LMFDB - Embedded newform 441.2.w.a.377.19

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			377.19
Character	$\chi$	$=$	441.377
Dual form			441.2.w.a.62.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.41221 + 0.550570i) q^{2} +(3.71367 + 1.78841i) q^{4} +(0.289860 - 0.363473i) q^{5} +(1.34601 - 2.27777i) q^{7} +(4.10462 + 3.27333i) q^{8} +O(q^{10})$	\(q+(2.41221 + 0.550570i) q^{2} +(3.71367 + 1.78841i) q^{4} +(0.289860 - 0.363473i) q^{5} +(1.34601 - 2.27777i) q^{7} +(4.10462 + 3.27333i) q^{8} +(0.899319 - 0.717183i) q^{10} +(0.267404 + 0.0610333i) q^{11} +(-3.38129 - 0.771758i) q^{13} +(4.50093 - 4.75339i) q^{14} +(2.95912 + 3.71062i) q^{16} +(-5.26026 + 2.53321i) q^{17} +3.10999i q^{19} +(1.72648 - 0.831431i) q^{20} +(0.611431 + 0.294450i) q^{22} +(-1.44944 + 3.00980i) q^{23} +(1.06451 + 4.66393i) q^{25} +(-7.73147 - 3.72328i) q^{26} +(9.07224 - 6.05169i) q^{28} +(1.84788 + 3.83716i) q^{29} -5.99695i q^{31} +(0.539260 + 1.11978i) q^{32} +(-14.0835 + 3.21448i) q^{34} +(-0.437754 - 1.14947i) q^{35} +(6.82215 - 3.28537i) q^{37} +(-1.71227 + 7.50194i) q^{38} +(2.37953 - 0.543112i) q^{40} +(1.56785 - 1.96602i) q^{41} +(-6.94691 - 8.71115i) q^{43} +(0.883900 + 0.704887i) q^{44} +(-5.15346 + 6.46224i) q^{46} +(-0.939237 + 4.11506i) q^{47} +(-3.37651 - 6.13182i) q^{49} +11.8364i q^{50} +(-11.1768 - 8.91320i) q^{52} +(-3.56861 + 7.41029i) q^{53} +(0.0996937 - 0.0795031i) q^{55} +(12.9808 - 4.94347i) q^{56} +(2.34484 + 10.2734i) q^{58} +(-1.06936 - 1.34094i) q^{59} +(-4.69592 - 9.75118i) q^{61} +(3.30174 - 14.4659i) q^{62} +(-1.42791 - 6.25608i) q^{64} +(-1.26061 + 1.00531i) q^{65} +4.14761 q^{67} -24.0653 q^{68} +(-0.423088 - 3.01378i) q^{70} +(-0.978461 + 2.03180i) q^{71} +(4.20001 - 0.958624i) q^{73} +(18.2653 - 4.16893i) q^{74} +(-5.56194 + 11.5495i) q^{76} +(0.498949 - 0.526935i) q^{77} +12.9042 q^{79} +2.20644 q^{80} +(4.86442 - 3.87924i) q^{82} +(3.33893 + 14.6288i) q^{83} +(-0.603986 + 2.64624i) q^{85} +(-11.9613 - 24.8378i) q^{86} +(0.897813 + 1.12582i) q^{88} +(-3.71116 - 16.2597i) q^{89} +(-6.30915 + 6.66303i) q^{91} +(-10.7655 + 8.58522i) q^{92} +(-4.53127 + 9.40927i) q^{94} +(1.13040 + 0.901461i) q^{95} +12.6849i q^{97} +(-4.76884 - 16.6502i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{14}\right)$	$-1$

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 $

$2$	2.41221	+	0.550570i	1.70569	+	0.389312i	0.960661	−	0.277723i	$-0.0895797\pi$
$2$	2.41221	+	0.550570i	1.70569	+	0.389312i	0.745026	+	0.667035i	$0.232437\pi$
$3$		0			0
$3$		0			0
$4$	3.71367	+	1.78841i	1.85684	+	0.894206i
$5$	0.289860	−	0.363473i	0.129629	−	0.162550i	−0.712781	−	0.701387i	$-0.752565\pi$
$5$	0.289860	−	0.363473i	0.129629	−	0.162550i	0.842410	+	0.538837i	$0.181136\pi$
$6$		0			0
$7$	1.34601	−	2.27777i	0.508744	−	0.860918i
$7$	1.34601	−	2.27777i	0.508744	−	0.860918i
$8$	4.10462	+	3.27333i	1.45120	+	1.15730i
$9$		0			0
$10$	0.899319	−	0.717183i	0.284390	−	0.226793i
$11$	0.267404	+	0.0610333i	0.0806255	+	0.0184022i	0.262643	−	0.964893i	$-0.415406\pi$
$11$	0.267404	+	0.0610333i	0.0806255	+	0.0184022i	−0.182018	+	0.983295i	$0.558263\pi$
$12$		0			0
$13$	−3.38129	−	0.771758i	−0.937802	−	0.214047i	−0.273807	−	0.961785i	$-0.588283\pi$
$13$	−3.38129	−	0.771758i	−0.937802	−	0.214047i	−0.663995	+	0.747737i	$0.731140\pi$
$14$	4.50093	−	4.75339i	1.20292	−	1.27040i
$15$		0			0
$16$	2.95912	+	3.71062i	0.739780	+	0.927654i
$17$	−5.26026	+	2.53321i	−1.27580	+	0.614393i	−0.944308	−	0.329064i	$-0.893267\pi$
$17$	−5.26026	+	2.53321i	−1.27580	+	0.614393i	−0.331494	+	0.943457i	$0.607553\pi$
$18$		0			0
$19$			3.10999i			0.713481i	0.934204	+	0.356740i	$0.116112\pi$
$19$			3.10999i			0.713481i	−0.934204	+	0.356740i	$0.883888\pi$
$20$	1.72648	−	0.831431i	0.386053	−	0.185914i
$21$		0			0
$22$	0.611431	+	0.294450i	0.130358	+	0.0627769i
$23$	−1.44944	+	3.00980i	−0.302230	+	0.627587i	−0.995673	−	0.0929245i	$-0.970378\pi$
$23$	−1.44944	+	3.00980i	−0.302230	+	0.627587i	0.693443	+	0.720511i	$0.256093\pi$
$24$		0			0
$25$	1.06451	+	4.66393i	0.212902	+	0.932785i
$26$	−7.73147	−	3.72328i	−1.51627	−	0.730195i
$27$		0			0
$28$	9.07224	−	6.05169i	1.71449	−	1.14366i
$29$	1.84788	+	3.83716i	0.343142	+	0.712542i	0.999107	−	0.0422494i	$-0.0134524\pi$
$29$	1.84788	+	3.83716i	0.343142	+	0.712542i	−0.655965	+	0.754791i	$0.727738\pi$
$30$		0			0
$31$		−	5.99695i		−	1.07708i	−0.842599	−	0.538542i	$-0.818975\pi$
$31$		−	5.99695i		−	1.07708i	0.842599	−	0.538542i	$-0.181025\pi$
$32$	0.539260	+	1.11978i	0.0953286	+	0.197952i
$33$		0			0
$34$	−14.0835	+	3.21448i	−2.41531	+	0.551278i
$35$	−0.437754	−	1.14947i	−0.0739940	−	0.194296i
$36$		0			0
$37$	6.82215	−	3.28537i	1.12155	−	0.540112i	0.221182	−	0.975233i	$-0.429009\pi$
$37$	6.82215	−	3.28537i	1.12155	−	0.540112i	0.900372	+	0.435121i	$0.143294\pi$
$38$	−1.71227	+	7.50194i	−0.277767	+	1.21698i
$39$		0			0
$40$	2.37953	−	0.543112i	0.376237	−	0.0858736i
$41$	1.56785	−	1.96602i	0.244857	−	0.307041i	−0.644182	−	0.764872i	$-0.722802\pi$
$41$	1.56785	−	1.96602i	0.244857	−	0.307041i	0.889039	+	0.457831i	$0.151373\pi$
$42$		0			0
$43$	−6.94691	−	8.71115i	−1.05939	−	1.32844i	−0.942097	−	0.335340i	$-0.891149\pi$
$43$	−6.94691	−	8.71115i	−1.05939	−	1.32844i	−0.117296	−	0.993097i	$-0.537423\pi$
$44$	0.883900	+	0.704887i	0.133253	+	0.106266i
$45$		0			0
$46$	−5.15346	+	6.46224i	−0.759837	+	0.952805i
$47$	−0.939237	+	4.11506i	−0.137002	+	0.600244i	0.859083	+	0.511837i	$0.171035\pi$
$47$	−0.939237	+	4.11506i	−0.137002	+	0.600244i	−0.996084	+	0.0884071i	$0.971822\pi$
$48$		0			0
$49$	−3.37651	−	6.13182i	−0.482359	−	0.875974i
$50$			11.8364i			1.67393i
$51$		0			0
$52$	−11.1768	−	8.91320i	−1.54994	−	1.23604i
$53$	−3.56861	+	7.41029i	−0.490186	+	1.01788i	0.498362	+	0.866969i	$0.333935\pi$
$53$	−3.56861	+	7.41029i	−0.490186	+	1.01788i	−0.988547	+	0.150912i	$0.951779\pi$
$54$		0			0
$55$	0.0996937	−	0.0795031i	0.0134427	−	0.0107202i
$56$	12.9808	−	4.94347i	1.73463	−	0.660599i
$57$		0			0
$58$	2.34484	+	10.2734i	0.307892	+	1.34896i
$59$	−1.06936	−	1.34094i	−0.139219	−	0.174575i	0.707334	−	0.706880i	$-0.249898\pi$
$59$	−1.06936	−	1.34094i	−0.139219	−	0.174575i	−0.846553	+	0.532304i	$0.821326\pi$
$60$		0			0
$61$	−4.69592	−	9.75118i	−0.601251	−	1.24851i	−0.950279	−	0.311399i	$-0.899202\pi$
$61$	−4.69592	−	9.75118i	−0.601251	−	1.24851i	0.349028	−	0.937112i	$-0.386512\pi$
$62$	3.30174	−	14.4659i	0.419322	−	1.83717i
$63$		0			0
$64$	−1.42791	−	6.25608i	−0.178489	−	0.782010i
$65$	−1.26061	+	1.00531i	−0.156360	+	0.124693i
$66$		0			0
$67$	4.14761			0.506711			0.253355	−	0.967373i	$-0.418466\pi$
$67$	4.14761			0.506711			0.253355	+	0.967373i	$0.418466\pi$
$68$	−24.0653			−2.91835
$69$		0			0
$70$	−0.423088	−	3.01378i	−0.0505687	−	0.360216i
$71$	−0.978461	+	2.03180i	−0.116122	+	0.241130i	−0.950927	−	0.309417i	$-0.899866\pi$
$71$	−0.978461	+	2.03180i	−0.116122	+	0.241130i	0.834805	+	0.550546i	$0.185581\pi$
$72$		0			0
$73$	4.20001	−	0.958624i	0.491573	−	0.112198i	0.0304534	−	0.999536i	$-0.490305\pi$
$73$	4.20001	−	0.958624i	0.491573	−	0.112198i	0.461120	+	0.887338i	$0.347448\pi$
$74$	18.2653	−	4.16893i	2.12329	−	0.484628i
$75$		0			0
$76$	−5.56194	+	11.5495i	−0.637999	+	1.32482i
$77$	0.498949	−	0.526935i	0.0568605	−	0.0600499i
$78$		0			0
$79$	12.9042			1.45184			0.725918	−	0.687781i	$-0.241415\pi$
$79$	12.9042			1.45184			0.725918	+	0.687781i	$0.241415\pi$
$80$	2.20644			0.246687
$81$		0			0
$82$	4.86442	−	3.87924i	0.537185	−	0.428391i
$83$	3.33893	+	14.6288i	0.366495	+	1.60572i	0.736330	+	0.676623i	$0.236557\pi$
$83$	3.33893	+	14.6288i	0.366495	+	1.60572i	−0.369835	+	0.929098i	$0.620586\pi$
$84$		0			0
$85$	−0.603986	+	2.64624i	−0.0655115	+	0.287025i
$86$	−11.9613	−	24.8378i	−1.28982	−	2.67833i
$87$		0			0
$88$	0.897813	+	1.12582i	0.0957071	+	0.120013i
$89$	−3.71116	−	16.2597i	−0.393383	−	1.72352i	−0.652600	−	0.757703i	$-0.726322\pi$
$89$	−3.71116	−	16.2597i	−0.393383	−	1.72352i	0.259217	−	0.965819i	$-0.416535\pi$
$90$		0			0
$91$	−6.30915	+	6.66303i	−0.661378	+	0.698475i
$92$	−10.7655	+	8.58522i	−1.12238	+	0.895071i
$93$		0			0
$94$	−4.53127	+	9.40927i	−0.467364	+	0.970492i
$95$	1.13040	+	0.901461i	0.115976	+	0.0924880i
$96$		0			0
$97$			12.6849i			1.28795i	0.765045	+	0.643977i	$0.222717\pi$
$97$			12.6849i			1.28795i	−0.765045	+	0.643977i	$0.777283\pi$
$98$	−4.76884	−	16.6502i	−0.481726	−	1.68193i
$99$		0			0
$100$	−4.38777	+	19.2241i	−0.438777	+	1.92241i
$101$	9.28383	−	11.6416i	0.923776	−	1.15838i	−0.0632795	−	0.997996i	$-0.520156\pi$
$101$	9.28383	−	11.6416i	0.923776	−	1.15838i	0.987055	−	0.160382i	$-0.0512726\pi$
$102$		0			0
$103$	10.3074	+	8.21989i	1.01562	+	0.809930i	0.981880	−	0.189501i	$-0.0606871\pi$
$103$	10.3074	+	8.21989i	1.01562	+	0.809930i	0.0337390	+	0.999431i	$0.489259\pi$
$104$	−11.3527	−	14.2359i	−1.11323	−	1.39594i
$105$		0			0
$106$	−12.6881	+	15.9104i	−1.23238	+	1.54535i
$107$	5.08824	−	1.16136i	0.491899	−	0.112273i	0.0306257	−	0.999531i	$-0.490250\pi$
$107$	5.08824	−	1.16136i	0.491899	−	0.112273i	0.461273	+	0.887258i	$0.347393\pi$
$108$		0			0
$109$	−0.190621	+	0.835166i	−0.0182582	+	0.0799944i	−0.983236	−	0.182336i	$-0.941634\pi$
$109$	−0.190621	+	0.835166i	−0.0182582	+	0.0799944i	0.964978	+	0.262331i	$0.0844912\pi$
$110$	0.284254	−	0.136889i	0.0271025	−	0.0130519i
$111$		0			0
$112$	12.4350	−	1.74567i	1.17499	−	0.164951i
$113$	−15.3704	+	3.50820i	−1.44593	+	0.330024i	−0.872251	−	0.489058i	$-0.837340\pi$
$113$	−15.3704	+	3.50820i	−1.44593	+	0.330024i	−0.573677	+	0.819082i	$0.694483\pi$
$114$		0			0
$115$	0.673845	+	1.39925i	0.0628363	+	0.130481i
$116$			17.5547i			1.62991i
$117$		0			0
$118$	−1.84124	−	3.82338i	−0.169500	−	0.351971i
$119$	−1.31029	+	15.3914i	−0.120114	+	1.41093i
$120$		0			0
$121$	−9.84288	−	4.74008i	−0.894807	−	0.430916i
$122$	−5.95882	−	26.1073i	−0.539486	−	2.36364i
$123$		0			0
$124$	10.7250	−	22.2707i	0.963134	−	1.99997i
$125$	4.09807	+	1.97352i	0.366542	+	0.176517i
$126$		0			0
$127$	−2.94340	+	1.41747i	−0.261184	+	0.125780i	−0.559894	−	0.828564i	$-0.689158\pi$
$127$	−2.94340	+	1.41747i	−0.261184	+	0.125780i	0.298710	+	0.954344i	$0.403444\pi$
$128$		−	18.3628i		−	1.62306i
$129$		0			0
$130$	−3.59435	+	1.73095i	−0.315246	+	0.151814i
$131$	10.2389	+	12.8392i	0.894575	+	1.12176i	0.991965	+	0.126516i	$0.0403794\pi$
$131$	10.2389	+	12.8392i	0.894575	+	1.12176i	−0.0973892	+	0.995246i	$0.531049\pi$
$132$		0			0
$133$	7.08386	+	4.18608i	0.614248	+	0.362979i
$134$	10.0049	+	2.28355i	0.864290	+	0.197269i
$135$		0			0
$136$	−29.8834	−	6.82070i	−2.56248	−	0.584870i
$137$	10.8055	−	8.61712i	0.923178	−	0.736210i	−0.0416387	−	0.999133i	$-0.513258\pi$
$137$	10.8055	−	8.61712i	0.923178	−	0.736210i	0.964817	+	0.262923i	$0.0846864\pi$
$138$		0			0
$139$	0.617085	+	0.492109i	0.0523404	+	0.0417401i	0.649311	−	0.760523i	$-0.275058\pi$
$139$	0.617085	+	0.492109i	0.0523404	+	0.0417401i	−0.596970	+	0.802263i	$0.703629\pi$
$140$	0.430054	−	5.05165i	0.0363462	−	0.426943i
$141$		0			0
$142$	−3.47890	+	4.36240i	−0.291943	+	0.366084i
$143$	−0.857070	−	0.412743i	−0.0716718	−	0.0345153i
$144$		0			0
$145$	1.93033	+	0.440584i	0.160305	+	0.0365885i
$146$	10.6591			0.882151
$147$		0			0
$148$	31.2108			2.56551
$149$	−4.17377	−	0.952636i	−0.341929	−	0.0780430i	0.0481085	−	0.998842i	$-0.484681\pi$
$149$	−4.17377	−	0.952636i	−0.341929	−	0.0780430i	−0.390037	+	0.920799i	$0.627538\pi$
$150$		0			0
$151$	20.5436	+	9.89326i	1.67181	+	0.805102i	0.997794	+	0.0663866i	$0.0211471\pi$
$151$	20.5436	+	9.89326i	1.67181	+	0.805102i	0.674017	+	0.738715i	$0.264567\pi$
$152$	−10.1800	+	12.7653i	−0.825709	+	1.03541i
$153$		0			0
$154$	1.49368	−	0.996370i	0.120364	−	0.0802898i
$155$	−2.17973	−	1.73827i	−0.175080	−	0.139621i
$156$		0			0
$157$	6.80022	−	5.42299i	0.542716	−	0.432802i	−0.313373	−	0.949630i	$-0.601459\pi$
$157$	6.80022	−	5.42299i	0.542716	−	0.432802i	0.856089	+	0.516828i	$0.172887\pi$
$158$	31.1276	+	7.10467i	2.47638	+	0.565218i
$159$		0			0
$160$	0.563321	+	0.128574i	0.0445344	+	0.0101647i
$161$	4.90468	+	7.35273i	0.386543	+	0.579476i
$162$		0			0
$163$	−3.09028	−	3.87508i	−0.242049	−	0.303520i	0.645937	−	0.763391i	$-0.276467\pi$
$163$	−3.09028	−	3.87508i	−0.242049	−	0.303520i	−0.887986	+	0.459871i	$0.847896\pi$
$164$	9.33855	−	4.49721i	0.729219	−	0.351173i
$165$		0			0
$166$			37.1260i			2.88154i
$167$	−10.7170	+	5.16105i	−0.829309	+	0.399374i	−0.799856	−	0.600192i	$-0.795091\pi$
$167$	−10.7170	+	5.16105i	−0.829309	+	0.399374i	−0.0294533	+	0.999566i	$0.509377\pi$
$168$		0			0
$169$	−0.875065	−	0.421409i	−0.0673127	−	0.0324161i
$170$	−2.91388	+	6.05073i	−0.223484	+	0.464070i
$171$		0			0
$172$	−10.2194	−	44.7743i	−0.779225	−	3.41401i
$173$	22.1786	+	10.6807i	1.68621	+	0.812036i	0.996090	+	0.0883405i	$0.0281563\pi$
$173$	22.1786	+	10.6807i	1.68621	+	0.812036i	0.690120	+	0.723695i	$0.257558\pi$
$174$		0			0
$175$	12.0562	+	3.85298i	0.911364	+	0.291258i
$176$	0.564810	+	1.17284i	0.0425742	+	0.0884062i
$177$		0			0
$178$		−	41.2649i		−	3.09294i
$179$	−7.44333	−	15.4562i	−0.556341	−	1.15525i	−0.969613	−	0.244645i	$-0.921328\pi$
$179$	−7.44333	−	15.4562i	−0.556341	−	1.15525i	0.413272	−	0.910608i	$-0.364386\pi$
$180$		0			0
$181$	−12.3505	+	2.81891i	−0.918002	+	0.209528i	−0.655317	−	0.755354i	$-0.727465\pi$
$181$	−12.3505	+	2.81891i	−0.918002	+	0.209528i	−0.262685	+	0.964882i	$0.584608\pi$
$182$	−18.8874	+	12.5990i	−1.40003	+	0.933898i
$183$		0			0
$184$	−15.8015	+	7.60959i	−1.16490	+	0.560987i
$185$	0.783323	−	3.43196i	0.0575910	−	0.252323i
$186$		0			0
$187$	−1.56123	+	0.356340i	−0.114168	+	0.0260582i
$188$	−10.8474	+	13.6023i	−0.791131	+	0.992047i
$189$		0			0
$190$	2.23043	+	2.79687i	0.161813	+	0.202907i
$191$	−6.21040	−	4.95263i	−0.449369	−	0.358360i	0.372504	−	0.928031i	$-0.378499\pi$
$191$	−6.21040	−	4.95263i	−0.449369	−	0.358360i	−0.821873	+	0.569671i	$0.807071\pi$
$192$		0			0
$193$	−1.30350	+	1.63454i	−0.0938283	+	0.117657i	−0.826529	−	0.562894i	$-0.809688\pi$
$193$	−1.30350	+	1.63454i	−0.0938283	+	0.117657i	0.732701	+	0.680551i	$0.238259\pi$
$194$	−6.98391	+	30.5985i	−0.501416	+	2.19685i
$195$		0			0
$196$	−1.57305	−	28.8102i	−0.112361	−	2.05787i
$197$		−	20.7361i		−	1.47739i	−0.674041	−	0.738694i	$-0.735443\pi$
$197$		−	20.7361i		−	1.47739i	0.674041	−	0.738694i	$-0.264557\pi$
$198$		0			0
$199$	−2.37906	−	1.89724i	−0.168647	−	0.134492i	0.535529	−	0.844517i	$-0.320112\pi$
$199$	−2.37906	−	1.89724i	−0.168647	−	0.134492i	−0.704176	+	0.710025i	$0.748684\pi$
$200$	−10.8971	+	22.6282i	−0.770545	+	1.60005i
$201$		0			0
$202$	28.8040	−	22.9704i	2.02664	−	1.61619i
$203$	11.2274	+	0.955806i	0.788011	+	0.0670844i
$204$		0			0
$205$	−0.260139	−	1.13974i	−0.0181689	−	0.0796031i
$206$	20.3380	+	25.5030i	1.41701	+	1.77688i
$207$		0			0
$208$	−7.14195	−	14.8304i	−0.495205	−	1.02830i
$209$	−0.189813	+	0.831625i	−0.0131296	+	0.0575247i
$210$		0			0
$211$	0.523859	+	2.29518i	0.0360639	+	0.158006i	0.989754	−	0.142786i	$-0.0456060\pi$
$211$	0.523859	+	2.29518i	0.0360639	+	0.158006i	−0.953690	+	0.300792i	$0.902749\pi$
$212$	−26.5053	+	21.1373i	−1.82039	+	1.45171i
$213$		0			0
$214$	12.9133			0.882734
$215$	−5.17989			−0.353266
$216$		0			0
$217$	−13.6597	−	8.07195i	−0.927280	−	0.547960i
$218$	−0.919636	+	1.90964i	−0.0622856	+	0.129337i
$219$		0			0
$220$	0.512414	−	0.116955i	0.0345470	−	0.00788512i
$221$	19.7415	−	4.50587i	1.32796	−	0.303098i
$222$		0			0
$223$	−11.8915	+	24.6929i	−0.796311	+	1.65356i	−0.0401292	+	0.999194i	$0.512777\pi$
$223$	−11.8915	+	24.6929i	−0.796311	+	1.65356i	−0.756182	+	0.654362i	$0.772937\pi$
$224$	3.27647	+	0.278930i	0.218918	+	0.0186368i
$225$		0			0
$226$	−39.0081			−2.59478
$227$	−9.07729			−0.602481			−0.301240	−	0.953548i	$-0.597401\pi$
$227$	−9.07729			−0.602481			−0.301240	+	0.953548i	$0.597401\pi$
$228$		0			0
$229$	−5.11405	+	4.07832i	−0.337946	+	0.269503i	−0.777727	−	0.628602i	$-0.783627\pi$
$229$	−5.11405	+	4.07832i	−0.337946	+	0.269503i	0.439781	+	0.898105i	$0.355056\pi$
$230$	0.855065	+	3.74629i	0.0563813	+	0.247023i
$231$		0			0
$232$	−4.97543	+	21.7988i	−0.326653	+	1.43116i
$233$	0.156646	+	0.325279i	0.0102622	+	0.0213097i	0.906037	−	0.423199i	$-0.139093\pi$
$233$	0.156646	+	0.325279i	0.0102622	+	0.0213097i	−0.895775	+	0.444508i	$0.853378\pi$
$234$		0			0
$235$	1.22347	+	1.53418i	0.0798102	+	0.100079i
$236$	−1.57312	−	6.89228i	−0.102401	−	0.448649i
$237$		0			0
$238$	−11.6348	+	36.4059i	−0.754169	+	2.35984i
$239$	−13.0101	+	10.3752i	−0.841550	+	0.671114i	−0.946266	−	0.323388i	$-0.895178\pi$
$239$	−13.0101	+	10.3752i	−0.841550	+	0.671114i	0.104716	+	0.994502i	$0.466607\pi$
$240$		0			0
$241$	−7.41986	+	15.4075i	−0.477955	+	0.992484i	0.513012	+	0.858381i	$0.328530\pi$
$241$	−7.41986	+	15.4075i	−0.477955	+	0.992484i	−0.990967	+	0.134103i	$0.957185\pi$
$242$	−21.1333	−	16.8532i	−1.35850	−	1.08337i
$243$		0			0
$244$		−	44.6110i		−	2.85592i
$245$	−3.20746	−	0.550098i	−0.204917	−	0.0351444i
$246$		0			0
$247$	2.40016	−	10.5158i	0.152719	−	0.669104i
$248$	19.6300	−	24.6152i	1.24650	−	1.56307i
$249$		0			0
$250$	8.79882	+	7.01682i	0.556486	+	0.443783i
$251$	−2.40449	−	3.01513i	−0.151770	−	0.190313i	0.700134	−	0.714011i	$-0.253124\pi$
$251$	−2.40449	−	3.01513i	−0.151770	−	0.190313i	−0.851904	+	0.523698i	$0.824552\pi$
$252$		0			0
$253$	−0.571285	+	0.716369i	−0.0359164	+	0.0450378i
$254$	−7.88049	+	1.79867i	−0.494466	+	0.112859i
$255$		0			0
$256$	7.25422	−	31.7828i	0.453389	−	1.98643i
$257$	24.4380	−	11.7687i	1.52440	−	0.734113i	0.530846	−	0.847468i	$-0.321874\pi$
$257$	24.4380	−	11.7687i	1.52440	−	0.734113i	0.993555	+	0.113355i	$0.0361598\pi$
$258$		0			0
$259$	1.69935	−	19.9615i	0.105592	−	1.24034i
$260$	−6.47941	+	1.47888i	−0.401836	+	0.0917164i
$261$		0			0
$262$	17.6294	+	36.6079i	1.08915	+	2.26164i
$263$			16.7436i			1.03245i	0.856452	+	0.516227i	$0.172664\pi$
$263$			16.7436i			1.03245i	−0.856452	+	0.516227i	$0.827336\pi$
$264$		0			0
$265$	1.65904	+	3.44503i	0.101914	+	0.211627i
$266$	14.7830	+	13.9979i	0.906404	+	0.858264i
$267$		0			0
$268$	15.4029	+	7.41763i	0.940879	+	0.453104i
$269$	−5.81577	−	25.4805i	−0.354594	−	1.55358i	−0.766436	−	0.642321i	$-0.777972\pi$
$269$	−5.81577	−	25.4805i	−0.354594	−	1.55358i	0.411842	−	0.911255i	$-0.364886\pi$
$270$		0			0
$271$	−9.66282	+	20.0651i	−0.586975	+	1.21887i	0.370091	+	0.928995i	$0.379326\pi$
$271$	−9.66282	+	20.0651i	−0.586975	+	1.21887i	−0.957066	+	0.289870i	$0.906388\pi$
$272$	−24.9655	−	12.0228i	−1.51376	−	0.728987i
$273$		0			0
$274$	30.8095	−	14.8371i	1.86127	−	0.896340i
$275$			1.31213i			0.0791241i
$276$		0			0
$277$	4.27615	−	2.05929i	0.256929	−	0.123730i	−0.300986	−	0.953629i	$-0.597316\pi$
$277$	4.27615	−	2.05929i	0.256929	−	0.123730i	0.557915	+	0.829898i	$0.311601\pi$
$278$	1.21760	+	1.52682i	0.0730265	+	0.0915723i
$279$		0			0
$280$	1.96579	−	6.15107i	0.117478	−	0.367597i
$281$	1.18131	+	0.269626i	0.0704708	+	0.0160845i	0.257611	−	0.966249i	$-0.417065\pi$
$281$	1.18131	+	0.269626i	0.0704708	+	0.0160845i	−0.187140	+	0.982333i	$0.559922\pi$
$282$		0			0
$283$	16.0021	+	3.65238i	0.951227	+	0.217111i	0.669859	−	0.742488i	$-0.266355\pi$
$283$	16.0021	+	3.65238i	0.951227	+	0.217111i	0.281368	+	0.959600i	$0.409212\pi$
$284$	−7.26737	+	5.79554i	−0.431239	+	0.343902i
$285$		0			0
$286$	−1.84018	−	1.46750i	−0.108812	−	0.0867750i
$287$	−2.36781	−	6.21750i	−0.139768	−	0.367008i
$288$		0			0
$289$	10.6539	−	13.3596i	0.626699	−	0.785856i
$290$	4.41377	+	2.12556i	0.259186	+	0.124817i
$291$		0			0
$292$	17.3119	+	3.95132i	1.01310	+	0.231234i
$293$	−3.00563			−0.175591			−0.0877954	−	0.996139i	$-0.527982\pi$
$293$	−3.00563			−0.175591			−0.0877954	+	0.996139i	$0.527982\pi$
$294$		0			0
$295$	−0.797360			−0.0464241
$296$	38.7565	+	8.84591i	2.25267	+	0.514158i
$297$		0			0
$298$	−9.54350	−	4.59591i	−0.552840	−	0.266234i
$299$	7.22383	−	9.05839i	0.417765	−	0.523860i
$300$		0			0
$301$	−29.1926	+	4.09819i	−1.68264	+	0.236216i
$302$	44.1084	+	35.1753i	2.53815	+	2.02411i
$303$		0			0
$304$	−11.5400	+	9.20283i	−0.661864	+	0.527819i
$305$	−4.90545	−	1.11964i	−0.280885	−	0.0641102i
$306$		0			0
$307$	22.3238	+	5.09526i	1.27409	+	0.290802i	0.805490	−	0.592610i	$-0.201902\pi$
$307$	22.3238	+	5.09526i	1.27409	+	0.290802i	0.468597	+	0.883412i	$0.344760\pi$
$308$	2.79531	−	1.06454i	0.159278	−	0.0606578i
$309$		0			0
$310$	−4.30091	−	5.39317i	−0.244275	−	0.306311i
$311$	19.9238	−	9.59478i	1.12977	−	0.544070i	0.226875	−	0.973924i	$-0.427149\pi$
$311$	19.9238	−	9.59478i	1.12977	−	0.544070i	0.902898	+	0.429854i	$0.141435\pi$
$312$		0			0
$313$			8.58891i			0.485474i	0.970092	+	0.242737i	$0.0780452\pi$
$313$			8.58891i			0.485474i	−0.970092	+	0.242737i	$0.921955\pi$
$314$	19.3893	−	9.33738i	1.09420	−	0.526939i
$315$		0			0
$316$	47.9220	+	23.0780i	2.69582	+	1.29824i
$317$	−5.09122	+	10.5720i	−0.285951	+	0.593784i	−0.993622	−	0.112758i	$-0.964032\pi$
$317$	−5.09122	+	10.5720i	−0.285951	+	0.593784i	0.707671	+	0.706542i	$0.249746\pi$
$318$		0			0
$319$	0.259936	+	1.13885i	0.0145536	+	0.0637636i
$320$	−2.68781	−	1.29438i	−0.150253	−	0.0723580i
$321$		0			0
$322$	7.78290	+	20.4367i	0.433724	+	1.13889i
$323$	−7.87826	−	16.3594i	−0.438358	−	0.910260i
$324$		0			0
$325$		−	16.5916i		−	0.920339i
$326$	−5.32088	−	11.0489i	−0.294696	−	0.611943i
$327$		0			0
$328$	12.8709	−	2.93770i	0.710676	−	0.162207i
$329$	8.10897	+	7.67829i	0.447062	+	0.423318i
$330$		0			0
$331$	5.79305	−	2.78978i	0.318415	−	0.153340i	−0.267849	−	0.963461i	$-0.586313\pi$
$331$	5.79305	−	2.78978i	0.318415	−	0.153340i	0.586263	+	0.810121i	$0.300598\pi$
$332$	−13.7626	+	60.2980i	−0.755322	+	3.30928i
$333$		0			0
$334$	−28.6932	+	6.54904i	−1.57002	+	0.358348i
$335$	1.20222	−	1.50754i	0.0656845	−	0.0823658i
$336$		0			0
$337$	−15.0120	−	18.8244i	−0.817754	−	1.02543i	−0.999117	−	0.0420144i	$-0.986622\pi$
$337$	−15.0120	−	18.8244i	−0.817754	−	1.02543i	0.181363	−	0.983416i	$-0.441949\pi$
$338$	−1.87882	−	1.49831i	−0.102194	−	0.0814973i
$339$		0			0
$340$	−6.97557	+	8.74709i	−0.378303	+	0.474377i
$341$	0.366014	−	1.60361i	0.0198207	−	0.0868403i
$342$		0			0
$343$	−18.5117	−	0.562561i	−0.999539	−	0.0303755i
$344$		−	58.4955i		−	3.15387i
$345$		0			0
$346$	47.6190	+	37.9749i	2.56001	+	2.04154i
$347$	−11.7236	+	24.3443i	−0.629356	+	1.30687i	0.305618	+	0.952154i	$0.401137\pi$
$347$	−11.7236	+	24.3443i	−0.629356	+	1.30687i	−0.934974	+	0.354716i	$0.884577\pi$
$348$		0			0
$349$	−2.20326	+	1.75704i	−0.117938	+	0.0940523i	−0.680683	−	0.732578i	$-0.738317\pi$
$349$	−2.20326	+	1.75704i	−0.117938	+	0.0940523i	0.562745	+	0.826631i	$0.309745\pi$
$350$	26.9607	+	15.9320i	1.44111	+	0.851600i
$351$		0			0
$352$	0.0758563	+	0.332348i	0.00404315	+	0.0177142i
$353$	−2.58504	−	3.24154i	−0.137588	−	0.172530i	0.708264	−	0.705948i	$-0.249479\pi$
$353$	−2.58504	−	3.24154i	−0.137588	−	0.172530i	−0.845852	+	0.533418i	$0.820907\pi$
$354$		0			0
$355$	0.454886	+	0.944580i	0.0241428	+	0.0501331i
$356$	15.2969	−	67.0202i	0.810736	−	3.55206i
$357$		0			0
$358$	−9.44510	−	41.3817i	−0.499189	−	2.18709i
$359$	−3.87879	+	3.09323i	−0.204715	+	0.163255i	−0.720481	−	0.693475i	$-0.756079\pi$
$359$	−3.87879	+	3.09323i	−0.204715	+	0.163255i	0.515766	+	0.856730i	$0.327507\pi$
$360$		0			0
$361$	9.32795			0.490945
$362$	−31.3439			−1.64740
$363$		0			0
$364$	−35.3464	+	13.4610i	−1.85265	+	0.705546i
$365$	0.868979	−	1.80445i	0.0454844	−	0.0944494i
$366$		0			0
$367$	10.4094	−	2.37589i	0.543368	−	0.124020i	0.0579779	−	0.998318i	$-0.481535\pi$
$367$	10.4094	−	2.37589i	0.543368	−	0.124020i	0.485390	+	0.874298i	$0.338678\pi$
$368$	−15.4573	+	3.52803i	−0.805767	+	0.183911i
$369$		0			0
$370$	3.77907	−	7.84733i	0.196465	−	0.407963i
$371$	12.0756	+	18.1028i	0.626933	+	0.939851i
$372$		0			0
$373$	4.03774			0.209066			0.104533	−	0.994521i	$-0.466665\pi$
$373$	4.03774			0.209066			0.104533	+	0.994521i	$0.466665\pi$
$374$	−3.96219			−0.204880
$375$		0			0
$376$	−17.3252	+	13.8164i	−0.893478	+	0.712525i
$377$	−3.28686	−	14.4007i	−0.169282	−	0.741672i
$378$		0			0
$379$	3.18338	−	13.9473i	0.163519	−	0.716425i	−0.824975	−	0.565169i	$-0.808811\pi$
$379$	3.18338	−	13.9473i	0.163519	−	0.716425i	0.988495	−	0.151256i	$-0.0483319\pi$
$380$	2.58574	+	5.36935i	0.132646	+	0.275442i
$381$		0			0
$382$	−12.2540	−	15.3660i	−0.626969	−	0.786194i
$383$	−2.24978	−	9.85692i	−0.114958	−	0.503665i	−0.999320	−	0.0368635i	$-0.988263\pi$
$383$	−2.24978	−	9.85692i	−0.114958	−	0.503665i	0.884362	−	0.466802i	$-0.154594\pi$
$384$		0			0
$385$	−0.0469013	−	0.334092i	−0.00239031	−	0.0170269i
$386$	−4.04425	+	3.22518i	−0.205847	+	0.164157i
$387$		0			0
$388$	−22.6858	+	47.1075i	−1.15170	+	2.39152i
$389$	−29.6202	−	23.6213i	−1.50180	−	1.19765i	−0.924537	−	0.381093i	$-0.875548\pi$
$389$	−29.6202	−	23.6213i	−1.50180	−	1.19765i	−0.577267	−	0.816556i	$-0.695881\pi$
$390$		0			0
$391$		−	19.5041i		−	0.986364i
$392$	6.21214	−	36.2212i	0.313761	−	1.82945i
$393$		0			0
$394$	11.4167	−	50.0198i	0.575165	−	2.51996i
$395$	3.74041	−	4.69033i	0.188200	−	0.235996i
$396$		0			0
$397$	−0.794963	−	0.633962i	−0.0398980	−	0.0318176i	0.603338	−	0.797486i	$-0.293837\pi$
$397$	−0.794963	−	0.633962i	−0.0398980	−	0.0318176i	−0.643236	+	0.765668i	$0.722409\pi$
$398$	−4.69422	−	5.88637i	−0.235300	−	0.295057i
$399$		0			0
$400$	−14.1560	+	17.7511i	−0.707802	+	0.887555i
$401$	−26.2157	+	5.98356i	−1.30915	+	0.298805i	−0.819482	−	0.573105i	$-0.805739\pi$
$401$	−26.2157	+	5.98356i	−1.30915	+	0.298805i	−0.489667	+	0.871910i	$0.662882\pi$
$402$		0			0
$403$	−4.62819	+	20.2774i	−0.230547	+	1.01009i
$404$	55.2970	−	26.6296i	2.75113	−	1.32487i
$405$		0			0
$406$	26.5567	+	8.48710i	1.31798	+	0.421207i
$407$	2.02479	−	0.462145i	0.100365	−	0.0229077i
$408$		0			0
$409$	9.82904	+	20.4102i	0.486015	+	1.00922i	0.989408	+	0.145163i	$0.0463705\pi$
$409$	9.82904	+	20.4102i	0.486015	+	1.00922i	−0.503393	+	0.864058i	$0.667915\pi$
$410$		−	2.89252i		−	0.142851i
$411$		0			0
$412$	23.5778	+	48.9599i	1.16160	+	2.41208i
$413$	−4.49373	+	0.630850i	−0.221122	+	0.0310421i
$414$		0			0
$415$	6.28499	+	3.02669i	0.308518	+	0.148575i
$416$	−0.959193	−	4.20250i	−0.0470283	−	0.206044i
$417$		0			0
$418$	−0.915737	+	1.90155i	−0.0447901	+	0.0930077i
$419$	−24.2221	−	11.6647i	−1.18333	−	0.569860i	−0.264447	−	0.964400i	$-0.585189\pi$
$419$	−24.2221	−	11.6647i	−1.18333	−	0.569860i	−0.918879	+	0.394541i	$0.870904\pi$
$420$		0			0
$421$	−8.45415	+	4.07130i	−0.412030	+	0.198423i	−0.628404	−	0.777887i	$-0.716291\pi$
$421$	−8.45415	+	4.07130i	−0.412030	+	0.198423i	0.216374	+	0.976311i	$0.430577\pi$
$422$			5.82486i			0.283550i
$423$		0			0
$424$	−38.9041	+	18.7352i	−1.88935	+	0.909863i
$425$	−17.4143	−	21.8369i	−0.844718	−	1.05924i
$426$		0			0
$427$	−28.5318	−	2.42895i	−1.38075	−	0.117545i
$428$	20.9730	+	4.78696i	1.01377	+	0.231387i
$429$		0			0
$430$	−12.4950	−	2.85190i	−0.602561	−	0.137531i
$431$	−19.6867	+	15.6996i	−0.948273	+	0.756222i	−0.969890	−	0.243544i	$-0.921690\pi$
$431$	−19.6867	+	15.6996i	−0.948273	+	0.756222i	0.0216169	+	0.999766i	$0.493119\pi$
$432$		0			0
$433$	−27.7077	−	22.0962i	−1.33155	−	1.06187i	−0.992646	−	0.121053i	$-0.961373\pi$
$433$	−27.7077	−	22.0962i	−1.33155	−	1.06187i	−0.338902	−	0.940822i	$-0.610056\pi$
$434$	−28.5058	−	26.9918i	−1.36832	−	1.29565i
$435$		0			0
$436$	−2.20153	+	2.76063i	−0.105434	+	0.132210i
$437$	−9.36045	−	4.50776i	−0.447771	−	0.215635i
$438$		0			0
$439$	−10.6351	−	2.42739i	−0.507585	−	0.115853i	−0.0389434	−	0.999241i	$-0.512399\pi$
$439$	−10.6351	−	2.42739i	−0.507585	−	0.115853i	−0.468641	+	0.883389i	$0.655256\pi$
$440$	0.669445			0.0319145
$441$		0			0
$442$	50.1014			2.38308
$443$	6.54022	+	1.49276i	0.310735	+	0.0709233i	0.375045	−	0.927007i	$-0.377627\pi$
$443$	6.54022	+	1.49276i	0.310735	+	0.0709233i	−0.0643096	+	0.997930i	$0.520485\pi$
$444$		0			0
$445$	−6.98566	−	3.36412i	−0.331152	−	0.159474i
$446$	−42.2798	+	53.0172i	−2.00201	+	2.51044i
$447$		0			0
$448$	−16.1719	−	5.16829i	−0.764051	−	0.244179i
$449$	−0.0107612	−	0.00858176i	−0.000507852	−	0.000404998i	0.623236	−	0.782034i	$-0.285818\pi$
$449$	−0.0107612	−	0.00858176i	−0.000507852	−	0.000404998i	−0.623744	+	0.781629i	$0.714389\pi$
$450$		0			0
$451$	0.539244	−	0.430032i	0.0253920	−	0.0202494i
$452$	−63.3548	−	14.4603i	−2.97996	−	0.680157i
$453$		0			0
$454$	−21.8963	−	4.99769i	−1.02764	−	0.234553i
$455$	0.593060	+	4.22455i	0.0278031	+	0.198050i
$456$		0			0
$457$	5.57422	+	6.98986i	0.260751	+	0.326972i	0.894923	−	0.446220i	$-0.147230\pi$
$457$	5.57422	+	6.98986i	0.260751	+	0.326972i	−0.634172	+	0.773192i	$0.718659\pi$
$458$	−14.5816	+	7.02211i	−0.681351	+	0.328121i
$459$		0			0
$460$			6.40148i			0.298471i
$461$	24.7350	−	11.9117i	1.15202	−	0.554785i	0.242383	−	0.970181i	$-0.422071\pi$
$461$	24.7350	−	11.9117i	1.15202	−	0.554785i	0.909641	+	0.415395i	$0.136357\pi$
$462$		0			0
$463$	−11.9492	−	5.75445i	−0.555328	−	0.267432i	0.135101	−	0.990832i	$-0.456864\pi$
$463$	−11.9492	−	5.75445i	−0.555328	−	0.267432i	−0.690429	+	0.723400i	$0.742578\pi$
$464$	−8.77013	+	18.2114i	−0.407143	+	0.845441i
$465$		0			0
$466$	0.198774	+	0.870885i	0.00920802	+	0.0403430i
$467$	19.1979	+	9.24522i	0.888373	+	0.427818i	0.821675	−	0.569956i	$-0.193040\pi$
$467$	19.1979	+	9.24522i	0.888373	+	0.427818i	0.0666971	+	0.997773i	$0.478754\pi$
$468$		0			0
$469$	5.58272	−	9.44731i	0.257786	−	0.436236i
$470$	2.10658	+	4.37436i	0.0971693	+	0.201774i
$471$		0			0
$472$		−	9.00443i		−	0.414463i
$473$	−1.32596	−	2.75339i	−0.0609679	−	0.126601i
$474$		0			0
$475$	−14.5048	+	3.31062i	−0.665525	+	0.151902i
$476$	−32.3922	+	54.8154i	−1.48469	+	2.51246i
$477$		0			0
$478$	−37.0952	+	17.8641i	−1.69670	+	0.817085i
$479$	−1.69302	+	7.41762i	−0.0773563	+	0.338920i	−0.998765	−	0.0496737i	$-0.984182\pi$
$479$	−1.69302	+	7.41762i	−0.0773563	+	0.338920i	0.921409	+	0.388594i	$0.127039\pi$
$480$		0			0
$481$	−25.6032	+	5.84376i	−1.16741	+	0.266453i
$482$	−26.3812	+	33.0809i	−1.20163	+	1.50679i
$483$		0			0
$484$	−28.0760	−	35.2062i	−1.27618	−	1.60028i
$485$	4.61060	+	3.67683i	0.209357	+	0.166956i
$486$		0			0
$487$	9.46779	−	11.8722i	0.429027	−	0.537982i	−0.519588	−	0.854417i	$-0.673914\pi$
$487$	9.46779	−	11.8722i	0.429027	−	0.537982i	0.948614	+	0.316435i	$0.102486\pi$
$488$	12.6438	−	55.3962i	0.572359	−	2.50767i
$489$		0			0
$490$	−7.43419	−	3.09288i	−0.335843	−	0.139722i
$491$		−	1.76154i		−	0.0794970i	−0.999210	−	0.0397485i	$-0.987344\pi$
$491$		−	1.76154i		−	0.0794970i	0.999210	−	0.0397485i	$-0.0126557\pi$
$492$		0			0
$493$	−19.4406	−	15.5034i	−0.875562	−	0.698237i
$494$	11.5794	−	24.0448i	0.520980	−	1.08183i
$495$		0			0
$496$	22.2524	−	17.7457i	0.999161	−	0.796804i
$497$	3.31095	+	4.96353i	0.148517	+	0.222645i
$498$		0			0
$499$	−6.94371	−	30.4224i	−0.310843	−	1.36189i	−0.853130	−	0.521699i	$-0.825298\pi$
$499$	−6.94371	−	30.4224i	−0.310843	−	1.36189i	0.542287	−	0.840194i	$-0.317559\pi$
$500$	11.6894	+	14.6581i	0.522766	+	0.655528i
$501$		0			0
$502$	−4.14008	−	8.59696i	−0.184781	−	0.383701i
$503$	−5.72523	+	25.0839i	−0.255275	+	1.11843i	0.670961	+	0.741492i	$0.265882\pi$
$503$	−5.72523	+	25.0839i	−0.255275	+	1.11843i	−0.926237	+	0.376942i	$0.876975\pi$
$504$		0			0
$505$	−1.54038	−	6.74884i	−0.0685459	−	0.300319i
$506$	−1.77247	+	1.41350i	−0.0787959	+	0.0628376i
$507$		0			0
$508$	−13.4658			−0.597449
$509$	2.15795			0.0956496			0.0478248	−	0.998856i	$-0.484771\pi$
$509$	2.15795			0.0956496			0.0478248	+	0.998856i	$0.484771\pi$
$510$		0			0
$511$	3.46972	−	10.8570i	0.153492	−	0.480285i
$512$	19.0627	−	39.5841i	0.842460	−	1.74939i
$513$		0			0
$514$	65.4290	−	14.9337i	2.88595	−	0.658699i
$515$	5.97541	−	1.36385i	0.263308	−	0.0600983i
$516$		0			0
$517$	−0.502312	+	1.04306i	−0.0220917	+	0.0458738i
$518$	15.0894	−	47.2156i	0.662988	−	2.07453i
$519$		0			0
$520$	−8.46504			−0.371217
$521$	−6.68030			−0.292669			−0.146335	−	0.989235i	$-0.546748\pi$
$521$	−6.68030			−0.292669			−0.146335	+	0.989235i	$0.546748\pi$
$522$		0			0
$523$	19.3444	−	15.4266i	0.845872	−	0.674560i	−0.101451	−	0.994841i	$-0.532349\pi$
$523$	19.3444	−	15.4266i	0.845872	−	0.674560i	0.947323	+	0.320280i	$0.103777\pi$
$524$	15.0622	+	65.9918i	0.657995	+	2.88286i
$525$		0			0
$526$	−9.21852	+	40.3890i	−0.401947	+	1.76104i
$527$	15.1915	+	31.5455i	0.661753	+	1.37414i
$528$		0			0
$529$	7.38226	+	9.25706i	0.320968	+	0.402481i
$530$	2.10522	+	9.22355i	0.0914447	+	0.400646i
$531$		0			0
$532$	18.8207	+	28.2146i	0.815981	+	1.22326i
$533$	−6.81866	+	5.43770i	−0.295349	+	0.235533i
$534$		0			0
$535$	1.05275	−	2.18607i	0.0455145	−	0.0945119i
$536$	17.0244	+	13.5765i	0.735341	+	0.586415i
$537$		0			0
$538$		−	64.6663i		−	2.78796i
$539$	−0.528649	−	1.84575i	−0.0227705	−	0.0795023i
$540$		0			0
$541$	3.65988	−	16.0350i	0.157351	−	0.689398i	−0.833283	−	0.552847i	$-0.813541\pi$
$541$	3.65988	−	16.0350i	0.157351	−	0.689398i	0.990633	−	0.136551i	$-0.0436016\pi$
$542$	−34.3560	+	43.0810i	−1.47571	+	1.85049i
$543$		0			0
$544$	−5.67330	−	4.52430i	−0.243241	−	0.193978i
$545$	0.248307	+	0.311367i	0.0106363	+	0.0133375i
$546$		0			0
$547$	−20.4759	+	25.6759i	−0.875485	+	1.09782i	0.118994	+	0.992895i	$0.462033\pi$
$547$	−20.4759	+	25.6759i	−0.875485	+	1.09782i	−0.994480	+	0.104929i	$0.966538\pi$
$548$	55.5392	−	12.6764i	2.37251	−	0.541511i
$549$		0			0
$550$	−0.722417	+	3.16512i	−0.0308040	+	0.134961i
$551$	−11.9335	+	5.74688i	−0.508385	+	0.244825i
$552$		0			0
$553$	17.3692	−	29.3929i	0.738613	−	1.24991i
$554$	11.4487	−	2.61310i	0.486410	−	0.111020i
$555$		0			0
$556$	1.41156	+	2.93113i	0.0598634	+	0.124308i
$557$		−	30.7575i		−	1.30324i	−0.758546	−	0.651619i	$-0.774090\pi$
$557$		−	30.7575i		−	1.30324i	0.758546	−	0.651619i	$-0.225910\pi$
$558$		0			0
$559$	16.7666	+	34.8163i	0.709153	+	1.47257i
$560$	2.96989	−	5.02577i	0.125501	−	0.212377i
$561$		0			0
$562$	2.70111	+	1.30078i	0.113939	+	0.0548703i
$563$	−5.89361	−	25.8216i	−0.248386	−	1.08825i	−0.933150	−	0.359486i	$-0.882952\pi$
$563$	−5.89361	−	25.8216i	−0.248386	−	1.08825i	0.684764	−	0.728765i	$-0.259905\pi$
$564$		0			0
$565$	−3.18013	+	6.60361i	−0.133789	+	0.277816i
$566$	36.5895	+	17.6206i	1.53797	+	0.740648i
$567$		0			0
$568$	−10.6670	+	5.13693i	−0.447575	+	0.215541i
$569$		−	2.06199i		−	0.0864433i	−0.999066	−	0.0432216i	$-0.986238\pi$
$569$		−	2.06199i		−	0.0864433i	0.999066	−	0.0432216i	$-0.0137622\pi$
$570$		0			0
$571$	28.5194	−	13.7342i	1.19350	−	0.574758i	0.271682	−	0.962387i	$-0.412420\pi$
$571$	28.5194	−	13.7342i	1.19350	−	0.574758i	0.921816	+	0.387629i	$0.126706\pi$
$572$	−2.44472	−	3.06559i	−0.102219	−	0.128179i
$573$		0			0
$574$	−2.28848	−	16.3016i	−0.0955195	−	0.680414i
$575$	−15.5804	−	3.55613i	−0.649749	−	0.148301i
$576$		0			0
$577$	−26.0429	−	5.94412i	−1.08418	−	0.247457i	−0.357139	−	0.934051i	$-0.616248\pi$
$577$	−26.0429	−	5.94412i	−1.08418	−	0.247457i	−0.727041	+	0.686595i	$0.759105\pi$
$578$	33.0548	−	26.3603i	1.37490	−	1.09644i
$579$		0			0
$580$	6.38066	+	5.08840i	0.264942	+	0.211284i
$581$	37.8154	+	12.0852i	1.56885	+	0.501379i
$582$		0			0
$583$	−1.40654	+	1.76374i	−0.0582527	+	0.0730466i
$584$	20.3773	+	9.81321i	0.843220	+	0.406073i
$585$		0			0
$586$	−7.25020	−	1.65481i	−0.299503	−	0.0683596i
$587$	−18.3422			−0.757065			−0.378532	−	0.925588i	$-0.623571\pi$
$587$	−18.3422			−0.757065			−0.378532	+	0.925588i	$0.623571\pi$
$588$		0			0
$589$	18.6505			0.768479
$590$	−1.92340	−	0.439003i	−0.0791850	−	0.0180735i
$591$		0			0
$592$	32.3783	+	15.5926i	1.33074	+	0.640851i
$593$	25.5534	−	32.0429i	1.04935	−	1.31585i	0.102305	−	0.994753i	$-0.467378\pi$
$593$	25.5534	−	32.0429i	1.04935	−	1.31585i	0.947048	−	0.321093i	$-0.104050\pi$
$594$		0			0
$595$	5.21456	+	4.93761i	0.213776	+	0.202422i
$596$	−13.7963	−	11.0022i	−0.565119	−	0.450668i
$597$		0			0
$598$	22.4126	−	17.8735i	0.916521	−	0.730901i
$599$	38.8081	+	8.85770i	1.58566	+	0.361916i	0.922327	−	0.386411i	$-0.126285\pi$
$599$	38.8081	+	8.85770i	1.58566	+	0.361916i	0.663330	+	0.748327i	$0.269143\pi$
$600$		0			0
$601$	1.30917	+	0.298810i	0.0534023	+	0.0121887i	0.249139	−	0.968468i	$-0.419853\pi$
$601$	1.30917	+	0.298810i	0.0534023	+	0.0121887i	−0.195736	+	0.980657i	$0.562710\pi$
$602$	−72.6750	−	6.18692i	−2.96201	−	0.252160i
$603$		0			0
$604$	58.5989	+	73.4807i	2.38436	+	2.98989i
$605$	−4.57594	+	2.20366i	−0.186039	+	0.0895914i
$606$		0			0
$607$		−	30.5499i		−	1.23998i	−0.784608	−	0.619992i	$-0.787136\pi$
$607$		−	30.5499i		−	1.23998i	0.784608	−	0.619992i	$-0.212864\pi$
$608$	−3.48252	+	1.67709i	−0.141235	+	0.0680151i
$609$		0			0
$610$	−11.2165	−	5.40159i	−0.454143	−	0.218704i
$611$	6.35167	−	13.1894i	0.256961	−	0.533585i
$612$		0			0
$613$	5.51054	+	24.1433i	0.222569	+	0.975137i	0.955536	+	0.294874i	$0.0952775\pi$
$613$	5.51054	+	24.1433i	0.222569	+	0.975137i	−0.732968	+	0.680264i	$0.761865\pi$
$614$	51.0443	+	24.5817i	2.05998	+	0.992035i
$615$		0			0
$616$	3.77283	−	0.529647i	0.152012	−	0.0213401i
$617$	2.47360	+	5.13649i	0.0995835	+	0.206787i	0.944808	−	0.327624i	$-0.106248\pi$
$617$	2.47360	+	5.13649i	0.0995835	+	0.206787i	−0.845225	+	0.534411i	$0.820533\pi$
$618$		0			0
$619$		−	24.7711i		−	0.995636i	−0.867282	−	0.497818i	$-0.834135\pi$
$619$		−	24.7711i		−	0.995636i	0.867282	−	0.497818i	$-0.165865\pi$
$620$	−4.98605	−	10.3536i	−0.200244	−	0.415812i
$621$		0			0
$622$	53.3428	−	12.1752i	2.13885	−	0.488179i
$623$	−42.0311	−	13.4325i	−1.68394	−	0.538162i
$624$		0			0
$625$	−19.6454	+	9.46073i	−0.785816	+	0.378429i
$626$	−4.72880	+	20.7182i	−0.189001	+	0.828067i
$627$		0			0
$628$	34.9523	−	7.97764i	1.39475	−	0.318343i
$629$	−27.5638	+	34.5639i	−1.09904	+	1.37815i
$630$		0			0
$631$	8.38118	+	10.5097i	0.333650	+	0.418383i	0.920150	−	0.391565i	$-0.128066\pi$
$631$	8.38118	+	10.5097i	0.333650	+	0.418383i	−0.586501	+	0.809949i	$0.699495\pi$
$632$	52.9669	+	42.2397i	2.10691	+	1.68021i
$633$		0			0
$634$	−18.1017	+	22.6988i	−0.718911	+	0.901485i
$635$	−0.337962	+	1.48071i	−0.0134116	+	0.0587602i
$636$		0			0
$637$	6.68469	+	23.3393i	0.264857	+	0.924737i
$638$			2.89026i			0.114427i
$639$		0			0
$640$	−6.67439	−	5.32265i	−0.263829	−	0.210396i
$641$	−5.47326	+	11.3653i	−0.216181	+	0.448904i	−0.980653	−	0.195752i	$-0.937285\pi$
$641$	−5.47326	+	11.3653i	−0.216181	+	0.448904i	0.764473	+	0.644656i	$0.222999\pi$
$642$		0			0
$643$	−23.8248	+	18.9996i	−0.939557	+	0.749271i	−0.968163	−	0.250319i	$-0.919464\pi$
$643$	−23.8248	+	18.9996i	−0.939557	+	0.749271i	0.0286066	+	0.999591i	$0.490893\pi$
$644$	5.06468	+	36.0772i	0.199576	+	1.42164i
$645$		0			0
$646$	−9.99700	−	43.7997i	−0.393327	−	1.72328i
$647$	−20.1221	−	25.2324i	−0.791083	−	0.991986i	−0.999902	−	0.0140318i	$-0.995533\pi$
$647$	−20.1221	−	25.2324i	−0.791083	−	0.991986i	0.208819	−	0.977954i	$-0.433038\pi$
$648$		0			0
$649$	−0.204111	−	0.423840i	−0.00801204	−	0.0166372i
$650$	9.13487	−	40.0225i	0.358299	−	1.56981i
$651$		0			0
$652$	−4.54604	−	19.9175i	−0.178037	−	0.780029i
$653$	1.52294	−	1.21451i	0.0595973	−	0.0475273i	−0.593238	−	0.805027i	$-0.702151\pi$
$653$	1.52294	−	1.21451i	0.0595973	−	0.0475273i	0.652835	+	0.757500i	$0.273579\pi$
$654$		0			0
$655$	7.63452			0.298305
$656$	11.9346			0.465969
$657$		0			0
$658$	15.3331	+	22.9862i	0.597745	+	0.896094i
$659$	12.6617	−	26.2923i	0.493230	−	1.02420i	−0.494665	−	0.869084i	$-0.664709\pi$
$659$	12.6617	−	26.2923i	0.493230	−	1.02420i	0.987896	−	0.155120i	$-0.0495764\pi$
$660$		0			0
$661$	−18.6240	+	4.25081i	−0.724390	+	0.165337i	−0.568790	−	0.822483i	$-0.692588\pi$
$661$	−18.6240	+	4.25081i	−0.724390	+	0.165337i	−0.155600	+	0.987820i	$0.549731\pi$
$662$	15.5100	−	3.54006i	0.602813	−	0.137588i
$663$		0			0
$664$	−34.1798	+	70.9752i	−1.32644	+	2.75437i
$665$	3.57485	−	1.36141i	0.138627	−	0.0527933i
$666$		0			0
$667$	−14.2275			−0.550890
$668$	−49.0297			−1.89702
$669$		0			0
$670$	3.73002	−	2.97459i	0.144103	−	0.114919i
$671$	−0.660563	−	2.89412i	−0.0255008	−	0.111726i
$672$		0			0
$673$	−3.66267	+	16.0472i	−0.141186	+	0.618575i	0.853975	+	0.520314i	$0.174185\pi$
$673$	−3.66267	+	16.0472i	−0.141186	+	0.618575i	−0.995161	+	0.0982609i	$0.968672\pi$
$674$	−25.8478	−	53.6735i	−0.995620	−	2.06743i
$675$		0			0
$676$	−2.49605	−	3.12995i	−0.0960020	−	0.120383i
$677$	8.67246	+	37.9965i	0.333310	+	1.46032i	0.812679	+	0.582712i	$0.198008\pi$
$677$	8.67246	+	37.9965i	0.333310	+	1.46032i	−0.479369	+	0.877613i	$0.659135\pi$
$678$		0			0
$679$	28.8933	+	17.0740i	1.10882	+	0.655239i
$680$	−11.1411	+	8.88476i	−0.427243	+	0.340715i
$681$		0			0
$682$	1.76580	−	3.66672i	0.0676160	−	0.140406i
$683$	22.4726	+	17.9213i	0.859889	+	0.685739i	0.950694	−	0.310130i	$-0.100373\pi$
$683$	22.4726	+	17.9213i	0.859889	+	0.685739i	−0.0908050	+	0.995869i	$0.528944\pi$
$684$		0			0
$685$		−	6.42527i		−	0.245497i
$686$	−44.3443	−	11.5490i	−1.69307	−	0.440943i
$687$		0			0
$688$	11.7670	−	51.5546i	0.448613	−	1.96550i
$689$	17.7854	−	22.3022i	0.677572	−	0.849648i
$690$		0			0
$691$	12.0241	+	9.58891i	0.457419	+	0.364779i	0.824925	−	0.565242i	$-0.191217\pi$
$691$	12.0241	+	9.58891i	0.457419	+	0.364779i	−0.367507	+	0.930021i	$0.619788\pi$
$692$	63.2628	+	79.3290i	2.40489	+	3.01564i
$693$		0			0
$694$	−41.6830	+	52.2688i	−1.58226	+	1.98410i
$695$	0.357736	−	0.0816509i	0.0135697	−	0.00309720i
$696$		0			0
$697$	−3.26696	+	14.3135i	−0.123745	+	0.542163i
$698$	−6.28210	+	3.02530i	−0.237781	+	0.114509i
$699$		0			0
$700$	37.8822	+	35.8702i	1.43181	+	1.35577i
$701$	−42.5887	+	9.72059i	−1.60855	+	0.367142i	−0.930043	−	0.367450i	$-0.880231\pi$
$701$	−42.5887	+	9.72059i	−1.60855	+	0.367142i	−0.678509	+	0.734592i	$0.737374\pi$
$702$		0			0
$703$	10.2175	+	21.2168i	0.385360	+	0.800208i
$704$		−	1.76005i		−	0.0663345i
$705$		0			0
$706$	−4.45096	−	9.24252i	−0.167514	−	0.347847i
$707$	−14.0207	−	36.8161i	−0.527303	−	1.38461i
$708$		0			0
$709$	38.6916	+	18.6329i	1.45309	+	0.699773i	0.983129	−	0.182912i	$-0.0585522\pi$
$709$	38.6916	+	18.6329i	1.45309	+	0.699773i	0.469965	+	0.882685i	$0.344267\pi$
$710$	0.577220	+	2.52897i	0.0216627	+	0.0949105i
$711$		0			0
$712$	37.9903	−	78.8877i	1.42375	−	2.95644i
$713$	18.0496	+	8.69223i	0.675963	+	0.325527i
$714$		0			0
$715$	−0.398451	+	0.191884i	−0.0149012	+	0.00717605i
$716$		−	70.7112i		−	2.64260i
$717$		0			0
$718$	−11.0595	+	5.32597i	−0.412737	+	0.198763i
$719$	9.64893	+	12.0994i	0.359844	+	0.451231i	0.928493	−	0.371350i	$-0.121105\pi$
$719$	9.64893	+	12.0994i	0.359844	+	0.451231i	−0.568649	+	0.822581i	$0.692534\pi$
$720$		0			0
$721$	32.5969	−	12.4139i	1.21397	−	0.462318i
$722$	22.5009	+	5.13569i	0.837399	+	0.191131i
$723$		0			0
$724$	−50.9069	−	11.6192i	−1.89194	−	0.431823i
$725$	−15.9291	+	12.7031i	−0.591593	+	0.471780i
$726$		0			0
$727$	25.4859	+	20.3243i	0.945220	+	0.753788i	0.969289	−	0.245923i	$-0.0790909\pi$
$727$	25.4859	+	20.3243i	0.945220	+	0.753788i	−0.0240697	+	0.999710i	$0.507662\pi$
$728$	−47.7070	+	6.69731i	−1.76814	+	0.248219i
$729$		0			0
$730$	3.08964	−	3.87428i	0.114353	−	0.143394i
$731$	58.6097	+	28.2249i	2.16776	+	1.04394i
$732$		0			0
$733$	−14.8936	−	3.39937i	−0.550108	−	0.125559i	−0.0615726	−	0.998103i	$-0.519612\pi$
$733$	−14.8936	−	3.39937i	−0.550108	−	0.125559i	−0.488535	+	0.872544i	$0.662469\pi$
$734$	26.4178			0.975099
$735$		0			0
$736$	−4.15195			−0.153043
$737$	1.10909	+	0.253142i	0.0408538	+	0.00932461i
$738$		0			0
$739$	−34.9615	−	16.8366i	−1.28608	−	0.619343i	−0.339134	−	0.940738i	$-0.610134\pi$
$739$	−34.9615	−	16.8366i	−1.28608	−	0.619343i	−0.946945	+	0.321395i	$0.895848\pi$
$740$	9.04677	−	11.3443i	0.332566	−	0.417024i
$741$		0			0
$742$	19.1619	+	50.3162i	0.703456	+	1.84716i
$743$	4.76166	+	3.79730i	0.174688	+	0.139309i	0.706931	−	0.707283i	$-0.250079\pi$
$743$	4.76166	+	3.79730i	0.174688	+	0.139309i	−0.532243	+	0.846592i	$0.678651\pi$
$744$		0			0
$745$	−1.55607	+	1.24092i	−0.0570098	+	0.0454638i
$746$	9.73987	+	2.22306i	0.356602	+	0.0813921i
$747$		0			0
$748$	−6.43517	−	1.46879i	−0.235293	−	0.0537041i
$749$	4.20351	−	13.1531i	0.153593	−	0.480602i
$750$		0			0
$751$	6.41375	+	8.04259i	0.234041	+	0.293478i	0.884958	−	0.465671i	$-0.154187\pi$
$751$	6.41375	+	8.04259i	0.234041	+	0.293478i	−0.650917	+	0.759149i	$0.725615\pi$
$752$	−18.0487	+	8.69182i	−0.658170	+	0.316958i
$753$		0			0
$754$		−	36.5470i		−	1.33096i
$755$	9.55068	−	4.59937i	0.347585	−	0.167388i
$756$		0			0
$757$	−8.52729	−	4.10652i	−0.309929	−	0.149254i	0.272453	−	0.962169i	$-0.412165\pi$
$757$	−8.52729	−	4.10652i	−0.309929	−	0.149254i	−0.582382	+	0.812915i	$0.697879\pi$
$758$	15.3580	−	31.8911i	0.557826	−	1.15834i
$759$		0			0
$760$	1.68907	+	7.40032i	0.0612692	+	0.268438i
$761$	−13.6168	−	6.55753i	−0.493610	−	0.237710i	0.170482	−	0.985361i	$-0.445468\pi$
$761$	−13.6168	−	6.55753i	−0.493610	−	0.237710i	−0.664092	+	0.747651i	$0.731182\pi$
$762$		0			0
$763$	1.64574	+	1.55834i	0.0595799	+	0.0564155i
$764$	−14.2061	−	29.4992i	−0.513957	−	1.06724i
$765$		0			0
$766$		−	25.0156i		−	0.903850i
$767$	2.58095	+	5.35940i	0.0931927	+	0.193517i
$768$		0			0
$769$	28.0448	−	6.40104i	1.01132	−	0.230827i	0.315410	−	0.948956i	$-0.397858\pi$
$769$	28.0448	−	6.40104i	1.01132	−	0.230827i	0.695911	+	0.718128i	$0.255001\pi$
$770$	0.0708055	−	0.831721i	0.00255165	−	0.0299731i
$771$		0			0
$772$	−7.76402	+	3.73896i	−0.279433	+	0.134568i
$773$	0.349947	−	1.53322i	0.0125867	−	0.0551460i	−0.968245	−	0.250005i	$-0.919568\pi$
$773$	0.349947	−	1.53322i	0.0125867	−	0.0551460i	0.980831	+	0.194859i	$0.0624249\pi$
$774$		0			0
$775$	27.9693	−	6.38382i	1.00469	−	0.229313i
$776$	−41.5218	+	52.0666i	−1.49054	+	1.86908i
$777$		0			0
$778$	−58.4448	−	73.2875i	−2.09535	−	2.62748i
$779$	6.11432	+	4.87601i	0.219068	+	0.174701i
$780$		0			0
$781$	−0.385652	+	0.483592i	−0.0137997	+	0.0173043i
$782$	10.7384	−	47.0479i	0.384003	−	1.68243i
$783$		0			0
$784$	12.7613	−	30.6737i	0.455762	−	1.09549i
$785$		−	4.04360i		−	0.144322i
$786$		0			0
$787$	−19.5376	−	15.5807i	−0.696441	−	0.555393i	0.210012	−	0.977699i	$-0.432650\pi$
$787$	−19.5376	−	15.5807i	−0.696441	−	0.555393i	−0.906454	+	0.422305i	$0.861221\pi$
$788$	37.0847	−	77.0072i	1.32109	−	2.74327i
$789$		0			0
$790$	11.6050	−	9.25468i	0.412887	−	0.329267i
$791$	−12.6979	+	39.7324i	−0.451484	+	1.41272i
$792$		0			0
$793$	8.35274	+	36.5957i	0.296614	+	1.29955i
$794$	−1.56857	−	1.96693i	−0.0556666	−	0.0698037i
$795$		0			0
$796$	−5.44201	−	11.3005i	−0.192887	−	0.400534i
$797$	0.308597	−	1.35205i	0.0109311	−	0.0478922i	−0.969168	−	0.246400i	$-0.920752\pi$
$797$	0.308597	−	1.35205i	0.0109311	−	0.0478922i	0.980099	+	0.198508i	$0.0636095\pi$
$798$		0			0
$799$	−5.48369	−	24.0256i	−0.193999	−	0.849965i
$800$	−4.64855	+	3.70709i	−0.164351	+	0.131065i
$801$		0			0
$802$	−66.5320			−2.34933
$803$	1.18161			0.0416980
$804$		0			0
$805$	4.09418	+	0.348543i	0.144301	+	0.0122845i
$806$	−22.3283	+	46.3652i	−0.786481	+	1.63314i
$807$		0			0
$808$	76.2133	−	17.3952i	2.68117	−	0.611960i
$809$	3.22034	−	0.735021i	0.113221	−	0.0258420i	−0.165535	−	0.986204i	$-0.552935\pi$
$809$	3.22034	−	0.735021i	0.113221	−	0.0258420i	0.278756	+	0.960362i	$0.410078\pi$
$810$		0			0
$811$	−6.77950	+	14.0778i	−0.238061	+	0.494338i	−0.985432	−	0.170068i	$-0.945601\pi$
$811$	−6.77950	+	14.0778i	−0.238061	+	0.494338i	0.747372	+	0.664406i	$0.231315\pi$
$812$	39.9857	+	23.6288i	1.40322	+	0.829209i
$813$		0			0
$814$	5.13865			0.180110
$815$	−2.30423			−0.0807138
$816$		0			0
$817$	27.0916	−	21.6048i	0.947815	−	0.755857i
$818$	12.4724	+	54.6452i	0.436088	+	1.91063i
$819$		0			0
$820$	1.07226	−	4.69787i	0.0374449	−	0.164057i
$821$	−6.50174	−	13.5010i	−0.226912	−	0.471188i	0.756165	−	0.654382i	$-0.227071\pi$
$821$	−6.50174	−	13.5010i	−0.226912	−	0.471188i	−0.983077	+	0.183193i	$0.941357\pi$
$822$		0			0
$823$	13.2759	+	16.6474i	0.462768	+	0.580292i	0.957384	−	0.288819i	$-0.0932627\pi$
$823$	13.2759	+	16.6474i	0.462768	+	0.580292i	−0.494616	+	0.869112i	$0.664691\pi$
$824$	15.4017	+	67.4791i	0.536542	+	2.35075i
$825$		0			0
$826$	−11.1871	−	0.952376i	−0.389250	−	0.0331374i
$827$	−4.99290	+	3.98170i	−0.173620	+	0.138457i	−0.706444	−	0.707768i	$-0.749702\pi$
$827$	−4.99290	+	3.98170i	−0.173620	+	0.138457i	0.532825	+	0.846226i	$0.321131\pi$
$828$		0			0
$829$	−4.74248	+	9.84785i	−0.164713	+	0.342030i	−0.966946	−	0.254981i	$-0.917931\pi$
$829$	−4.74248	+	9.84785i	−0.164713	+	0.342030i	0.802233	+	0.597011i	$0.203645\pi$
$830$	13.4943	+	10.7613i	0.468394	+	0.373532i
$831$		0			0
$832$			22.2556i			0.771575i
$833$	33.2945	+	23.7016i	1.15359	+	0.821210i
$834$		0			0
$835$	−1.23054	+	5.39133i	−0.0425845	+	0.186575i
$836$	−2.19219	+	2.74892i	−0.0758186	+	0.0950735i
$837$		0			0
$838$	−52.0064	−	41.4737i	−1.79653	−	1.43269i
$839$	−1.05023	−	1.31694i	−0.0362578	−	0.0454659i	0.763372	−	0.645959i	$-0.223542\pi$
$839$	−1.05023	−	1.31694i	−0.0362578	−	0.0454659i	−0.799630	+	0.600493i	$0.794971\pi$
$840$		0			0
$841$	6.77209	−	8.49193i	0.233520	−	0.292825i
$842$	−22.6347	+	5.16622i	−0.780043	+	0.178040i
$843$		0			0
$844$	−2.15928	+	9.46041i	−0.0743254	+	0.325641i
$845$	−0.406817	+	0.195913i	−0.0139949	+	0.00673960i
$846$		0			0
$847$	−24.0454	+	16.0397i	−0.826211	+	0.551129i
$848$	−38.0567	+	8.68619i	−1.30687	+	0.298285i
$849$		0			0
$850$	−29.9842	−	62.2628i	−1.02845	−	2.13560i
$851$			25.2953i			0.867110i
$852$		0			0
$853$	4.35887	+	9.05129i	0.149245	+	0.309910i	0.962166	−	0.272463i	$-0.0878383\pi$
$853$	4.35887	+	9.05129i	0.149245	+	0.309910i	−0.812921	+	0.582374i	$0.802124\pi$
$854$	−67.4872	−	21.5679i	−2.30936	−	0.738037i
$855$		0			0
$856$	24.6868	+	11.8885i	0.843778	+	0.406342i
$857$	11.5103	+	50.4298i	0.393183	+	1.72265i	0.653325	+	0.757077i	$0.273373\pi$
$857$	11.5103	+	50.4298i	0.393183	+	1.72265i	−0.260142	+	0.965570i	$0.583769\pi$
$858$		0			0
$859$	−0.668565	+	1.38829i	−0.0228111	+	0.0473678i	−0.912063	−	0.410050i	$-0.865511\pi$
$859$	−0.668565	+	1.38829i	−0.0228111	+	0.0473678i	0.889252	+	0.457418i	$0.151226\pi$
$860$	−19.2364	−	9.26378i	−0.655957	−	0.315892i
$861$		0			0
$862$	−56.1320	+	27.0318i	−1.91186	+	0.920705i
$863$			8.35209i			0.284308i	0.989845	+	0.142154i	$0.0454029\pi$
$863$			8.35209i			0.284308i	−0.989845	+	0.142154i	$0.954597\pi$
$864$		0			0
$865$	10.3108	−	4.96543i	0.350578	−	0.168830i
$866$	−54.6713	−	68.5556i	−1.85780	−	2.32961i
$867$		0			0
$868$	−36.2917	−	54.4058i	−1.23182	−	1.84665i
$869$	3.45064	+	0.787586i	0.117055	+	0.0267170i
$870$		0			0
$871$	−14.0243	−	3.20095i	−0.475194	−	0.108460i
$872$	−3.51620	+	2.80408i	−0.119074	+	0.0949581i
$873$		0			0
$874$	−20.0975	−	16.0272i	−0.679808	−	0.542129i
$875$	10.0113	−	6.67808i	0.338443	−	0.225760i
$876$		0			0
$877$	4.33980	−	5.44194i	0.146545	−	0.183761i	−0.703141	−	0.711050i	$-0.748220\pi$
$877$	4.33980	−	5.44194i	0.146545	−	0.183761i	0.849686	+	0.527289i	$0.176791\pi$
$878$	−24.3176	−	11.7107i	−0.820678	−	0.395218i
$879$		0			0
$880$	0.590011	+	0.134666i	0.0198893	+	0.00453960i
$881$	7.32559			0.246805			0.123403	−	0.992357i	$-0.460619\pi$
$881$	7.32559			0.246805			0.123403	+	0.992357i	$0.460619\pi$
$882$		0			0
$883$	−22.5244			−0.758006			−0.379003	−	0.925395i	$-0.623733\pi$
$883$	−22.5244			−0.758006			−0.379003	+	0.925395i	$0.623733\pi$
$884$	81.3719	+	18.5726i	2.73683	+	0.624664i
$885$		0			0
$886$	14.9545	+	7.20170i	0.502406	+	0.241946i
$887$	−11.5791	+	14.5198i	−0.388790	+	0.487527i	−0.937254	−	0.348647i	$-0.886641\pi$
$887$	−11.5791	+	14.5198i	−0.388790	+	0.487527i	0.548464	+	0.836174i	$0.315213\pi$
$888$		0			0
$889$	−0.733178	+	8.61232i	−0.0245900	+	0.288848i
$890$	−14.9987	−	11.9610i	−0.502757	−	0.400935i
$891$		0			0
$892$	−88.3220	+	70.4344i	−2.95724	+	2.35832i
$893$	−12.7978	−	2.92102i	−0.428263	−	0.0977481i
$894$		0			0
$895$	−7.77544	−	1.77469i	−0.259904	−	0.0593215i
$896$	−41.8264	−	24.7166i	−1.39732	−	0.825723i
$897$		0			0
$898$	−0.0212333	−	0.0266258i	−0.000708566	−	0.000888513i
$899$	23.0112	−	11.0816i	0.767467	−	0.369593i
$900$		0			0
$901$		−	48.0201i		−	1.59978i
$902$	1.53753	−	0.740435i	0.0511941	−	0.0246538i
$903$		0			0
$904$	−74.5733	−	35.9126i	−2.48027	−	1.19444i
$905$	−2.55530	+	5.30614i	−0.0849411	+	0.176382i
$906$		0			0
$907$	3.11869	+	13.6639i	0.103554	+	0.453701i	0.999946	+	0.0104375i	$0.00332241\pi$
$907$	3.11869	+	13.6639i	0.103554	+	0.453701i	−0.896391	+	0.443264i	$0.853820\pi$
$908$	−33.7101	−	16.2339i	−1.11871	−	0.538742i
$909$		0			0
$910$	−0.895326	+	10.5170i	−0.0296798	+	0.348635i
$911$	−0.300343	−	0.623669i	−0.00995082	−	0.0206631i	0.895934	−	0.444187i	$-0.146507\pi$
$911$	−0.300343	−	0.623669i	−0.00995082	−	0.0206631i	−0.905885	+	0.423524i	$0.860793\pi$
$912$		0			0
$913$			4.11559i			0.136206i
$914$	9.59777	+	19.9300i	0.317466	+	0.659225i
$915$		0			0
$916$	−26.2856	+	5.99953i	−0.868502	+	0.198230i
$917$	43.0263	−	6.04023i	1.42085	−	0.199466i
$918$		0			0
$919$	20.3863	−	9.81750i	0.672480	−	0.323850i	−0.0662961	−	0.997800i	$-0.521118\pi$
$919$	20.3863	−	9.81750i	0.672480	−	0.323850i	0.738777	+	0.673950i	$0.235404\pi$
$920$	−1.81434	+	7.94912i	−0.0598169	+	0.262075i
$921$		0			0
$922$	66.2242	−	15.1152i	2.18098	−	0.497794i
$923$	4.87652	−	6.11496i	0.160513	−	0.201276i
$924$		0			0
$925$	22.5850	+	28.3207i	0.742590	+	0.931178i
$926$	−25.6558	−	20.4598i	−0.843102	−	0.672352i
$927$		0			0
$928$	−3.30030	+	4.13845i	−0.108338	+	0.135851i
$929$	−2.08686	+	9.14312i	−0.0684675	+	0.299976i	−0.997555	−	0.0698839i	$-0.977737\pi$
$929$	−2.08686	+	9.14312i	−0.0684675	+	0.299976i	0.929088	+	0.369860i	$0.120594\pi$
$930$		0			0
$931$	19.0699	−	10.5009i	0.624991	−	0.344154i
$932$			1.48813i			0.0487453i
$933$		0			0
$934$	41.2191	+	32.8712i	1.34873	+	1.07558i
$935$	−0.323017	+	0.670752i	−0.0105638	+	0.0219359i
$936$		0			0
$937$	30.2732	−	24.1421i	0.988982	−	0.788687i	0.0115496	−	0.999933i	$-0.496324\pi$
$937$	30.2732	−	24.1421i	0.988982	−	0.788687i	0.977433	+	0.211246i	$0.0677522\pi$
$938$	18.6681	−	19.7152i	0.609535	−	0.643724i
$939$		0			0
$940$	1.79981	+	7.88550i	0.0587035	+	0.257197i
$941$	−32.7472	−	41.0637i	−1.06753	−	1.33864i	−0.937834	−	0.347084i	$-0.887172\pi$
$941$	−32.7472	−	41.0637i	−1.06753	−	1.33864i	−0.129694	−	0.991554i	$-0.541400\pi$
$942$		0			0
$943$	3.64483	+	7.56856i	0.118692	+	0.246466i
$944$	1.81134	−	7.93600i	0.0589541	−	0.258295i
$945$		0			0
$946$	−1.68256	−	7.37178i	−0.0547048	−	0.239677i
$947$	11.7143	−	9.34187i	0.380665	−	0.303570i	−0.414400	−	0.910095i	$-0.636008\pi$
$947$	11.7143	−	9.34187i	0.380665	−	0.303570i	0.795064	+	0.606525i	$0.207437\pi$
$948$		0			0
$949$	−14.9413			−0.485014
$950$	−36.8112			−1.19431
$951$		0			0
$952$	−55.7594	+	58.8870i	−1.80717	+	1.90854i
$953$	−1.61247	+	3.34833i	−0.0522330	+	0.108463i	−0.925452	−	0.378866i	$-0.876314\pi$
$953$	−1.61247	+	3.34833i	−0.0522330	+	0.108463i	0.873219	+	0.487328i	$0.162029\pi$
$954$		0			0
$955$	−3.60029	+	0.821743i	−0.116503	+	0.0265910i
$956$	−66.8702	+	15.2627i	−2.16274	+	0.493630i
$957$		0			0
$958$	−8.16785	+	16.9607i	−0.263891	+	0.547976i
$959$	−5.08350	−	36.2113i	−0.164155	−	1.16932i
$960$		0			0
$961$	−4.96337			−0.160109
$962$	−64.9776			−2.09496
$963$		0			0
$964$	−55.1099	+	43.9487i	−1.77497	+	1.41549i
$965$	0.216278	+	0.947576i	0.00696224	+	0.0305036i
$966$		0			0
$967$	−12.0131	+	52.6327i	−0.386314	+	1.69255i	0.290888	+	0.956757i	$0.406049\pi$
$967$	−12.0131	+	52.6327i	−0.386314	+	1.69255i	−0.677203	+	0.735797i	$0.736808\pi$
$968$	−24.8855	−	51.6752i	−0.799849	−	1.66090i
$969$		0			0
$970$	9.09737	+	11.4077i	0.292099	+	0.366281i
$971$	−5.17843	−	22.6882i	−0.166184	−	0.728099i	−0.987499	−	0.157624i	$-0.949617\pi$
$971$	−5.17843	−	22.6882i	−0.166184	−	0.728099i	0.821315	−	0.570474i	$-0.193241\pi$
$972$		0			0
$973$	1.95151	−	0.743196i	0.0625627	−	0.0238258i
$974$	29.3748	−	23.4256i	0.941228	−	0.750604i
$975$		0			0
$976$	22.2871	−	46.2797i	0.713393	−	1.48138i
$977$	7.02179	+	5.59969i	0.224647	+	0.179150i	0.729345	−	0.684146i	$-0.239825\pi$
$977$	7.02179	+	5.59969i	0.224647	+	0.179150i	−0.504698	+	0.863296i	$0.668396\pi$
$978$		0			0
$979$		−	4.57441i		−	0.146199i
$980$	−10.9277	−	7.77915i	−0.349072	−	0.248496i
$981$		0			0
$982$	0.969850	−	4.24919i	0.0309491	−	0.135597i
$983$	−33.6961	+	42.2536i	−1.07474	+	1.34768i	−0.140887	+	0.990026i	$0.544995\pi$
$983$	−33.6961	+	42.2536i	−1.07474	+	1.34768i	−0.933853	+	0.357656i	$0.883576\pi$
$984$		0			0
$985$	−7.53702	−	6.01057i	−0.240149	−	0.191513i
$986$	−38.3591	−	48.1008i	−1.22160	−	1.53184i
$987$		0			0
$988$	27.7200	−	34.7598i	0.881890	−	1.10586i
$989$	36.2879	−	8.28249i	1.15389	−	0.263368i
$990$		0			0
$991$	−8.02693	+	35.1683i	−0.254984	+	1.11716i	0.671554	+	0.740956i	$0.265627\pi$
$991$	−8.02693	+	35.1683i	−0.254984	+	1.11716i	−0.926538	+	0.376202i	$0.877230\pi$
$992$	6.71529	−	3.23391i	0.213211	−	0.102677i
$993$		0			0
$994$	5.25393	+	13.7960i	0.166644	+	0.437582i
$995$	−1.37919	+	0.314791i	−0.0437232	+	0.00997953i
$996$		0			0
$997$	18.8351	+	39.1115i	0.596514	+	1.23867i	0.952602	+	0.304221i	$0.0983960\pi$
$997$	18.8351	+	39.1115i	0.596514	+	1.23867i	−0.356088	+	0.934452i	$0.615890\pi$
$998$		−	77.2080i		−	2.44398i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.377.19	yes	120
3.2	odd	2	inner	441.2.w.a.377.2	yes	120
49.13	odd	14	inner	441.2.w.a.62.2	✓	120
147.62	even	14	inner	441.2.w.a.62.19	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.2	✓	120	49.13	odd	14	inner
441.2.w.a.62.19	yes	120	147.62	even	14	inner
441.2.w.a.377.2	yes	120	3.2	odd	2	inner
441.2.w.a.377.19	yes	120	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(2.41221 + 0.550570i) q^{2} +(3.71367 + 1.78841i) q^{4} +(0.289860 - 0.363473i) q^{5} +(1.34601 - 2.27777i) q^{7} +(4.10462 + 3.27333i) q^{8} +O(q^{10})\)	\(q+(2.41221 + 0.550570i) q^{2} +(3.71367 + 1.78841i) q^{4} +(0.289860 - 0.363473i) q^{5} +(1.34601 - 2.27777i) q^{7} +(4.10462 + 3.27333i) q^{8} +(0.899319 - 0.717183i) q^{10} +(0.267404 + 0.0610333i) q^{11} +(-3.38129 - 0.771758i) q^{13} +(4.50093 - 4.75339i) q^{14} +(2.95912 + 3.71062i) q^{16} +(-5.26026 + 2.53321i) q^{17} +3.10999i q^{19} +(1.72648 - 0.831431i) q^{20} +(0.611431 + 0.294450i) q^{22} +(-1.44944 + 3.00980i) q^{23} +(1.06451 + 4.66393i) q^{25} +(-7.73147 - 3.72328i) q^{26} +(9.07224 - 6.05169i) q^{28} +(1.84788 + 3.83716i) q^{29} -5.99695i q^{31} +(0.539260 + 1.11978i) q^{32} +(-14.0835 + 3.21448i) q^{34} +(-0.437754 - 1.14947i) q^{35} +(6.82215 - 3.28537i) q^{37} +(-1.71227 + 7.50194i) q^{38} +(2.37953 - 0.543112i) q^{40} +(1.56785 - 1.96602i) q^{41} +(-6.94691 - 8.71115i) q^{43} +(0.883900 + 0.704887i) q^{44} +(-5.15346 + 6.46224i) q^{46} +(-0.939237 + 4.11506i) q^{47} +(-3.37651 - 6.13182i) q^{49} +11.8364i q^{50} +(-11.1768 - 8.91320i) q^{52} +(-3.56861 + 7.41029i) q^{53} +(0.0996937 - 0.0795031i) q^{55} +(12.9808 - 4.94347i) q^{56} +(2.34484 + 10.2734i) q^{58} +(-1.06936 - 1.34094i) q^{59} +(-4.69592 - 9.75118i) q^{61} +(3.30174 - 14.4659i) q^{62} +(-1.42791 - 6.25608i) q^{64} +(-1.26061 + 1.00531i) q^{65} +4.14761 q^{67} -24.0653 q^{68} +(-0.423088 - 3.01378i) q^{70} +(-0.978461 + 2.03180i) q^{71} +(4.20001 - 0.958624i) q^{73} +(18.2653 - 4.16893i) q^{74} +(-5.56194 + 11.5495i) q^{76} +(0.498949 - 0.526935i) q^{77} +12.9042 q^{79} +2.20644 q^{80} +(4.86442 - 3.87924i) q^{82} +(3.33893 + 14.6288i) q^{83} +(-0.603986 + 2.64624i) q^{85} +(-11.9613 - 24.8378i) q^{86} +(0.897813 + 1.12582i) q^{88} +(-3.71116 - 16.2597i) q^{89} +(-6.30915 + 6.66303i) q^{91} +(-10.7655 + 8.58522i) q^{92} +(-4.53127 + 9.40927i) q^{94} +(1.13040 + 0.901461i) q^{95} +12.6849i q^{97} +(-4.76884 - 16.6502i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 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

Introduction

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