0.102115	−	0.212045i	0.0100617	−	0.0208934i	−0.895877	−	0.444301i	$-0.853452\pi$
$103$	0.102115	−	0.212045i	0.0100617	−	0.0208934i	0.905939	+	0.423408i	$0.139166\pi$
$104$	20.5447	−	9.89382i	2.01458	−	0.970169i
$105$		0			0
$106$	−3.49268	−	1.68199i	−0.339239	−	0.163369i
$107$	7.97075	−	6.35646i	0.770562	−	0.614502i	−0.157247	−	0.987559i	$-0.550262\pi$
$107$	7.97075	−	6.35646i	0.770562	−	0.614502i	0.927808	+	0.373057i	$0.121690\pi$
$108$		0			0
$109$	1.90055	−	2.38321i	0.182039	−	0.228270i	−0.682436	−	0.730945i	$-0.739079\pi$
$109$	1.90055	−	2.38321i	0.182039	−	0.228270i	0.864475	+	0.502675i	$0.167651\pi$
$110$	−4.34489	+	19.0362i	−0.414269	+	1.81503i
$111$		0			0
$112$	−2.80666	−	37.6609i	−0.265204	−	3.55863i
$113$	−7.60077	+	6.06141i	−0.715020	+	0.570210i	−0.911996	−	0.410199i	$-0.865459\pi$
$113$	−7.60077	+	6.06141i	−0.715020	+	0.570210i	0.196976	+	0.980408i	$0.436888\pi$
$114$		0			0
$115$	−24.3413	−	5.55575i	−2.26984	−	0.518076i
$116$			14.6069i			1.35622i
$117$		0			0
$118$	−16.5688	−	3.78172i	−1.52528	−	0.348135i
$119$	−11.3039	−	7.71374i	−1.03623	−	0.707117i
$120$		0			0
$121$	−1.17293	−	5.13894i	−0.106630	−	0.467177i
$122$	−21.0553	−	26.4025i	−1.90625	−	2.39037i
$123$		0			0
$124$	−44.9681	+	10.2637i	−4.03825	+	0.921705i
$125$	−0.664359	−	2.91075i	−0.0594221	−	0.260345i
$126$		0			0
$127$	−0.361736	+	1.58487i	−0.0320989	+	0.140634i	−0.988438	−	0.151624i	$-0.951550\pi$
$127$	−0.361736	+	1.58487i	−0.0320989	+	0.140634i	0.956339	+	0.292259i	$0.0944068\pi$
$128$			32.1975i			2.84588i
$129$		0			0
$130$	4.49137	−	19.6780i	0.393919	−	1.72587i
$131$	5.01771	−	2.41640i	0.438399	−	0.211122i	−0.201647	−	0.979458i	$-0.564629\pi$
$131$	5.01771	−	2.41640i	0.438399	−	0.211122i	0.640046	+	0.768336i	$0.278915\pi$
$132$		0			0
$133$	−0.667008	−	0.262099i	−0.0578369	−	0.0227269i
$134$	19.5261	+	15.5715i	1.68679	+	1.34517i
$135$		0			0
$136$	37.2706	+	29.7223i	3.19593	+	2.54867i
$137$	−5.88936	−	12.2294i	−0.503162	−	1.04483i	−0.985631	−	0.168913i	$-0.945974\pi$
$137$	−5.88936	−	12.2294i	−0.503162	−	1.04483i	0.482469	−	0.875913i	$-0.339740\pi$
$138$		0			0
$139$	5.46003	−	11.3379i	0.463114	−	0.961666i	−0.530378	−	0.847761i	$-0.677950\pi$
$139$	5.46003	−	11.3379i	0.463114	−	0.961666i	0.993492	−	0.113905i	$-0.0363358\pi$
$140$	−35.3494	−	24.1222i	−2.98757	−	2.03870i
$141$		0			0
$142$	−8.63909	−	4.16037i	−0.724976	−	0.349130i
$143$	−1.31778	−	5.77356i	−0.110198	−	0.482809i
$144$		0			0
$145$	6.35783	+	5.07020i	0.527989	+	0.421057i
$146$	22.9007			1.89528
$147$		0			0
$148$	31.9163			2.62350
$149$	13.7999	+	11.0051i	1.13053	+	0.901569i	0.996001	−	0.0893399i	$-0.0284757\pi$
$149$	13.7999	+	11.0051i	1.13053	+	0.901569i	0.134531	+	0.990909i	$0.457047\pi$
$150$		0			0
$151$	1.46652	+	6.42522i	0.119343	+	0.522877i	0.998892	+	0.0470678i	$0.0149877\pi$
$151$	1.46652	+	6.42522i	0.119343	+	0.522877i	−0.879548	+	0.475809i	$0.842155\pi$
$152$	2.24919	+	1.08316i	0.182434	+	0.0878555i
$153$		0			0
$154$	−17.0219	−	2.57283i	−1.37166	−	0.207324i
$155$	−11.1415	+	23.1355i	−0.894906	+	1.85829i
$156$		0			0
$157$	3.49186	+	7.25092i	0.278681	+	0.578686i	0.992584	−	0.121558i	$-0.0387889\pi$
$157$	3.49186	+	7.25092i	0.278681	+	0.578686i	−0.713904	+	0.700244i	$0.753075\pi$
$158$	−18.2121	−	14.5236i	−1.44887	−	1.15544i
$159$		0			0
$160$	47.7939	+	38.1144i	3.77844	+	3.01321i
$161$	3.28984	−	21.7656i	0.259275	−	1.71537i
$162$		0			0
$163$	1.76194	−	0.848503i	0.138005	−	0.0664599i	−0.363607	−	0.931553i	$-0.618455\pi$
$163$	1.76194	−	0.848503i	0.138005	−	0.0664599i	0.501612	+	0.865093i	$0.332740\pi$
$164$	1.14828	−	5.03096i	0.0896659	−	0.392852i
$165$		0			0
$166$		−	3.05759i		−	0.237315i
$167$	0.178441	−	0.781800i	0.0138082	−	0.0604975i	−0.967554	−	0.252663i	$-0.918694\pi$
$167$	0.178441	−	0.781800i	0.0138082	−	0.0604975i	0.981363	+	0.192165i	$0.0615509\pi$
$168$		0			0
$169$	−1.53057	−	6.70587i	−0.117736	−	0.515836i
$170$	41.1379	−	9.38947i	3.15514	−	0.720139i
$171$		0			0
$172$	20.0547	+	25.1478i	1.52916	+	1.91750i
$173$	−3.18902	−	13.9720i	−0.242457	−	1.06227i	−0.938773	−	0.344537i	$-0.888036\pi$
$173$	−3.18902	−	13.9720i	−0.242457	−	1.06227i	0.696316	−	0.717736i	$-0.254821\pi$
$174$		0			0
$175$	−10.1270	+	3.11918i	−0.765527	+	0.235788i
$176$	33.3083	+	7.60241i	2.51071	+	0.573053i
$177$		0			0
$178$		−	45.3380i		−	3.39823i
$179$	−4.91685	−	1.12224i	−0.367502	−	0.0838800i	0.0347817	−	0.999395i	$-0.488926\pi$
$179$	−4.91685	−	1.12224i	−0.367502	−	0.0838800i	−0.402284	+	0.915515i	$0.631784\pi$
$180$		0			0
$181$	4.24460	−	3.38496i	0.315499	−	0.251602i	−0.452917	−	0.891553i	$-0.649617\pi$
$181$	4.24460	−	3.38496i	0.315499	−	0.251602i	0.768416	+	0.639951i	$0.221045\pi$
$182$	17.5957	+	2.65956i	1.30428	+	0.197140i
$183$		0			0
$184$	−17.0629	+	74.7577i	−1.25790	+	5.51121i
$185$	11.0785	−	13.8920i	0.814505	−	1.02136i
$186$		0			0
$187$	9.67936	−	7.71903i	0.707825	−	0.564471i
$188$	−42.1133	−	20.2807i	−3.07142	−	1.47912i
$189$		0			0
$190$	1.99087	−	0.958755i	0.144433	−	0.0695554i
$191$	−9.56076	+	19.8531i	−0.691793	+	1.43652i	0.198021	+	0.980198i	$0.436549\pi$
$191$	−9.56076	+	19.8531i	−0.691793	+	1.43652i	−0.889814	+	0.456324i	$0.849166\pi$
$192$		0			0
$193$	9.46536	+	4.55828i	0.681331	+	0.328112i	0.742338	−	0.670025i	$-0.233717\pi$
$193$	9.46536	+	4.55828i	0.681331	+	0.328112i	−0.0610068	+	0.998137i	$0.519431\pi$
$194$	2.94364	−	3.69121i	0.211341	−	0.265013i
$195$		0			0
$196$	18.8927	−	32.6608i	1.34948	−	2.33292i
$197$			2.45389i			0.174833i	0.996172	+	0.0874164i	$0.0278611\pi$
$197$			2.45389i			0.174833i	−0.996172	+	0.0874164i	$0.972139\pi$
$198$		0			0
$199$	9.14326	−	18.9862i	0.648149	−	1.34589i	−0.274997	−	0.961445i	$-0.588677\pi$
$199$	9.14326	−	18.9862i	0.648149	−	1.34589i	0.923146	−	0.384450i	$-0.125609\pi$
$200$	35.9865	−	8.21368i	2.54463	−	0.580795i
$201$		0			0
$202$	−7.88307	−	16.3694i	−0.554651	−	1.15175i
$203$	−4.04128	+	5.92222i	−0.283642	+	0.415658i
$204$		0			0
$205$	−1.79121	−	2.24610i	−0.125103	−	0.156874i
$206$	−0.576442	+	0.277600i	−0.0401626	+	0.0193413i
$207$		0			0
$208$	−34.4312	−	7.85871i	−2.38738	−	0.544903i
$209$	0.404228	−	0.506886i	0.0279611	−	0.0350621i
$210$		0			0
$211$	−13.2934	−	16.6694i	−0.915154	−	1.14757i	−0.988645	−	0.150271i	$-0.951985\pi$
$211$	−13.2934	−	16.6694i	−0.915154	−	1.14757i	0.0734905	−	0.997296i	$-0.476586\pi$
$212$	3.33503	+	6.92526i	0.229051	+	0.475629i
$213$		0			0
$214$	−27.7150			−1.89456
$215$	17.9071			1.22125
$216$		0			0
$217$	−21.0715	−	8.28000i	−1.43043	−	0.562083i
$218$	−8.07886	+	1.84395i	−0.547169	+	0.124888i
$219$		0			0
$220$	30.2690	−	24.1387i	2.04074	−	1.62743i
$221$	−10.0057	+	7.97925i	−0.673054	+	0.536743i
$222$		0			0
$223$	−5.73095	+	1.30805i	−0.383773	+	0.0875937i	−0.410055	−	0.912061i	$-0.634490\pi$
$223$	−5.73095	+	1.30805i	−0.383773	+	0.0875937i	0.0262818	+	0.999655i	$0.491633\pi$
$224$	−30.3797	+	44.5193i	−2.02983	+	2.97457i
$225$		0			0
$226$	26.4285			1.75800
$227$	1.71036			0.113520			0.0567602	−	0.998388i	$-0.481923\pi$
$227$	1.71036			0.113520			0.0567602	+	0.998388i	$0.481923\pi$
$228$		0			0
$229$	−8.18552	−	16.9974i	−0.540915	−	1.12322i	−0.974970	−	0.222335i	$-0.928632\pi$
$229$	−8.18552	−	16.9974i	−0.540915	−	1.12322i	0.434056	−	0.900886i	$-0.357082\pi$
$230$	42.3184	+	53.0656i	2.79039	+	3.49904i
$231$		0			0
$232$	15.5717	−	19.5263i	1.02233	−	1.28197i
$233$	6.22666	+	1.42120i	0.407922	+	0.0931056i	0.421558	−	0.906801i	$-0.361483\pi$
$233$	6.22666	+	1.42120i	0.407922	+	0.0931056i	−0.0136357	+	0.999907i	$0.504341\pi$
$234$		0			0
$235$	−23.4453	+	11.2907i	−1.52941	+	0.736523i
$236$	21.0099	+	26.3456i	1.36763	+	1.71495i
$237$		0			0
$238$	10.9510	+	35.5545i	0.709850	+	2.30465i
$239$	2.07872	+	4.31651i	0.134461	+	0.279212i	0.957318	−	0.289037i	$-0.0933352\pi$
$239$	2.07872	+	4.31651i	0.134461	+	0.279212i	−0.822856	+	0.568249i	$0.807621\pi$
$240$		0			0
$241$	−14.6103	+	3.33471i	−0.941134	+	0.214808i	−0.665452	−	0.746441i	$-0.731761\pi$
$241$	−14.6103	+	3.33471i	−0.941134	+	0.214808i	−0.275683	+	0.961249i	$0.588904\pi$
$242$	−6.21732	+	12.9104i	−0.399664	+	0.829912i
$243$		0			0
$244$			66.9590i			4.28661i
$245$	−7.65817	−	19.5602i	−0.489263	−	1.24966i
$246$		0			0
$247$	−0.417856	+	0.523975i	−0.0265875	+	0.0333397i
$248$	71.0544	+	34.2180i	4.51196	+	2.17285i
$249$		0			0
$250$	−3.52155	+	7.31257i	−0.222722	+	0.462488i
$251$	6.93459	−	3.33952i	0.437707	−	0.210789i	−0.202035	−	0.979378i	$-0.564755\pi$
$251$	6.93459	−	3.33952i	0.437707	−	0.210789i	0.639742	+	0.768590i	$0.279041\pi$
$252$		0			0
$253$	17.9421	+	8.64046i	1.12801	+	0.543221i
$254$	3.45511	−	2.75536i	0.216793	−	0.172887i
$255$		0			0
$256$	21.1156	−	26.4781i	1.31973	−	1.65488i
$257$	0.244069	−	1.06934i	0.0152246	−	0.0667033i	−0.966745	−	0.255742i	$-0.917680\pi$
$257$	0.244069	−	1.06934i	0.0152246	−	0.0667033i	0.981970	+	0.189039i	$0.0605373\pi$
$258$		0			0
$259$	12.9401	+	8.83026i	0.804060	+	0.548686i
$260$	−31.2895	+	24.9525i	−1.94049	+	1.54749i
$261$		0			0
$262$	−14.7604	−	3.36895i	−0.911898	−	0.208135i
$263$		−	2.81416i		−	0.173529i	−0.996229	−	0.0867643i	$-0.972347\pi$
$263$		−	2.81416i		−	0.173529i	0.996229	−	0.0867643i	$-0.0276527\pi$
$264$		0			0
$265$	4.17193	+	0.952215i	0.256279	+	0.0584941i
$266$	0.973416	+	1.68762i	0.0596840	+	0.103474i
$267$		0			0
$268$	−11.0192	−	48.2782i	−0.673104	−	2.94906i
$269$	−17.7274	−	22.2294i	−1.08086	−	1.35535i	−0.930320	−	0.366749i	$-0.880471\pi$
$269$	−17.7274	−	22.2294i	−1.08086	−	1.35535i	−0.150538	−	0.988604i	$-0.548101\pi$
$270$		0			0
$271$	28.4023	−	6.48263i	1.72531	−	0.393792i	0.758987	−	0.651106i	$-0.225695\pi$
$271$	28.4023	−	6.48263i	1.72531	−	0.393792i	0.966328	+	0.257314i	$0.0828374\pi$
$272$	−16.4291	−	71.9805i	−0.996160	−	4.36446i
$273$		0			0
$274$	−8.21096	+	35.9746i	−0.496042	+	2.17330i
$275$		−	9.58621i		−	0.578070i
$276$		0			0
$277$	−4.11057	+	18.0096i	−0.246980	+	1.08209i	0.687531	+	0.726155i	$0.258695\pi$
$277$	−4.11057	+	18.0096i	−0.246980	+	1.08209i	−0.934511	+	0.355935i	$0.884163\pi$
$278$	−30.8220	+	14.8431i	−1.84858	+	0.890228i
$279$		0			0
$280$	21.5391	+	69.9306i	1.28721	+	4.17915i
$281$	−12.2493	−	9.76846i	−0.730729	−	0.582737i	0.185856	−	0.982577i	$-0.440494\pi$
$281$	−12.2493	−	9.76846i	−0.730729	−	0.582737i	−0.916585	+	0.399840i	$0.869066\pi$
$282$		0			0
$283$	−15.4090	−	12.2882i	−0.915968	−	0.730460i	0.0473341	−	0.998879i	$-0.484927\pi$
$283$	−15.4090	−	12.2882i	−0.915968	−	0.730460i	−0.963302	+	0.268419i	$0.913499\pi$
$284$	8.24915	+	17.1295i	0.489497	+	1.01645i
$285$		0			0
$286$	−6.98510	+	14.5047i	−0.413038	+	0.857682i
$287$	1.85747	−	1.72206i	0.109643	−	0.101650i
$288$		0			0
$289$	−8.78842	−	4.23228i	−0.516966	−	0.248958i
$290$	−4.91921	−	21.5525i	−0.288866	−	1.26560i
$291$		0			0
$292$	−35.5009	−	28.3111i	−2.07754	−	1.65678i
$293$	19.1934			1.12129			0.560645	−	0.828056i	$-0.310553\pi$
$293$	19.1934			1.12129			0.560645	+	0.828056i	$0.310553\pi$
$294$		0			0
$295$	18.7600			1.09225
$296$	−42.6653	−	34.0245i	−2.47987	−	1.97763i
$297$		0			0
$298$	−10.6773	−	46.7804i	−0.618521	−	2.70992i
$299$	−18.5470	−	8.93175i	−1.07260	−	0.516536i
$300$		0			0
$301$	1.17335	+	15.7444i	0.0676305	+	0.907495i
$302$	7.77352	−	16.1419i	0.447316	−	0.928861i
$303$		0			0
$304$	−1.67757	−	3.48351i	−0.0962151	−	0.199793i
$305$	29.1447	+	23.2421i	1.66882	+	1.33084i
$306$		0			0
$307$	−12.3704	−	9.86507i	−0.706016	−	0.563029i	0.203309	−	0.979115i	$-0.434830\pi$
$307$	−12.3704	−	9.86507i	−0.706016	−	0.563029i	−0.909326	+	0.416085i	$0.863402\pi$
$308$	23.2069	+	25.0318i	1.32233	+	1.42632i
$309$		0			0
$310$	62.8938	−	30.2881i	3.57213	−	1.72025i
$311$	−7.30205	+	31.9924i	−0.414061	+	1.81412i	0.150358	+	0.988632i	$0.451957\pi$
$311$	−7.30205	+	31.9924i	−0.414061	+	1.81412i	−0.564419	+	0.825488i	$0.690900\pi$
$312$		0			0
$313$			22.7644i			1.28672i	0.765564	+	0.643360i	$0.222460\pi$
$313$			22.7644i			1.28672i	−0.765564	+	0.643360i	$0.777540\pi$
$314$	4.86836	−	21.3297i	0.274737	−	1.20370i
$315$		0			0
$316$	10.2777	+	45.0294i	0.578163	+	2.53310i
$317$	22.8351	−	5.21197i	1.28255	−	0.292733i	0.473667	−	0.880704i	$-0.342930\pi$
$317$	22.8351	−	5.21197i	1.28255	−	0.292733i	0.808882	+	0.587971i	$0.200073\pi$
$318$		0			0
$319$	−4.04405	−	5.07108i	−0.226424	−	0.283926i
$320$	−17.9164	−	78.4969i	−1.00156	−	4.38811i
$321$		0			0
$322$	−43.8840	+	40.6847i	−2.44556	+	2.26727i
$323$	−1.36594	−	0.311767i	−0.0760030	−	0.0173472i
$324$		0			0
$325$			9.90938i			0.549674i
$326$	−5.18300	−	1.18299i	−0.287060	−	0.0655195i
$327$		0			0
$328$	−6.89828	+	5.50120i	−0.380894	+	0.303753i
$329$	−11.4633	−	19.8740i	−0.631995	−	1.09569i
$330$		0			0
$331$	2.82186	−	12.3634i	0.155103	−	0.679553i	−0.836252	−	0.548346i	$-0.815258\pi$
$331$	2.82186	−	12.3634i	0.155103	−	0.679553i	0.991355	−	0.131207i	$-0.0418852\pi$
$332$	−3.77995	+	4.73990i	−0.207452	+	0.260136i
$333$		0			0
$334$	−1.70437	+	1.35919i	−0.0932592	+	0.0743717i
$335$	−24.8386	−	11.9616i	−1.35708	−	0.653533i
$336$		0			0
$337$	3.43373	−	1.65360i	0.187047	−	0.0900771i	−0.338016	−	0.941140i	$-0.609756\pi$
$337$	3.43373	−	1.65360i	0.187047	−	0.0900771i	0.525063	+	0.851063i	$0.324042\pi$
$338$	−8.11305	+	16.8469i	−0.441292	+	0.916352i
$339$		0			0
$340$	−75.3802	−	36.3012i	−4.08806	−	1.96871i
$341$	12.7700	−	16.0131i	0.691534	−	0.867157i
$342$		0			0
$343$	16.6961	−	8.01496i	0.901506	−	0.432767i
$344$		−	54.9967i		−	2.96522i
$345$		0			0
$346$	−16.9040	+	35.1014i	−0.908763	+	1.88707i
$347$	4.35892	−	0.994896i	0.233999	−	0.0534088i	−0.103913	−	0.994586i	$-0.533136\pi$
$347$	4.35892	−	0.994896i	0.233999	−	0.0534088i	0.337912	+	0.941178i	$0.390279\pi$
$348$		0			0
$349$	−6.92086	−	14.3713i	−0.370465	−	0.769278i	0.629505	−	0.776996i	$-0.283258\pi$
$349$	−6.92086	−	14.3713i	−0.370465	−	0.769278i	−0.999970	+	0.00771786i	$0.997543\pi$
$350$	26.8108	+	10.5352i	1.43310	+	0.563132i
$351$		0			0
$352$	−30.4005	−	38.1210i	−1.62035	−	2.03186i
$353$	13.1168	−	6.31673i	0.698138	−	0.336206i	−0.0509266	−	0.998702i	$-0.516217\pi$
$353$	13.1168	−	6.31673i	0.698138	−	0.336206i	0.749065	+	0.662497i	$0.230503\pi$
$354$		0			0
$355$	10.3192	+	2.35529i	0.547686	+	0.125006i
$356$	−56.0492	+	70.2835i	−2.97060	+	3.72502i
$357$		0			0
$358$	8.54815	+	10.7190i	0.451784	+	0.566519i
$359$	1.62133	+	3.36672i	0.0855703	+	0.177688i	0.939363	−	0.342925i	$-0.111418\pi$
$359$	1.62133	+	3.36672i	0.0855703	+	0.177688i	−0.853793	+	0.520613i	$0.825703\pi$
$360$		0			0
$361$	18.9266			0.996138
$362$	−14.7589			−0.775708
$363$		0			0
$364$	−23.9892	−	25.8757i	−1.25738	−	1.35625i
$365$	−24.6455	+	5.62517i	−1.29000	+	0.294435i
$366$		0			0
$367$	8.56520	−	6.83052i	0.447100	−	0.356550i	−0.373909	−	0.927465i	$-0.621983\pi$
$367$	8.56520	−	6.83052i	0.447100	−	0.356550i	0.821009	+	0.570915i	$0.193411\pi$
$368$	92.8508	−	74.0461i	4.84018	−	3.85992i
$369$		0			0
$370$	−47.0924	+	10.7485i	−2.44822	+	0.558790i
$371$	−0.563854	+	3.73048i	−0.0292739	+	0.193677i
$372$		0			0
$373$	32.1769			1.66605			0.833027	−	0.553232i	$-0.186606\pi$
$373$	32.1769			1.66605			0.833027	+	0.553232i	$0.186606\pi$
$374$	−33.6559			−1.74031
$375$		0			0
$376$	34.6762	+	72.0059i	1.78829	+	3.71342i
$377$	4.18039	+	5.24204i	0.215301	+	0.269979i
$378$		0			0
$379$	−2.16842	+	2.71912i	−0.111384	+	0.139672i	−0.834398	−	0.551162i	$-0.814185\pi$
$379$	−2.16842	+	2.71912i	−0.111384	+	0.139672i	0.723014	+	0.690833i	$0.242756\pi$
$380$	−4.27154	−	0.974950i	−0.219125	−	0.0500139i
$381$		0			0
$382$	53.9706	−	25.9909i	2.76138	−	1.32981i
$383$	−15.1494	−	18.9968i	−0.774100	−	0.970691i	0.225894	−	0.974152i	$-0.427470\pi$
$383$	−15.1494	−	18.9968i	−0.774100	−	0.970691i	−0.999994	+	0.00346120i	$0.998898\pi$
$384$		0			0
$385$	18.9507	−	1.41229i	0.965818	−	0.0719770i
$386$	−12.3916	−	25.7315i	−0.630718	−	1.30970i
$387$		0			0
$388$	−9.12653	+	2.08307i	−0.463329	+	0.105752i
$389$	11.1089	−	23.0679i	0.563245	−	1.16959i	−0.403768	−	0.914861i	$-0.632300\pi$
$389$	11.1089	−	23.0679i	0.563245	−	1.16959i	0.967013	−	0.254728i	$-0.0819861\pi$
$390$		0			0
$391$		−	43.0354i		−	2.17639i
$392$	−60.0738	+	23.5200i	−3.03418	+	1.18794i
$393$		0			0
$394$	4.15924	−	5.21552i	0.209539	−	0.262754i
$395$	23.1671	+	11.1567i	1.16566	+	0.561353i
$396$		0			0
$397$	−0.366625	+	0.761304i	−0.0184004	+	0.0382088i	−0.909966	−	0.414682i	$-0.863893\pi$
$397$	−0.366625	+	0.761304i	−0.0184004	+	0.0382088i	0.891566	+	0.452891i	$0.149607\pi$
$398$	−51.6138	+	24.8559i	−2.58717	+	1.24591i
$399$		0			0
$400$	−51.5070	−	24.8044i	−2.57535	−	1.24022i
$401$	−7.59276	+	6.05502i	−0.379164	+	0.302373i	−0.794464	−	0.607311i	$-0.792248\pi$
$401$	−7.59276	+	6.05502i	−0.379164	+	0.302373i	0.415300	+	0.909685i	$0.363677\pi$
$402$		0			0
$403$	−13.2005	+	16.5529i	−0.657564	+	0.824559i
$404$	−8.01624	+	35.1214i	−0.398823	+	1.74736i
$405$		0			0
$406$	18.6272	−	5.73732i	0.924455	−	0.284738i
$407$	−11.0804	+	8.83632i	−0.549235	+	0.438000i
$408$		0			0
$409$	−5.13723	−	1.17254i	−0.254019	−	0.0579783i	0.0936148	−	0.995608i	$-0.470158\pi$
$409$	−5.13723	−	1.17254i	−0.254019	−	0.0579783i	−0.347634	+	0.937630i	$0.613015\pi$
$410$			7.80988i			0.385703i
$411$		0			0
$412$	1.23679	+	0.282289i	0.0609323	+	0.0139074i
$413$	1.22923	+	16.4944i	0.0604866	+	0.811635i
$414$		0			0
$415$	0.751043	+	3.29054i	0.0368673	+	0.161526i
$416$	31.4254	+	39.4062i	1.54076	+	1.93205i
$417$		0			0
$418$	−1.71830	+	0.392190i	−0.0840447	+	0.0191827i
$419$	−6.55607	−	28.7240i	−0.320285	−	1.40326i	−0.837047	−	0.547132i	$-0.815720\pi$
$419$	−6.55607	−	28.7240i	−0.320285	−	1.40326i	0.516761	−	0.856129i	$-0.327137\pi$
$420$		0			0
$421$	−2.72489	+	11.9385i	−0.132803	+	0.581849i	0.864108	+	0.503307i	$0.167884\pi$
$421$	−2.72489	+	11.9385i	−0.132803	+	0.581849i	−0.996911	+	0.0785417i	$0.974974\pi$
$422$			57.9608i			2.82149i
$423$		0			0
$424$	2.92447	−	12.8129i	0.142025	−	0.622251i
$425$	−18.6646	+	8.98840i	−0.905366	+	0.436001i
$426$		0			0
$427$	−18.5255	+	27.1478i	−0.896512	+	1.31378i
$428$	42.9640	+	34.2627i	2.07675	+	1.65615i
$429$		0			0
$430$	−38.0598	−	30.3517i	−1.83541	−	1.46369i
$431$	−8.65432	−	17.9709i	−0.416864	−	0.865626i	−0.998633	−	0.0522725i	$-0.983354\pi$
$431$	−8.65432	−	17.9709i	−0.416864	−	0.865626i	0.581769	−	0.813354i	$-0.302361\pi$
$432$		0			0
$433$	−5.39220	+	11.1970i	−0.259133	+	0.538094i	−0.989426	−	0.145039i	$-0.953669\pi$
$433$	−5.39220	+	11.1970i	−0.259133	+	0.538094i	0.730293	+	0.683134i	$0.239383\pi$
$434$	30.7512	+	53.3135i	1.47611	+	2.55913i
$435$		0			0
$436$	14.8035	+	7.12900i	0.708960	+	0.341417i
$437$	−0.501488	−	2.19716i	−0.0239894	−	0.105104i
$438$		0			0
$439$	21.4607	+	17.1144i	1.02426	+	0.816824i	0.983237	−	0.182334i	$-0.0583653\pi$
$439$	21.4607	+	17.1144i	1.02426	+	0.816824i	0.0410281	+	0.999158i	$0.486937\pi$
$440$	−66.1965			−3.15579
$441$		0			0
$442$	34.7906			1.65482
$443$	17.9005	+	14.2752i	0.850480	+	0.678236i	0.948441	−	0.316955i	$-0.102660\pi$
$443$	17.9005	+	14.2752i	0.850480	+	0.678236i	−0.0979602	+	0.995190i	$0.531232\pi$
$444$		0			0
$445$	11.1365	+	48.7922i	0.527921	+	2.31297i
$446$	14.3977	+	6.93356i	0.681750	+	0.328314i
$447$		0			0
$448$	67.8429	−	20.8961i	3.20528	−	0.987247i
$449$	−5.24856	+	10.8987i	−0.247695	+	0.514344i	−0.987333	−	0.158661i	$-0.949282\pi$
$449$	−5.24856	+	10.8987i	−0.247695	+	0.514344i	0.739638	+	0.673005i	$0.234997\pi$
$450$		0			0
$451$	0.994217	+	2.06451i	0.0468158	+	0.0972141i
$452$	−40.9698	−	32.6723i	−1.92706	−	1.53678i
$453$		0			0
$454$	−3.63520	−	2.89898i	−0.170609	−	0.136056i
$455$	−19.5896	+	1.45990i	−0.918374	+	0.0684413i
$456$		0			0
$457$	−6.92848	+	3.33658i	−0.324101	+	0.156079i	−0.588858	−	0.808236i	$-0.700422\pi$
$457$	−6.92848	+	3.33658i	−0.324101	+	0.156079i	0.264757	+	0.964315i	$0.414708\pi$
$458$	−11.4123	+	50.0005i	−0.533261	+	2.33637i
$459$		0			0
$460$		−	134.579i		−	6.27478i
$461$	−2.31255	+	10.1319i	−0.107706	+	0.471891i	0.892093	+	0.451851i	$0.149236\pi$
$461$	−2.31255	+	10.1319i	−0.107706	+	0.471891i	−0.999799	+	0.0200393i	$0.993621\pi$
$462$		0			0
$463$	0.620618	+	2.71911i	0.0288426	+	0.126368i	0.987300	−	0.158869i	$-0.0507849\pi$
$463$	0.620618	+	2.71911i	0.0288426	+	0.126368i	−0.958457	+	0.285237i	$0.907928\pi$
$464$	−37.7111	+	8.60732i	−1.75069	+	0.399585i
$465$		0			0
$466$	−10.8253	−	13.5745i	−0.501473	−	0.628828i
$467$	5.42836	+	23.7832i	0.251195	+	1.10056i	0.930382	+	0.366591i	$0.119475\pi$
$467$	5.42836	+	23.7832i	0.251195	+	1.10056i	−0.679187	+	0.733965i	$0.737668\pi$
$468$		0			0
$469$	8.88949	−	22.6226i	0.410479	−	1.04461i
$470$	68.9680	+	15.7415i	3.18126	+	0.726101i
$471$		0			0
$472$		−	57.6163i		−	2.65200i
$473$	−13.9248	−	3.17825i	−0.640263	−	0.146136i
$474$		0			0
$475$	−0.848176	+	0.676398i	−0.0389170	+	0.0310353i
$476$	26.9779	−	68.6551i	1.23653	−	3.14680i
$477$		0			0
$478$	2.89816	−	12.6977i	0.132559	−	0.580778i
$479$	−0.244479	+	0.306568i	−0.0111706	+	0.0140074i	−0.787385	−	0.616461i	$-0.788566\pi$
$479$	−0.244479	+	0.306568i	−0.0111706	+	0.0140074i	0.776215	+	0.630468i	$0.217137\pi$
$480$		0			0
$481$	11.4539	−	9.13421i	0.522255	−	0.416484i
$482$	36.7050	+	17.6762i	1.67187	+	0.805130i
$483$		0			0
$484$	25.5986	−	12.3277i	1.16357	−	0.560348i
$485$	−2.26123	+	4.69549i	−0.102677	+	0.213211i
$486$		0			0
$487$	15.9031	+	7.65855i	0.720640	+	0.347042i	0.757995	−	0.652260i	$-0.226179\pi$
$487$	15.9031	+	7.65855i	0.720640	+	0.347042i	−0.0373551	+	0.999302i	$0.511893\pi$
$488$	71.3818	−	89.5100i	3.23130	−	4.05193i
$489$		0			0
$490$	−16.8769	+	54.5536i	−0.762421	+	2.46448i
$491$			10.2550i			0.462802i	0.972859	+	0.231401i	$0.0743309\pi$
$491$			10.2550i			0.462802i	−0.972859	+	0.231401i	$0.925669\pi$
$492$		0			0
$493$	−6.08167	+	12.6287i	−0.273905	+	0.568769i
$494$	1.77623	−	0.405412i	0.0799162	−	0.0182403i
$495$		0			0
$496$	−52.9961	−	110.048i	−2.37960	−	4.94128i
$497$	−1.39469	+	9.22728i	−0.0625602	+	0.413900i
$498$		0			0
$499$	−20.1202	−	25.2300i	−0.900706	−	1.12945i	−0.991044	−	0.133538i	$-0.957366\pi$
$499$	−20.1202	−	25.2300i	−0.900706	−	1.12945i	0.0903377	−	0.995911i	$-0.471205\pi$
$500$	14.4993	−	6.98250i	0.648429	−	0.312267i
$501$		0			0
$502$	−20.3991	−	4.65597i	−0.910458	−	0.207806i
$503$	10.4008	−	13.0422i	0.463749	−	0.581523i	−0.493879	−	0.869531i	$-0.664421\pi$
$503$	10.4008	−	13.0422i	0.463749	−	0.581523i	0.957628	+	0.288008i	$0.0929929\pi$
$504$		0			0
$505$	12.5045	+	15.6802i	0.556444	+	0.697758i
$506$	−23.4890	−	48.7755i	−1.04422	−	2.16833i
$507$		0			0
$508$	−8.76248			−0.388772
$509$	11.5471			0.511816			0.255908	−	0.966701i	$-0.417626\pi$
$509$	11.5471			0.511816			0.255908	+	0.966701i	$0.417626\pi$
$510$		0			0
$511$	−6.56069	−	21.3004i	−0.290228	−	0.942276i
$512$	−26.9779	+	6.15754i	−1.19227	+	0.272127i
$513$		0			0
$514$	−2.33122	+	1.85909i	−0.102826	+	0.0820007i
$515$	0.552172	−	0.440342i	0.0243316	−	0.0194038i
$516$		0			0
$517$	20.2354	−	4.61859i	0.889951	−	0.203125i
$518$	−12.5361	−	40.7008i	−0.550806	−	1.78829i
$519$		0			0
$520$	68.4281			3.00077
$521$	43.6211			1.91107			0.955537	−	0.294871i	$-0.0952767\pi$
$521$	43.6211			1.91107			0.955537	+	0.294871i	$0.0952767\pi$
$522$		0			0
$523$	18.3822	+	38.1710i	0.803797	+	1.66910i	0.741412	+	0.671051i	$0.234157\pi$
$523$	18.3822	+	38.1710i	0.803797	+	1.66910i	0.0623858	+	0.998052i	$0.480129\pi$
$524$	18.7168	+	23.4701i	0.817646	+	1.02530i
$525$		0			0
$526$	−4.76987	+	5.98123i	−0.207976	+	0.260794i
$527$	−43.1515	−	9.84905i	−1.87971	−	0.429031i
$528$		0			0
$529$	41.6462	−	20.0558i	1.81070	−	0.871989i
$530$	−7.25307	−	9.09506i	−0.315053	−	0.395064i
$531$		0			0
$532$	0.577317	−	3.81955i	0.0250299	−	0.165598i
$533$	−1.02773	−	2.13411i	−0.0445161	−	0.0924387i
$534$		0			0
$535$	29.8265	−	6.80771i	1.28951	−	0.294323i
$536$	−36.7368	+	76.2848i	−1.58679	+	3.29500i
$537$		0			0
$538$			77.2937i			3.33237i
$539$	2.48346	+	16.5695i	0.106970	+	0.713699i
$540$		0			0
$541$	−21.0846	+	26.4392i	−0.906496	+	1.13671i	0.0836249	+	0.996497i	$0.473350\pi$
$541$	−21.0846	+	26.4392i	−0.906496	+	1.13671i	−0.990121	+	0.140213i	$0.955221\pi$
$542$	−71.3541	−	34.3623i	−3.06492	−	1.47599i
$543$		0			0
$544$	−45.7180	+	94.9344i	−1.96014	+	4.07028i
$545$	8.24143	−	3.96886i	0.353024	−	0.170007i
$546$		0			0
$547$	32.6267	+	15.7122i	1.39502	+	0.671805i	0.972144	−	0.234384i	$-0.0753073\pi$
$547$	32.6267	+	15.7122i	1.39502	+	0.671805i	0.422873	+	0.906189i	$0.361022\pi$
$548$	57.2023	−	45.6173i	2.44356	−	1.94868i
$549$		0			0
$550$	−16.2482	+	20.3746i	−0.692825	+	0.868775i
$551$	−0.163337	+	0.715626i	−0.00695839	+	0.0304867i
$552$		0			0
$553$	−8.29128	+	21.1002i	−0.352581	+	0.897272i
$554$	39.2620	−	31.3104i	1.66808	−	1.33025i
$555$		0			0
$556$	66.1303	+	15.0938i	2.80455	+	0.640120i
$557$		−	2.84407i		−	0.120507i	−0.998183	−	0.0602535i	$-0.980809\pi$
$557$		−	2.84407i		−	0.120507i	0.998183	−	0.0602535i	$-0.0191909\pi$
$558$		0			0
$559$	14.3942	+	3.28539i	0.608812	+	0.138957i
$560$	41.4470	−	105.477i	1.75145	−	4.45722i
$561$		0			0
$562$	9.47755	+	41.5238i	0.399786	+	1.75158i
$563$	−5.45793	−	6.84403i	−0.230024	−	0.288441i	0.653402	−	0.757011i	$-0.273341\pi$
$563$	−5.45793	−	6.84403i	−0.230024	−	0.288441i	−0.883427	+	0.468569i	$0.844770\pi$
$564$		0			0
$565$	−28.4420	+	6.49171i	−1.19657	+	0.273108i
$566$	11.9223	+	52.2350i	0.501131	+	2.19560i
$567$		0			0
$568$	7.23363	−	31.6926i	0.303516	−	1.32979i
$569$			12.6997i			0.532400i	0.963918	+	0.266200i	$0.0857681\pi$
$569$			12.6997i			0.532400i	−0.963918	+	0.266200i	$0.914232\pi$
$570$		0			0
$571$	−3.77390	+	16.5345i	−0.157933	+	0.691949i	0.832508	+	0.554013i	$0.186904\pi$
$571$	−3.77390	+	16.5345i	−0.157933	+	0.691949i	−0.990441	+	0.137936i	$0.955953\pi$
$572$	28.7599	−	13.8500i	1.20251	−	0.579098i
$573$		0			0
$574$	−6.86668	+	0.511735i	−0.286610	+	0.0213594i
$575$	−26.0527	−	20.7763i	−1.08647	−	0.866432i
$576$		0			0
$577$	−22.3053	−	17.7879i	−0.928582	−	0.740520i	0.0373534	−	0.999302i	$-0.488107\pi$
$577$	−22.3053	−	17.7879i	−0.928582	−	0.740520i	−0.965936	+	0.258782i	$0.916679\pi$
$578$	11.5054	+	23.8913i	0.478563	+	0.993746i
$579$		0			0
$580$	−19.0185	+	39.4922i	−0.789698	+	1.63983i
$581$	−2.84393	+	0.875949i	−0.117986	+	0.0363405i
$582$		0			0
$583$	−3.07515	−	1.48091i	−0.127360	−	0.0613331i
$584$	17.2762	+	75.6918i	0.714892	+	3.13215i
$585$		0			0
$586$	−40.7938	−	32.5319i	−1.68517	−	1.34388i
$587$	1.15074			0.0474962			0.0237481	−	0.999718i	$-0.492440\pi$
$587$	1.15074			0.0474962			0.0237481	+	0.999718i	$0.492440\pi$
$588$		0			0
$589$	−2.31786			−0.0955059
$590$	−39.8726	−	31.7974i	−1.64153	−	1.30908i
$591$		0			0
$592$	18.8071	+	82.3993i	0.772968	+	3.38659i
$593$	1.55219	+	0.747496i	0.0637408	+	0.0306960i	0.465483	−	0.885057i	$-0.345881\pi$
$593$	1.55219	+	0.747496i	0.0637408	+	0.0306960i	−0.401742	+	0.915753i	$0.631595\pi$
$594$		0			0
$595$	−20.5187	−	35.5733i	−0.841184	−	1.45836i
$596$	−41.2803	+	85.7193i	−1.69090	+	3.51120i
$597$		0			0
$598$	24.2809	+	50.4198i	0.992920	+	2.06182i
$599$	17.9381	+	14.3051i	0.732929	+	0.584491i	0.917220	−	0.398380i	$-0.130428\pi$
$599$	17.9381	+	14.3051i	0.732929	+	0.584491i	−0.184291	+	0.982872i	$0.558999\pi$
$600$		0			0
$601$	32.9543	+	26.2802i	1.34424	+	1.07199i	0.990626	+	0.136599i	$0.0436171\pi$
$601$	32.9543	+	26.2802i	1.34424	+	1.07199i	0.353609	+	0.935393i	$0.384954\pi$
$602$	24.1923	−	35.4521i	0.986004	−	1.44492i
$603$		0			0
$604$	−32.0060	+	15.4133i	−1.30231	+	0.627157i
$605$	3.51978	−	15.4212i	0.143100	−	0.626960i
$606$		0			0
$607$		−	27.4582i		−	1.11449i	−0.830347	−	0.557247i	$-0.811858\pi$
$607$		−	27.4582i		−	1.11449i	0.830347	−	0.557247i	$-0.188142\pi$
$608$	−1.22786	+	5.37960i	−0.0497963	+	0.218172i
$609$		0			0
$610$	−22.5500	−	98.7979i	−0.913022	−	4.00021i
$611$	−20.9176	+	4.77429i	−0.846234	+	0.193147i
$612$		0			0
$613$	−24.1730	−	30.3120i	−0.976340	−	1.22429i	−0.974522	−	0.224293i	$-0.927993\pi$
$613$	−24.1730	−	30.3120i	−0.976340	−	1.22429i	−0.00181824	−	0.999998i	$-0.500579\pi$
$614$	9.57128	+	41.9345i	0.386266	+	1.69234i
$615$		0			0
$616$	−4.33746	−	58.2019i	−0.174761	−	2.34502i
$617$	−1.98842	−	0.453844i	−0.0800508	−	0.0182711i	0.182308	−	0.983241i	$-0.441643\pi$
$617$	−1.98842	−	0.453844i	−0.0800508	−	0.0182711i	−0.262359	+	0.964970i	$0.584500\pi$
$618$		0			0
$619$			0.0855953i			0.00344037i	0.999999	+	0.00172018i	$0.000547552\pi$
$619$			0.0855953i			0.00344037i	−0.999999	+	0.00172018i	$0.999452\pi$
$620$	−134.942	−	30.7997i	−5.41941	−	1.23695i
$621$		0			0
$622$	69.7454	−	55.6201i	2.79653	−	2.23016i
$623$	−42.1699	+	12.9886i	−1.68950	+	0.520378i
$624$		0			0
$625$	6.44971	−	28.2580i	0.257988	−	1.13032i
$626$	38.5846	−	48.3835i	1.54215	−	1.93380i
$627$		0			0
$628$	−33.9158	+	27.0470i	−1.35339	+	1.07929i
$629$	27.5939	+	13.2885i	1.10024	+	0.529849i
$630$		0			0
$631$	−35.7609	+	17.2216i	−1.42362	+	0.685580i	−0.977800	−	0.209543i	$-0.932803\pi$
$631$	−35.7609	+	17.2216i	−1.42362	+	0.685580i	−0.445821	+	0.895122i	$0.647088\pi$
$632$	34.2646	−	71.1513i	1.36297	−	2.83025i
$633$		0			0
$634$	−57.3679	−	27.6269i	−2.27837	−	1.09721i
$635$	−3.04154	+	3.81397i	−0.120700	+	0.151353i
$636$		0			0
$637$	−2.56718	−	17.1281i	−0.101715	−	0.678640i
$638$			17.6326i			0.698081i
$639$		0			0
$640$	−41.9217	+	87.0514i	−1.65710	+	3.44101i
$641$	−38.8795	+	8.87399i	−1.53565	+	0.350501i	−0.904947	−	0.425525i	$-0.860089\pi$
$641$	−38.8795	+	8.87399i	−1.53565	+	0.350501i	−0.630700	+	0.776027i	$0.717232\pi$
$642$		0			0
$643$	6.45301	+	13.3998i	0.254482	+	0.528437i	0.988597	−	0.150588i	$-0.0481168\pi$
$643$	6.45301	+	13.3998i	0.254482	+	0.528437i	−0.734115	+	0.679026i	$0.762403\pi$
$644$	118.326	−	8.81817i	4.66270	−	0.347484i
$645$		0			0
$646$	2.37475	+	2.97784i	0.0934332	+	0.117161i
$647$	−9.84255	+	4.73992i	−0.386951	+	0.186346i	−0.617237	−	0.786777i	$-0.711748\pi$
$647$	−9.84255	+	4.73992i	−0.386951	+	0.186346i	0.230286	+	0.973123i	$0.426034\pi$
$648$		0			0
$649$	−14.5881	−	3.32963i	−0.572632	−	0.130699i
$650$	16.7959	−	21.0614i	0.658791	−	0.826098i
$651$		0			0
$652$	6.57227	+	8.24137i	0.257390	+	0.322757i
$653$	13.3105	+	27.6396i	0.520881	+	1.08162i	0.981044	+	0.193786i	$0.0620769\pi$
$653$	13.3105	+	27.6396i	0.520881	+	1.08162i	−0.460162	+	0.887835i	$0.652209\pi$
$654$		0			0
$655$	16.7124			0.653009
$656$	13.6652			0.533538
$657$		0			0
$658$	−9.32134	+	61.6702i	−0.363384	+	2.40416i
$659$	34.5048	−	7.87550i	1.34412	−	0.306786i	0.510857	−	0.859666i	$-0.329328\pi$
$659$	34.5048	−	7.87550i	1.34412	−	0.306786i	0.833261	+	0.552880i	$0.186471\pi$
$660$		0			0
$661$	−15.9364	+	12.7089i	−0.619856	+	0.494319i	−0.882337	−	0.470619i	$-0.844031\pi$
$661$	−15.9364	+	12.7089i	−0.619856	+	0.494319i	0.262481	+	0.964937i	$0.415459\pi$
$662$	−26.9529	+	21.4943i	−1.04756	+	0.835398i
$663$		0			0
$664$	10.1060	−	2.30662i	0.392188	−	0.0895144i
$665$	−1.46211	−	1.57709i	−0.0566982	−	0.0611568i
$666$		0			0
$667$	−22.5465			−0.873005
$668$	4.32244			0.167240
$669$		0			0
$670$	32.5176	+	67.5235i	1.25626	+	2.60866i
$671$	−18.5382	−	23.2462i	−0.715660	−	0.897409i
$672$		0			0
$673$	−16.9857	+	21.2993i	−0.654749	+	0.821030i	−0.992760	−	0.120113i	$-0.961674\pi$
$673$	−16.9857	+	21.2993i	−0.654749	+	0.821030i	0.338011	+	0.941142i	$0.390246\pi$
$674$	−10.1008	−	2.30545i	−0.389069	−	0.0888025i
$675$		0			0
$676$	33.4040	−	16.0865i	1.28477	−	0.618712i
$677$	−3.58349	−	4.49355i	−0.137725	−	0.172701i	0.708186	−	0.706026i	$-0.249514\pi$
$677$	−3.58349	−	4.49355i	−0.137725	−	0.172701i	−0.845911	+	0.533325i	$0.820942\pi$
$678$		0			0
$679$	−4.27658	−	1.68047i	−0.164120	−	0.0644906i
$680$	62.0684	+	128.886i	2.38021	+	4.94256i
$681$		0			0
$682$	−54.2828	+	12.3897i	−2.07860	+	0.474426i
$683$	8.42918	−	17.5034i	0.322533	−	0.669748i	−0.675157	−	0.737674i	$-0.735924\pi$
$683$	8.42918	−	17.5034i	0.322533	−	0.669748i	0.997690	+	0.0679266i	$0.0216384\pi$
$684$		0			0
$685$		−	40.7323i		−	1.55630i
$686$	−49.0710	−	11.2641i	−1.87354	−	0.430066i
$687$		0			0
$688$	−53.1074	+	66.5946i	−2.02470	+	2.53890i
$689$	3.17882	+	1.53084i	0.121103	+	0.0583202i
$690$		0			0
$691$	6.06239	−	12.5887i	0.230624	−	0.478896i	−0.753255	−	0.657728i	$-0.771518\pi$
$691$	6.06239	−	12.5887i	0.230624	−	0.478896i	0.983880	+	0.178832i	$0.0572319\pi$
$692$	69.5989	−	33.5171i	2.64575	−	1.27413i
$693$		0			0
$694$	−10.9508	−	5.27362i	−0.415686	−	0.200184i
$695$	29.5242	−	23.5448i	1.11992	−	0.893105i
$696$		0			0
$697$	3.08744	−	3.87153i	0.116945	−	0.146645i
$698$	−9.64908	+	42.2754i	−0.365223	+	1.60015i
$699$		0			0
$700$	−28.5381	−	49.4767i	−1.07864	−	1.87004i
$701$	−8.87667	+	7.07890i	−0.335267	+	0.267367i	−0.776623	−	0.629966i	$-0.783069\pi$
$701$	−8.87667	+	7.07890i	−0.335267	+	0.267367i	0.441356	+	0.897332i	$0.354498\pi$
$702$		0			0
$703$	1.56365	+	0.356894i	0.0589743	+	0.0134605i
$704$			64.2202i			2.42039i
$705$		0			0
$706$	−38.5851	−	8.80680i	−1.45217	−	0.331448i
$707$	−12.9671	+	12.0218i	−0.487679	+	0.452125i
$708$		0			0
$709$	−3.84875	−	16.8625i	−0.144543	−	0.633284i	−0.994346	−	0.106184i	$-0.966137\pi$
$709$	−3.84875	−	16.8625i	−0.144543	−	0.633284i	0.849803	−	0.527100i	$-0.176721\pi$
$710$	−17.9404	−	22.4965i	−0.673290	−	0.844279i
$711$		0			0
$712$	149.852	−	34.2027i	5.61594	−	1.28180i
$713$	−15.8425	−	69.4106i	−0.593307	−	2.59945i
$714$		0			0
$715$	3.95445	−	17.3256i	0.147888	−	0.647939i
$716$		−	27.1844i		−	1.01593i
$717$		0			0
$718$	2.26046	−	9.90371i	0.0843595	−	0.369603i
$719$	6.23567	−	3.00294i	0.232551	−	0.111991i	−0.313980	−	0.949430i	$-0.601662\pi$
$719$	6.23567	−	3.00294i	0.232551	−	0.111991i	0.546531	+	0.837439i	$0.315948\pi$
$720$		0			0
$721$	0.423343	+	0.456633i	0.0157661	+	0.0170059i
$722$	−40.2267	−	32.0798i	−1.49708	−	1.19389i
$723$		0			0
$724$	22.8793	+	18.2457i	0.850303	+	0.678094i
$725$	4.70909	+	9.77852i	0.174891	+	0.363165i
$726$		0			0
$727$	−1.33244	+	2.76683i	−0.0494173	+	0.102616i	−0.924215	−	0.381872i	$-0.875280\pi$
$727$	−1.33244	+	2.76683i	−0.0494173	+	0.102616i	0.874798	+	0.484488i	$0.160994\pi$
$728$	4.48369	+	60.1641i	0.166177	+	2.22983i
$729$		0			0
$730$	61.9160	+	29.8172i	2.29161	+	1.10358i
$731$	6.86831	+	30.0920i	0.254034	+	1.11299i
$732$		0			0
$733$	−35.6911	−	28.4627i	−1.31828	−	1.05129i	−0.994453	−	0.105177i	$-0.966459\pi$
$733$	−35.6911	−	28.4627i	−1.31828	−	1.05129i	−0.323827	−	0.946116i	$-0.604970\pi$
$734$	−29.7819			−1.09927
$735$		0			0
$736$	−169.490			−6.24748
$737$	17.1918	+	13.7100i	0.633268	+	0.505015i
$738$		0			0
$739$	2.36098	+	10.3441i	0.0868502	+	0.380515i	0.999608	−	0.0279849i	$-0.00890902\pi$
$739$	2.36098	+	10.3441i	0.0868502	+	0.380515i	−0.912758	+	0.408500i	$0.866052\pi$
$740$	86.2911	+	41.5556i	3.17212	+	1.52761i
$741$		0			0
$742$	7.52140	−	6.97306i	0.276119	−	0.255989i
$743$	13.5006	−	28.0342i	0.495287	−	1.02847i	−0.492157	−	0.870506i	$-0.663791\pi$
$743$	13.5006	−	28.0342i	0.495287	−	1.02847i	0.987444	−	0.157968i	$-0.0504943\pi$
$744$		0			0
$745$	22.9816	+	47.7218i	0.841980	+	1.74839i
$746$	−68.3889	−	54.5383i	−2.50389	−	1.99679i
$747$		0			0
$748$	52.1738	+	41.6072i	1.90766	+	1.52131i
$749$	7.93989	+	25.7783i	0.290117	+	0.941918i
$750$		0			0
$751$	−21.0103	+	10.1180i	−0.766677	+	0.369212i	−0.775991	−	0.630744i	$-0.782750\pi$
$751$	−21.0103	+	10.1180i	−0.766677	+	0.369212i	0.00931362	+	0.999957i	$0.497035\pi$
$752$	27.5435	−	120.676i	1.00441	−	4.40060i
$753$		0			0
$754$		−	18.2270i		−	0.663789i
$755$	−4.40079	+	19.2811i	−0.160161	+	0.701711i
$756$		0			0
$757$	−7.20955	−	31.5871i	−0.262036	−	1.14805i	−0.919039	−	0.394166i	$-0.871034\pi$
$757$	−7.20955	−	31.5871i	−0.262036	−	1.14805i	0.657004	−	0.753887i	$-0.271824\pi$
$758$	9.21755	−	2.10385i	0.334797	−	0.0764152i
$759$		0			0
$760$	4.67079	+	5.85699i	0.169427	+	0.212455i
$761$	0.723345	+	3.16918i	0.0262212	+	0.114883i	0.986345	−	0.164693i	$-0.0526633\pi$
$761$	0.723345	+	3.16918i	0.0262212	+	0.114883i	−0.960124	+	0.279576i	$0.909806\pi$
$762$		0			0
$763$	4.02956	+	6.98606i	0.145880	+	0.252912i
$764$	−115.797	−	26.4299i	−4.18939	−	0.956201i
$765$		0			0
$766$			66.0535i			2.38661i
$767$	15.0799	+	3.44188i	0.544502	+	0.124279i
$768$		0			0
$769$	0.571663	−	0.455886i	0.0206147	−	0.0164397i	−0.613128	−	0.789983i	$-0.710089\pi$
$769$	0.571663	−	0.455886i	0.0206147	−	0.0164397i	0.633743	+	0.773544i	$0.281518\pi$
$770$	−42.6717	−	29.1189i	−1.53778	−	1.04937i
$771$		0			0
$772$	−12.6010	+	55.2085i	−0.453519	+	1.98700i
$773$	4.27724	−	5.36348i	0.153841	−	0.192911i	−0.698938	−	0.715182i	$-0.746344\pi$
$773$	4.27724	−	5.36348i	0.153841	−	0.192911i	0.852779	+	0.522271i	$0.174915\pi$
$774$		0			0
$775$	−26.7948	+	21.3681i	−0.962497	+	0.767566i
$776$	14.4209	+	6.94474i	0.517680	+	0.249302i
$777$		0			0
$778$	−62.7100	+	30.1996i	−2.24826	+	1.08271i
$779$	0.112514	−	0.233638i	0.00403124	−	0.00837095i
$780$		0			0
$781$	−7.60633	−	3.66302i	−0.272176	−	0.131073i
$782$	−72.9429	+	91.4675i	−2.60843	+	3.27087i
$783$		0			0
$784$	95.4544	+	29.5301i	3.40909	+	1.05465i
$785$			24.1505i			0.861970i
$786$		0			0
$787$	2.23077	−	4.63224i	0.0795183	−	0.165121i	−0.857419	−	0.514619i	$-0.827933\pi$
$787$	2.23077	−	4.63224i	0.0795183	−	0.165121i	0.936937	+	0.349497i	$0.113648\pi$
$788$	−12.8954	+	2.94329i	−0.459379	+	0.104850i
$789$		0			0
$790$	−30.3293	−	62.9795i	−1.07907	−	2.24071i
$791$	−7.57134	−	24.5817i	−0.269206	−	0.874026i
$792$		0			0
$793$	19.1632	+	24.0299i	0.680504	+	0.853325i
$794$	2.06960	−	0.996668i	0.0734474	−	0.0353704i
$795$		0			0
$796$	110.740	+	25.2758i	3.92509	+	0.895877i
$797$	12.5307	−	15.7130i	0.443860	−	0.556583i	−0.508696	−	0.860946i	$-0.669872\pi$
$797$	12.5307	−	15.7130i	0.443860	−	0.556583i	0.952556	+	0.304363i	$0.0984436\pi$
$798$		0			0
$799$	−27.9660	−	35.0682i	−0.989365	−	1.24062i
$800$	35.3998	+	73.5084i	1.25157	+	2.59891i
$801$		0			0
$802$	26.4007			0.932240
$803$	20.1631			0.711539
$804$		0			0
$805$	37.2339	−	54.5637i	1.31232	−	1.92312i
$806$	56.1128	−	12.8074i	1.97649	−	0.451121i
$807$		0			0
$808$	48.1573	−	38.4042i	1.69417	−	1.35105i
$809$	38.3206	−	30.5596i	1.34728	−	1.07442i	0.357183	−	0.934034i	$-0.383737\pi$
$809$	38.3206	−	30.5596i	1.34728	−	1.07442i	0.990097	−	0.140385i	$-0.0448341\pi$
$810$		0			0
$811$	−52.1786	+	11.9094i	−1.83224	+	0.418197i	−0.992234	−	0.124383i	$-0.960305\pi$
$811$	−52.1786	+	11.9094i	−1.83224	+	0.418197i	−0.840004	+	0.542580i	$0.817448\pi$
$812$	−35.9689	−	14.1339i	−1.26226	−	0.496003i
$813$		0			0
$814$	38.5275			1.35039
$815$	5.86846			0.205563
$816$		0			0
$817$	0.701320	+	1.45631i	0.0245361	+	0.0509497i
$818$	8.93129	+	11.1995i	0.312275	+	0.391581i
$819$		0			0
$820$	9.65498	−	12.1070i	0.337166	−	0.422793i
$821$	−9.97604	−	2.27697i	−0.348166	−	0.0794667i	0.0448617	−	0.998993i	$-0.485715\pi$
$821$	−9.97604	−	2.27697i	−0.348166	−	0.0794667i	−0.393028	+	0.919527i	$0.628572\pi$
$822$		0			0
$823$	−33.8755	+	16.3136i	−1.18083	+	0.568656i	−0.918152	−	0.396228i	$-0.870319\pi$
$823$	−33.8755	+	16.3136i	−1.18083	+	0.568656i	−0.262675	+	0.964884i	$0.584605\pi$
$824$	−1.35239	−	1.69584i	−0.0471128	−	0.0590776i
$825$		0			0
$826$	25.3446	−	37.1407i	0.881851	−	1.29229i
$827$	−0.758739	−	1.57554i	−0.0263840	−	0.0547868i	0.887360	−	0.461077i	$-0.152537\pi$
$827$	−0.758739	−	1.57554i	−0.0263840	−	0.0547868i	−0.913744	+	0.406290i	$0.866822\pi$
$828$		0			0
$829$	−2.89167	+	0.660004i	−0.100432	+	0.0229229i	−0.272441	−	0.962172i	$-0.587831\pi$
$829$	−2.89167	+	0.660004i	−0.100432	+	0.0229229i	0.172010	+	0.985095i	$0.444974\pi$
$830$	3.98103	−	8.26670i	0.138184	−	0.286941i
$831$		0			0
$832$		−	66.3853i		−	2.30149i
$833$	29.9327	−	20.3716i	1.03711	−	0.705833i
$834$		0			0
$835$	1.50036	−	1.88140i	0.0519222	−	0.0651084i
$836$	3.14857	+	1.51627i	0.108896	+	0.0524413i
$837$		0			0
$838$	−34.7516	+	72.1624i	−1.20047	+	2.49281i
$839$	−2.99822	+	1.44387i	−0.103510	+	0.0498478i	−0.484922	−	0.874557i	$-0.661152\pi$
$839$	−2.99822	+	1.44387i	−0.103510	+	0.0498478i	0.381412	+	0.924405i	$0.375438\pi$
$840$		0			0
$841$	−19.5118	−	9.39640i	−0.672821	−	0.324014i
$842$	26.0268	−	20.7557i	0.896942	−	0.715287i
$843$		0			0
$844$	71.6542	−	89.8515i	2.46644	−	3.09282i
$845$	4.59301	−	20.1233i	0.158004	−	0.692262i
$846$		0			0
$847$	13.7894	+	2.08424i	0.473809	+	0.0716154i
$848$	−15.9140	+	12.6910i	−0.546488	+	0.435809i
$849$		0			0
$850$	54.9047	+	12.5317i	1.88322	+	0.429832i
$851$			49.2645i			1.68876i
$852$		0			0
$853$	27.7615	+	6.33638i	0.950535	+	0.216953i	0.669557	−	0.742761i	$-0.266484\pi$
$853$	27.7615	+	6.33638i	0.950535	+	0.216953i	0.280978	+	0.959714i	$0.409341\pi$
$854$	85.3885	−	26.3003i	2.92193	−	0.899976i
$855$		0			0
$856$	−20.9080	−	91.6039i	−0.714621	−	3.13096i
$857$	8.27911	+	10.3817i	0.282809	+	0.354631i	0.902863	−	0.429927i	$-0.141461\pi$
$857$	8.27911	+	10.3817i	0.282809	+	0.354631i	−0.620054	+	0.784559i	$0.712889\pi$
$858$		0			0
$859$	−10.1480	+	2.31622i	−0.346246	+	0.0790283i	−0.392107	−	0.919919i	$-0.628254\pi$
$859$	−10.1480	+	2.31622i	−0.346246	+	0.0790283i	0.0458616	+	0.998948i	$0.485397\pi$
$860$	21.4784	+	94.1030i	0.732407	+	3.20889i
$861$		0			0
$862$	−12.0659	+	52.8640i	−0.410965	+	1.80056i
$863$		−	18.1624i		−	0.618255i	−0.951021	−	0.309128i	$-0.899963\pi$
$863$		−	18.1624i		−	0.618255i	0.951021	−	0.309128i	$-0.100037\pi$
$864$		0			0
$865$	9.56977	−	41.9279i	0.325382	−	1.42559i
$866$	30.4390	−	14.6587i	1.03436	−	0.498122i
$867$		0			0
$868$	18.2381	−	120.663i	0.619040	−	4.09559i
$869$	−16.0349	−	12.7874i	−0.543946	−	0.433783i
$870$		0			0
$871$	−17.7714	−	14.1722i	−0.602160	−	0.480207i
$872$	−12.1893	−	25.3113i	−0.412781	−	0.857149i
$873$		0			0
$874$	−2.65822	+	5.51986i	−0.0899157	+	0.186712i
$875$	7.81045	+	1.18053i	0.264041	+	0.0399093i
$876$		0			0
$877$	−39.2871	−	18.9197i	−1.32663	−	0.638871i	−0.369690	−	0.929155i	$-0.620536\pi$
$877$	−39.2871	−	18.9197i	−1.32663	−	0.638871i	−0.956941	+	0.290284i	$0.906250\pi$
$878$	−16.6047	−	72.7499i	−0.560381	−	2.45519i
$879$		0			0
$880$	80.1563	+	63.9225i	2.70207	+	2.15483i
$881$	−2.08391			−0.0702089			−0.0351044	−	0.999384i	$-0.511176\pi$
$881$	−2.08391			−0.0702089			−0.0351044	+	0.999384i	$0.511176\pi$
$882$		0			0
$883$	−13.8180			−0.465013			−0.232506	−	0.972595i	$-0.574693\pi$
$883$	−13.8180			−0.465013			−0.232506	+	0.972595i	$0.574693\pi$
$884$	−53.9327	−	43.0099i	−1.81395	−	1.44658i
$885$		0			0
$886$	−13.8501	−	60.6812i	−0.465303	−	2.03862i
$887$	1.78898	+	0.861525i	0.0600679	+	0.0289272i	0.463677	−	0.886005i	$-0.346530\pi$
$887$	1.78898	+	0.861525i	0.0600679	+	0.0289272i	−0.403609	+	0.914932i	$0.632244\pi$
$888$		0			0
$889$	−3.55266	−	2.42431i	−0.119152	−	0.0813087i
$890$	59.0310	−	122.579i	1.97872	−	4.10886i
$891$		0			0
$892$	−13.7478	−	28.5476i	−0.460311	−	0.955846i
$893$	−1.83645	−	1.46452i	−0.0614543	−	0.0490082i
$894$		0			0
$895$	−11.8324	−	9.43599i	−0.395512	−	0.315410i
$896$	−79.2851	−	31.1549i	−2.64873	−	1.04081i
$897$		0			0
$898$	29.6282	−	14.2682i	0.988705	−	0.476135i
$899$	−5.15999	+	22.6074i	−0.172095	+	0.753999i
$900$		0			0
$901$			7.37595i			0.245729i
$902$	1.38614	−	6.07308i	0.0461534	−	0.202211i
$903$		0			0
$904$	19.9375	+	87.3519i	0.663112	+	2.90528i
$905$	15.8833	−	3.62526i	0.527978	−	0.120508i
$906$		0			0
$907$	6.37669	+	7.99612i	0.211735	+	0.265507i	0.876346	−	0.481683i	$-0.159974\pi$
$907$	6.37669	+	7.99612i	0.211735	+	0.265507i	−0.664611	+	0.747189i	$0.731403\pi$
$908$	2.05146	+	8.98805i	0.0680802	+	0.298279i
$909$		0			0
$910$	44.1103	+	30.1006i	1.46224	+	0.997824i
$911$	27.5717	+	6.29306i	0.913491	+	0.208498i	0.653336	−	0.757068i	$-0.273369\pi$
$911$	27.5717	+	6.29306i	0.913491	+	0.208498i	0.260155	+	0.965567i	$0.416226\pi$
$912$		0			0
$913$		−	2.69207i		−	0.0890944i
$914$	20.3812	+	4.65187i	0.674150	+	0.153870i
$915$		0			0
$916$	79.5046	−	63.4028i	2.62691	−	2.09489i
$917$	1.09507	+	14.6941i	0.0361623	+	0.485241i
$918$		0			0
$919$	−6.70348	+	29.3699i	−0.221127	+	0.968822i	0.735504	+	0.677521i	$0.236946\pi$
$919$	−6.70348	+	29.3699i	−0.221127	+	0.968822i	−0.956631	+	0.291302i	$0.905912\pi$
$920$	−143.468	+	179.904i	−4.73001	+	5.93125i
$921$		0			0
$922$	22.0882	−	17.6148i	0.727437	−	0.580112i
$923$	7.86276	+	3.78650i	0.258806	+	0.124634i
$924$		0			0
$925$	21.3662	−	10.2894i	0.702516	−	0.338314i
$926$	3.28969	−	6.83112i	0.108106	−	0.224484i
$927$		0			0
$928$	49.7368	+	23.9520i	1.63269	+	0.786262i
$929$	0.330121	−	0.413958i	0.0108309	−	0.0135815i	−0.776387	−	0.630257i	$-0.782950\pi$
$929$	0.330121	−	0.413958i	0.0108309	−	0.0135815i	0.787217	+	0.616676i	$0.211521\pi$
$930$		0			0
$931$	1.29082	−	1.38887i	0.0423049	−	0.0455184i
$932$			34.4262i			1.12767i
$933$		0			0
$934$	28.7740	−	59.7498i	0.941513	−	1.95507i
$935$	36.2201	−	8.26700i	1.18452	−	0.270360i
$936$		0			0
$937$	22.4684	+	46.6560i	0.734010	+	1.52419i	0.847586	+	0.530657i	$0.178055\pi$
$937$	22.4684	+	46.6560i	0.734010	+	1.52419i	−0.113577	+	0.993529i	$0.536231\pi$
$938$	−57.2380	+	33.0149i	−1.86889	+	1.07797i
$939$		0			0
$940$	−87.4545	−	109.664i	−2.85245	−	3.57686i
$941$	−49.3240	+	23.7532i	−1.60791	+	0.774331i	−0.999809	−	0.0195252i	$-0.993785\pi$
$941$	−49.3240	+	23.7532i	−1.60791	+	0.774331i	−0.608106	+	0.793856i	$0.708070\pi$
$942$		0			0
$943$	7.76555	+	1.77244i	0.252881	+	0.0577185i
$944$	−55.6370	+	69.7666i	−1.81083	+	2.27071i
$945$		0			0
$946$	24.2089	+	30.3570i	0.787098	+	0.986990i
$947$	19.0264	+	39.5088i	0.618275	+	1.28386i	0.941332	+	0.337482i	$0.109575\pi$
$947$	19.0264	+	39.5088i	0.618275	+	1.28386i	−0.323056	+	0.946380i	$0.604710\pi$
$948$		0			0
$949$	−20.8428			−0.676586
$950$	2.94918			0.0956841
$951$		0			0
$952$	−109.254	+	63.0175i	−3.54093	+	2.04241i
$953$	−16.9362	+	3.86559i	−0.548619	+	0.125219i	−0.487841	−	0.872933i	$-0.662215\pi$
$953$	−16.9362	+	3.86559i	−0.548619	+	0.125219i	−0.0607779	+	0.998151i	$0.519358\pi$
$954$		0			0
$955$	−51.6983	+	41.2280i	−1.67292	+	1.33411i
$956$	−20.1903	+	16.1012i	−0.653001	+	0.520751i
$957$		0			0
$958$	1.03924	−	0.237199i	0.0335762	−	0.00766354i
$959$	35.8130	−	2.66894i	1.15646	−	0.0861847i
$960$		0			0
$961$	−42.2237			−1.36206
$962$	−39.8263			−1.28405
$963$		0			0
$964$	−35.0483	−	72.7785i	−1.12883	−	2.34404i
$965$	19.6562	+	24.6481i	0.632757	+	0.793452i
$966$		0			0
$967$	−4.52853	+	5.67860i	−0.145628	+	0.182612i	−0.849296	−	0.527918i	$-0.822973\pi$
$967$	−4.52853	+	5.67860i	−0.145628	+	0.182612i	0.703668	+	0.710529i	$0.251544\pi$
$968$	−47.3619	−	10.8100i	−1.52227	−	0.347448i
$969$		0			0
$970$	12.7647	−	6.14713i	0.409848	−	0.197373i
$971$	12.4813	+	15.6510i	0.400543	+	0.502264i	0.940672	−	0.339318i	$-0.110196\pi$
$971$	12.4813	+	15.6510i	0.400543	+	0.502264i	−0.540129	+	0.841582i	$0.681625\pi$
$972$		0			0
$973$	22.6358	+	24.4159i	0.725672	+	0.782736i
$974$	−20.8197	−	43.2326i	−0.667107	−	1.38526i
$975$		0			0
$976$	−172.870	+	39.4565i	−5.53344	+	1.26297i
$977$	−8.13631	+	16.8952i	−0.260304	+	0.540526i	−0.989630	−	0.143640i	$-0.954119\pi$
$977$	−8.13631	+	16.8952i	−0.260304	+	0.540526i	0.729326	+	0.684166i	$0.239834\pi$
$978$		0			0
$979$		−	39.9181i		−	1.27579i
$980$	93.6047	−	63.7054i	2.99009	−	2.03500i
$981$		0			0
$982$	17.3817	−	21.7960i	0.554674	−	0.695539i
$983$	−37.0776	−	17.8556i	−1.18259	−	0.569505i	−0.263925	−	0.964543i	$-0.585017\pi$
$983$	−37.0776	−	17.8556i	−1.18259	−	0.569505i	−0.918665	+	0.395038i	$0.870732\pi$
$984$		0			0
$985$	−3.19502	+	6.63452i	−0.101802	+	0.211393i
$986$	34.3311	−	16.5330i	1.09333	−	0.526518i
$987$		0			0
$988$	−3.25471	−	1.56739i	−0.103546	−	0.0498652i
$989$	−38.8170	+	30.9555i	−1.23431	+	0.984328i
$990$		0			0
$991$	10.5763	−	13.2623i	0.335968	−	0.421290i	−0.584937	−	0.811079i	$-0.698881\pi$
$991$	10.5763	−	13.2623i	0.335968	−	0.421290i	0.920904	+	0.389789i	$0.127452\pi$
$992$	−38.7894	+	169.947i	−1.23156	+	5.39583i
$993$		0			0
$994$	18.6041	−	17.2478i	0.590086	−	0.547066i
$995$	49.4407	−	39.4277i	1.56738	−	1.24994i
$996$		0			0
$997$	38.7310	+	8.84009i	1.22662	+	0.279968i	0.786285	−	0.617864i	$-0.212002\pi$
$997$	38.7310	+	8.84009i	1.22662	+	0.279968i	0.440337	+	0.897833i	$0.354859\pi$
$998$			87.7268i			2.77694i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.251.2	yes	120
3.2	odd	2	inner	441.2.w.a.251.19	yes	120
49.41	odd	14	inner	441.2.w.a.188.19	yes	120
147.41	even	14	inner	441.2.w.a.188.2	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.188.2	✓	120	147.41	even	14	inner
441.2.w.a.188.19	yes	120	49.41	odd	14	inner
441.2.w.a.251.2	yes	120	1.1	even	1	trivial
441.2.w.a.251.19	yes	120	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.12540 - 1.69495i) q^{2} +(1.19944 + 5.25507i) q^{4} +(2.70367 + 1.30202i) q^{5} +(-0.967619 + 2.46246i) q^{7} +(3.99879 - 8.30358i) q^{8} +O(q^{10})\)	\(q+(-2.12540 - 1.69495i) q^{2} +(1.19944 + 5.25507i) q^{4} +(2.70367 + 1.30202i) q^{5} +(-0.967619 + 2.46246i) q^{7} +(3.99879 - 8.30358i) q^{8} +(-3.53953 - 7.34991i) q^{10} +(-1.87132 - 1.49233i) q^{11} +(1.93441 + 1.54264i) q^{13} +(6.23034 - 3.59366i) q^{14} +(-12.8604 + 6.19325i) q^{16} +(-1.15098 + 5.04278i) q^{17} +0.270871i q^{19} +(-3.59932 + 15.7697i) q^{20} +(1.44789 + 6.34361i) q^{22} +(-8.11148 + 1.85139i) q^{23} +(2.49713 + 3.13130i) q^{25} +(-1.49670 - 6.55747i) q^{26} +(-14.1010 - 2.13134i) q^{28} +(2.64195 + 0.603008i) q^{29} +8.55709i q^{31} +(19.8604 + 4.53301i) q^{32} +(10.9936 - 8.76709i) q^{34} +(-5.82229 + 5.39782i) q^{35} +(1.31758 - 5.77270i) q^{37} +(0.459113 - 0.575710i) q^{38} +(21.6228 - 17.2436i) q^{40} +(-0.862545 - 0.415380i) q^{41} +(5.37639 - 2.58913i) q^{43} +(5.59777 - 11.6239i) q^{44} +(20.3782 + 9.81363i) q^{46} +(-5.40670 + 6.77979i) q^{47} +(-5.12743 - 4.76545i) q^{49} -10.8878i q^{50} +(-5.78648 + 12.0158i) q^{52} +(1.39025 - 0.317315i) q^{53} +(-3.11640 - 6.47127i) q^{55} +(16.5779 + 17.8816i) q^{56} +(-4.59314 - 5.75962i) q^{58} +(5.63248 - 2.71246i) q^{59} +(12.1109 + 2.76423i) q^{61} +(14.5039 - 18.1873i) q^{62} +(-16.7288 - 20.9773i) q^{64} +(3.22146 + 6.68943i) q^{65} -9.18698 q^{67} -27.8807 q^{68} +(21.5238 - 1.60405i) q^{70} +(3.43876 - 0.784875i) q^{71} +(-6.58618 + 5.25231i) q^{73} +(-12.5848 + 10.0361i) q^{74} +(-1.42344 + 0.324892i) q^{76} +(5.48553 - 3.16405i) q^{77} +8.56875 q^{79} -42.8340 q^{80} +(1.12921 + 2.34483i) q^{82} +(0.701261 + 0.879353i) q^{83} +(-9.67767 + 12.1354i) q^{85} +(-15.8155 - 3.60978i) q^{86} +(-19.8747 + 9.57116i) q^{88} +(10.3983 + 13.0391i) q^{89} +(-5.67046 + 3.27072i) q^{91} +(-19.4584 - 40.4058i) q^{92} +(22.9829 - 5.24569i) q^{94} +(-0.352678 + 0.732344i) q^{95} +1.73671i q^{97} +(2.82065 + 18.8193i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 120 * q + 24 * q^4	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

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