LMFDB - Embedded newform 441.2.w.a.62.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [441,2,Mod(62,441)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			62.20
Character	$\chi$	$=$	441.62
Dual form			441.2.w.a.377.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.63522 - 0.601472i) q^{2} +(4.78069 - 2.30226i) q^{4} +(-2.19013 - 2.74633i) q^{5} +(-1.96904 + 1.76717i) q^{7} +(6.98686 - 5.57183i) q^{8} +(-7.42332 - 5.91990i) q^{10} +(3.05696 - 0.697731i) q^{11} +(-1.21079 + 0.276355i) q^{13} +(-4.12595 + 5.84121i) q^{14} +(8.44394 - 10.5884i) q^{16} +(4.83058 + 2.32629i) q^{17} +4.49882i q^{19} +(-16.7931 - 8.08712i) q^{20} +(7.63610 - 3.67735i) q^{22} +(-0.787106 - 1.63444i) q^{23} +(-1.63309 + 7.15501i) q^{25} +(-3.02448 + 1.45651i) q^{26} +(-5.34487 + 12.9815i) q^{28} +(-4.22069 + 8.76436i) q^{29} -0.728724i q^{31} +(8.12821 - 16.8784i) q^{32} +(14.1289 + 3.22482i) q^{34} +(9.16569 + 1.53731i) q^{35} +(-5.31902 - 2.56150i) q^{37} +(2.70591 + 11.8554i) q^{38} +(-30.6042 - 6.98521i) q^{40} +(0.545593 + 0.684152i) q^{41} +(-3.56964 + 4.47618i) q^{43} +(13.0080 - 10.3735i) q^{44} +(-3.05727 - 3.83370i) q^{46} +(-0.00115370 - 0.00505470i) q^{47} +(0.754221 - 6.95925i) q^{49} +19.8373i q^{50} +(-5.15217 + 4.10872i) q^{52} +(-0.0443955 - 0.0921883i) q^{53} +(-8.61134 - 6.86731i) q^{55} +(-3.91101 + 23.3181i) q^{56} +(-5.85094 + 25.6347i) q^{58} +(7.83482 - 9.82456i) q^{59} +(-1.46794 + 3.04820i) q^{61} +(-0.438307 - 1.92035i) q^{62} +(5.24054 - 22.9603i) q^{64} +(3.41075 + 2.71998i) q^{65} +10.1225 q^{67} +28.4492 q^{68} +(25.0783 - 1.46176i) q^{70} +(-2.81417 - 5.84369i) q^{71} +(-6.12750 - 1.39856i) q^{73} +(-15.5575 - 3.55089i) q^{74} +(10.3574 + 21.5074i) q^{76} +(-4.78626 + 6.77602i) q^{77} -2.32787 q^{79} -47.5725 q^{80} +(1.84926 + 1.47473i) q^{82} +(3.48021 - 15.2478i) q^{83} +(-4.19084 - 18.3613i) q^{85} +(-6.71448 + 13.9428i) q^{86} +(17.4709 - 21.9078i) q^{88} +(-0.595133 + 2.60745i) q^{89} +(1.89573 - 2.68383i) q^{91} +(-7.52581 - 6.00164i) q^{92} +(-0.00608053 - 0.0126263i) q^{94} +(12.3553 - 9.85299i) q^{95} +1.74875i q^{97} +(-2.19826 - 18.7928i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{14}\right)$	$-1$

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 $

$2$	2.63522	−	0.601472i	1.86338	−	0.425305i	0.866159	−	0.499768i	$-0.166581\pi$
$2$	2.63522	−	0.601472i	1.86338	−	0.425305i	0.997224	+	0.0744632i	$0.0237243\pi$
$3$		0			0
$3$		0			0
$4$	4.78069	−	2.30226i	2.39034	−	1.15113i
$5$	−2.19013	−	2.74633i	−0.979455	−	1.22820i	−0.973611	−	0.228215i	$-0.926711\pi$
$5$	−2.19013	−	2.74633i	−0.979455	−	1.22820i	−0.00584467	−	0.999983i	$-0.501860\pi$
$6$		0			0
$7$	−1.96904	+	1.76717i	−0.744226	+	0.667927i
$7$	−1.96904	+	1.76717i	−0.744226	+	0.667927i
$8$	6.98686	−	5.57183i	2.47023	−	1.96994i
$9$		0			0
$10$	−7.42332	−	5.91990i	−2.34746	−	1.87204i
$11$	3.05696	−	0.697731i	0.921708	−	0.210374i	0.264764	−	0.964313i	$-0.414706\pi$
$11$	3.05696	−	0.697731i	0.921708	−	0.210374i	0.656944	+	0.753939i	$0.271849\pi$
$12$		0			0
$13$	−1.21079	+	0.276355i	−0.335813	+	0.0766471i	−0.387102	−	0.922037i	$-0.626524\pi$
$13$	−1.21079	+	0.276355i	−0.335813	+	0.0766471i	0.0512894	+	0.998684i	$0.483667\pi$
$14$	−4.12595	+	5.84121i	−1.10271	+	1.56113i
$15$		0			0
$16$	8.44394	−	10.5884i	2.11098	−	2.64709i
$17$	4.83058	+	2.32629i	1.17159	+	0.564207i	0.915450	−	0.402433i	$-0.131835\pi$
$17$	4.83058	+	2.32629i	1.17159	+	0.564207i	0.256139	+	0.966640i	$0.417550\pi$
$18$		0			0
$19$			4.49882i			1.03210i	0.856559	+	0.516050i	$0.172598\pi$
$19$			4.49882i			1.03210i	−0.856559	+	0.516050i	$0.827402\pi$
$20$	−16.7931	−	8.08712i	−3.75505	−	1.80834i
$21$		0			0
$22$	7.63610	−	3.67735i	1.62802	−	0.784014i
$23$	−0.787106	−	1.63444i	−0.164123	−	0.340805i	0.802646	−	0.596455i	$-0.203425\pi$
$23$	−0.787106	−	1.63444i	−0.164123	−	0.340805i	−0.966769	+	0.255650i	$0.917710\pi$
$24$		0			0
$25$	−1.63309	+	7.15501i	−0.326617	+	1.43100i
$26$	−3.02448	+	1.45651i	−0.593150	+	0.285646i
$27$		0			0
$28$	−5.34487	+	12.9815i	−1.01009	+	2.45328i
$29$	−4.22069	+	8.76436i	−0.783763	+	1.62750i	−0.00515781	+	0.999987i	$0.501642\pi$
$29$	−4.22069	+	8.76436i	−0.783763	+	1.62750i	−0.778605	+	0.627514i	$0.784072\pi$
$30$		0			0
$31$		−	0.728724i		−	0.130883i	−0.997856	−	0.0654413i	$-0.979154\pi$
$31$		−	0.728724i		−	0.130883i	0.997856	−	0.0654413i	$-0.0208455\pi$
$32$	8.12821	−	16.8784i	1.43688	−	2.98371i
$33$		0			0
$34$	14.1289	+	3.22482i	2.42308	+	0.553052i
$35$	9.16569	+	1.53731i	1.54928	+	0.259852i
$36$		0			0
$37$	−5.31902	−	2.56150i	−0.874441	−	0.421109i	−0.0578500	−	0.998325i	$-0.518425\pi$
$37$	−5.31902	−	2.56150i	−0.874441	−	0.421109i	−0.816591	+	0.577217i	$0.804139\pi$
$38$	2.70591	+	11.8554i	0.438957	+	1.92320i
$39$		0			0
$40$	−30.6042	−	6.98521i	−4.83895	−	1.10446i
$41$	0.545593	+	0.684152i	0.0852073	+	0.106847i	0.822608	−	0.568609i	$-0.192518\pi$
$41$	0.545593	+	0.684152i	0.0852073	+	0.106847i	−0.737400	+	0.675456i	$0.763947\pi$
$42$		0			0
$43$	−3.56964	+	4.47618i	−0.544364	+	0.682611i	−0.975582	−	0.219637i	$-0.929513\pi$
$43$	−3.56964	+	4.47618i	−0.544364	+	0.682611i	0.431217	+	0.902248i	$0.358084\pi$
$44$	13.0080	−	10.3735i	1.96103	−	1.56387i
$45$		0			0
$46$	−3.05727	−	3.83370i	−0.450770	−	0.565248i
$47$	−0.00115370	−	0.00505470i	−0.000168285	−	0.000737304i	0.974844	−	0.222890i	$-0.0715489\pi$
$47$	−0.00115370	−	0.00505470i	−0.000168285	−	0.000737304i	−0.975012	+	0.222152i	$0.928692\pi$
$48$		0			0
$49$	0.754221	−	6.95925i	0.107746	−	0.994178i
$50$			19.8373i			2.80542i
$51$		0			0
$52$	−5.15217	+	4.10872i	−0.714478	+	0.569777i
$53$	−0.0443955	−	0.0921883i	−0.00609819	−	0.0126630i	0.897898	−	0.440205i	$-0.145094\pi$
$53$	−0.0443955	−	0.0921883i	−0.00609819	−	0.0126630i	−0.903996	+	0.427542i	$0.859380\pi$
$54$		0			0
$55$	−8.61134	−	6.86731i	−1.16115	−	0.925988i
$56$	−3.91101	+	23.3181i	−0.522631	+	3.11601i
$57$		0			0
$58$	−5.85094	+	25.6347i	−0.768267	+	3.36600i
$59$	7.83482	−	9.82456i	1.02001	−	1.27905i	0.0602600	−	0.998183i	$-0.480807\pi$
$59$	7.83482	−	9.82456i	1.02001	−	1.27905i	0.959747	−	0.280866i	$-0.0906216\pi$
$60$		0			0
$61$	−1.46794	+	3.04820i	−0.187950	+	0.390283i	−0.973557	−	0.228443i	$-0.926636\pi$
$61$	−1.46794	+	3.04820i	−0.187950	+	0.390283i	0.785607	+	0.618726i	$0.212351\pi$
$62$	−0.438307	−	1.92035i	−0.0556651	−	0.243885i
$63$		0			0
$64$	5.24054	−	22.9603i	0.655067	−	2.87004i
$65$	3.41075	+	2.71998i	0.423052	+	0.337373i
$66$		0			0
$67$	10.1225			1.23667			0.618333	−	0.785916i	$-0.287808\pi$
$67$	10.1225			1.23667			0.618333	+	0.785916i	$0.287808\pi$
$68$	28.4492			3.44997
$69$		0			0
$70$	25.0783	−	1.46176i	2.99743	−	0.174714i
$71$	−2.81417	−	5.84369i	−0.333981	−	0.693519i	0.664576	−	0.747221i	$-0.268612\pi$
$71$	−2.81417	−	5.84369i	−0.333981	−	0.693519i	−0.998557	+	0.0537020i	$0.982898\pi$
$72$		0			0
$73$	−6.12750	−	1.39856i	−0.717170	−	0.163689i	−0.151662	−	0.988432i	$-0.548463\pi$
$73$	−6.12750	−	1.39856i	−0.717170	−	0.163689i	−0.565508	+	0.824743i	$0.691320\pi$
$74$	−15.5575	−	3.55089i	−1.80852	−	0.412782i
$75$		0			0
$76$	10.3574	+	21.5074i	1.18808	+	2.46707i
$77$	−4.78626	+	6.77602i	−0.545445	+	0.772200i
$78$		0			0
$79$	−2.32787			−0.261906			−0.130953	−	0.991389i	$-0.541804\pi$
$79$	−2.32787			−0.261906			−0.130953	+	0.991389i	$0.541804\pi$
$80$	−47.5725			−5.31877
$81$		0			0
$82$	1.84926	+	1.47473i	0.204216	+	0.162857i
$83$	3.48021	−	15.2478i	0.382003	−	1.67366i	−0.309196	−	0.950998i	$-0.600060\pi$
$83$	3.48021	−	15.2478i	0.382003	−	1.67366i	0.691199	−	0.722665i	$-0.257083\pi$
$84$		0			0
$85$	−4.19084	−	18.3613i	−0.454560	−	1.99156i
$86$	−6.71448	+	13.9428i	−0.724041	+	1.50349i
$87$		0			0
$88$	17.4709	−	21.9078i	1.86240	−	2.33538i
$89$	−0.595133	+	2.60745i	−0.0630840	+	0.276389i	−0.996626	−	0.0820796i	$-0.973844\pi$
$89$	−0.595133	+	2.60745i	−0.0630840	+	0.276389i	0.933542	+	0.358469i	$0.116701\pi$
$90$		0			0
$91$	1.89573	−	2.68383i	0.198726	−	0.281342i
$92$	−7.52581	−	6.00164i	−0.784620	−	0.625714i
$93$		0			0
$94$	−0.00608053	−	0.0126263i	−0.000627158	−	0.00130231i
$95$	12.3553	−	9.85299i	1.26762	−	1.01090i
$96$		0			0
$97$			1.74875i			0.177558i	0.996051	+	0.0887792i	$0.0282965\pi$
$97$			1.74875i			0.177558i	−0.996051	+	0.0887792i	$0.971703\pi$
$98$	−2.19826	−	18.7928i	−0.222057	−	1.89836i
$99$		0			0
$100$	8.66541	+	37.9657i	0.866541	+	3.79657i
$101$	−2.74076	−	3.43681i	−0.272716	−	0.341975i	0.626547	−	0.779384i	$-0.284468\pi$
$101$	−2.74076	−	3.43681i	−0.272716	−	0.341975i	−0.899263	+	0.437409i	$0.855896\pi$
$102$		0			0
$103$	−13.1373	+	10.4766i	−1.29445	+	1.03229i	−0.297465	+	0.954733i	$0.596141\pi$
$103$	−13.1373	+	10.4766i	−1.29445	+	1.03229i	−0.996988	+	0.0775588i	$0.975287\pi$
$104$	−6.91982	+	8.67718i	−0.678544	+	0.850867i
$105$		0			0
$106$	−0.172441	−	0.216234i	−0.0167489	−	0.0210025i
$107$	−1.84795	−	0.421783i	−0.178648	−	0.0407753i	0.132261	−	0.991215i	$-0.457776\pi$
$107$	−1.84795	−	0.421783i	−0.178648	−	0.0407753i	−0.310909	+	0.950440i	$0.600633\pi$
$108$		0			0
$109$	1.28683	+	5.63798i	0.123256	+	0.540021i	0.998420	+	0.0561937i	$0.0178964\pi$
$109$	1.28683	+	5.63798i	0.123256	+	0.540021i	−0.875164	+	0.483827i	$0.839246\pi$
$110$	−26.8233	−	12.9174i	−2.55750	−	1.23163i
$111$		0			0
$112$	2.08500	+	35.7708i	0.197014	+	3.38002i
$113$	−18.6937	−	4.26671i	−1.75855	−	0.401378i	−0.783154	−	0.621827i	$-0.786391\pi$
$113$	−18.6937	−	4.26671i	−1.75855	−	0.401378i	−0.975398	+	0.220449i	$0.929248\pi$
$114$		0			0
$115$	−2.76486	+	5.74130i	−0.257825	+	0.535379i
$116$			51.6168i			4.79250i
$117$		0			0
$118$	14.7373	−	30.6023i	1.35668	−	2.81717i
$119$	−13.6225	+	3.95592i	−1.24878	+	0.362638i
$120$		0			0
$121$	−1.05249	+	0.506852i	−0.0956807	+	0.0460774i
$122$	−2.03493	+	8.91562i	−0.184234	+	0.807182i
$123$		0			0
$124$	−1.67771	−	3.48380i	−0.150663	−	0.312854i
$125$	7.40259	−	3.56490i	0.662108	−	0.318854i
$126$		0			0
$127$	−2.99505	−	1.44234i	−0.265767	−	0.127987i	0.296255	−	0.955109i	$-0.404262\pi$
$127$	−2.99505	−	1.44234i	−0.265767	−	0.127987i	−0.562022	+	0.827122i	$0.689977\pi$
$128$		−	26.1903i		−	2.31491i
$129$		0			0
$130$	10.6241	+	5.11629i	0.931794	+	0.448728i
$131$	−3.21181	+	4.02748i	−0.280617	+	0.351883i	−0.902086	−	0.431556i	$-0.857965\pi$
$131$	−3.21181	+	4.02748i	−0.280617	+	0.351883i	0.621469	+	0.783439i	$0.286536\pi$
$132$		0			0
$133$	−7.95017	−	8.85834i	−0.689368	−	0.768116i
$134$	26.6752	−	6.08843i	2.30438	−	0.525960i
$135$		0			0
$136$	46.7123	−	10.6618i	4.00554	−	0.914239i
$137$	5.70926	+	4.55298i	0.487775	+	0.388987i	0.836265	−	0.548325i	$-0.184734\pi$
$137$	5.70926	+	4.55298i	0.487775	+	0.388987i	−0.348491	+	0.937312i	$0.613306\pi$
$138$		0			0
$139$	8.69483	−	6.93389i	0.737486	−	0.588125i	−0.181045	−	0.983475i	$-0.557948\pi$
$139$	8.69483	−	6.93389i	0.737486	−	0.588125i	0.918531	+	0.395350i	$0.129377\pi$
$140$	47.3575	−	13.7524i	4.00244	−	1.16229i
$141$		0			0
$142$	−10.9308	−	13.7068i	−0.917292	−	1.15025i
$143$	−3.50852	+	1.68961i	−0.293397	+	0.141293i
$144$		0			0
$145$	33.3137	−	7.60364i	2.76655	−	0.631448i
$146$	−16.9885			−1.40598
$147$		0			0
$148$	−31.3258			−2.57496
$149$	13.9087	−	3.17456i	1.13944	−	0.260070i	0.389149	−	0.921175i	$-0.372769\pi$
$149$	13.9087	−	3.17456i	1.13944	−	0.260070i	0.750294	+	0.661105i	$0.229912\pi$
$150$		0			0
$151$	3.68761	−	1.77586i	0.300093	−	0.144517i	−0.277778	−	0.960645i	$-0.589598\pi$
$151$	3.68761	−	1.77586i	0.300093	−	0.144517i	0.577871	+	0.816128i	$0.303884\pi$
$152$	25.0666	+	31.4326i	2.03317	+	2.54952i
$153$		0			0
$154$	−8.53726	+	20.7351i	−0.687952	+	1.67088i
$155$	−2.00132	+	1.59600i	−0.160750	+	0.128194i
$156$		0			0
$157$	10.2787	+	8.19702i	0.820333	+	0.654194i	0.940965	−	0.338504i	$-0.109921\pi$
$157$	10.2787	+	8.19702i	0.820333	+	0.654194i	−0.120632	+	0.992697i	$0.538492\pi$
$158$	−6.13446	+	1.40015i	−0.488031	+	0.111390i
$159$		0			0
$160$	−64.1556	+	14.6431i	−5.07194	+	1.15764i
$161$	4.43818	+	1.82733i	0.349778	+	0.144014i
$162$		0			0
$163$	5.76384	−	7.22763i	0.451459	−	0.566112i	−0.503064	−	0.864249i	$-0.667794\pi$
$163$	5.76384	−	7.22763i	0.451459	−	0.566112i	0.954523	+	0.298138i	$0.0963654\pi$
$164$	4.18340	+	2.01462i	0.326669	+	0.157315i
$165$		0			0
$166$		−	42.2746i		−	3.28114i
$167$	−6.57511	−	3.16641i	−0.508797	−	0.245024i	0.161830	−	0.986819i	$-0.448261\pi$
$167$	−6.57511	−	3.16641i	−0.508797	−	0.245024i	−0.670627	+	0.741795i	$0.733975\pi$
$168$		0			0
$169$	−10.3230	+	4.97127i	−0.794073	+	0.382406i
$170$	−22.0876	−	45.8653i	−1.69404	−	3.51771i
$171$		0			0
$172$	−6.75999	+	29.6174i	−0.515444	+	2.25831i
$173$	7.94205	−	3.82469i	0.603823	−	0.290786i	−0.106887	−	0.994271i	$-0.534088\pi$
$173$	7.94205	−	3.82469i	0.603823	−	0.290786i	0.710710	+	0.703485i	$0.248374\pi$
$174$		0			0
$175$	−9.42852	−	16.9744i	−0.712729	−	1.28315i
$176$	18.4249	−	38.2598i	1.38883	−	2.88394i
$177$		0			0
$178$			7.22916i			0.541848i
$179$	5.12043	−	10.6327i	0.382719	−	0.794724i	−0.617250	−	0.786767i	$-0.711753\pi$
$179$	5.12043	−	10.6327i	0.382719	−	0.794724i	0.999968	−	0.00795628i	$-0.00253259\pi$
$180$		0			0
$181$	12.0574	+	2.75201i	0.896216	+	0.204555i	0.645731	−	0.763565i	$-0.276553\pi$
$181$	12.0574	+	2.75201i	0.896216	+	0.204555i	0.250485	+	0.968120i	$0.419410\pi$
$182$	3.38141	−	8.21271i	0.250647	−	0.608766i
$183$		0			0
$184$	−14.6062	−	7.03399i	−1.07679	−	0.518553i
$185$	4.61459	+	20.2178i	0.339271	+	1.48644i
$186$		0			0
$187$	16.3900	+	3.74091i	1.19856	+	0.273563i
$188$	−0.0171527	−	0.0215088i	−0.00125099	−	0.00156869i
$189$		0			0
$190$	26.6325	−	33.3961i	1.93213	−	2.42281i
$191$	−12.3610	+	9.85759i	−0.894413	+	0.713270i	−0.958627	−	0.284666i	$-0.908117\pi$
$191$	−12.3610	+	9.85759i	−0.894413	+	0.713270i	0.0642141	+	0.997936i	$0.479546\pi$
$192$		0			0
$193$	3.77084	+	4.72849i	0.271431	+	0.340364i	0.898801	−	0.438358i	$-0.144440\pi$
$193$	3.77084	+	4.72849i	0.271431	+	0.340364i	−0.627369	+	0.778722i	$0.715868\pi$
$194$	1.05182	+	4.60833i	0.0755164	+	0.330859i
$195$		0			0
$196$	−12.4163	−	35.0064i	−0.886878	−	2.50046i
$197$		−	15.4119i		−	1.09806i	−0.835804	−	0.549028i	$-0.814998\pi$
$197$		−	15.4119i		−	1.09806i	0.835804	−	0.549028i	$-0.185002\pi$
$198$		0			0
$199$	−11.6789	+	9.31358i	−0.827892	+	0.660222i	−0.942876	−	0.333145i	$-0.891890\pi$
$199$	−11.6789	+	9.31358i	−0.827892	+	0.660222i	0.114983	+	0.993367i	$0.463319\pi$
$200$	28.4564	+	59.0903i	2.01217	+	4.17832i
$201$		0			0
$202$	−9.28966	−	7.40826i	−0.653618	−	0.521243i
$203$	−7.17741	−	24.7160i	−0.503755	−	1.73473i
$204$		0			0
$205$	0.683992	−	2.99676i	0.0477720	−	0.209303i
$206$	−28.3182	+	35.5099i	−1.97302	+	2.47409i
$207$		0			0
$208$	−7.29769	+	15.1538i	−0.506004	+	1.05073i
$209$	3.13896	+	13.7527i	0.217127	+	0.951294i
$210$		0			0
$211$	0.543951	−	2.38321i	0.0374472	−	0.164067i	−0.952747	−	0.303765i	$-0.901756\pi$
$211$	0.543951	−	2.38321i	0.0374472	−	0.164067i	0.990194	+	0.139698i	$0.0446133\pi$
$212$	−0.424482	−	0.338513i	−0.0291536	−	0.0232492i
$213$		0			0
$214$	−5.12345			−0.350232
$215$	20.1111			1.37156
$216$		0			0
$217$	1.28778	+	1.43489i	0.0874201	+	0.0974063i
$218$	6.78218	+	14.0833i	0.459347	+	0.953844i
$219$		0			0
$220$	−56.9784	−	13.0049i	−3.84148	−	0.876794i
$221$	−6.49171	−	1.48169i	−0.436680	−	0.0996693i
$222$		0			0
$223$	−7.94696	−	16.5020i	−0.532168	−	1.10506i	−0.977742	−	0.209813i	$-0.932715\pi$
$223$	−7.94696	−	16.5020i	−0.532168	−	1.10506i	0.445574	−	0.895245i	$-0.353000\pi$
$224$	13.8223	+	47.5982i	0.923538	+	3.18029i
$225$		0			0
$226$	−51.8283			−3.44757
$227$	−22.3564			−1.48385			−0.741923	−	0.670485i	$-0.766086\pi$
$227$	−22.3564			−1.48385			−0.741923	+	0.670485i	$0.766086\pi$
$228$		0			0
$229$	21.5327	+	17.1717i	1.42292	+	1.13474i	0.969976	+	0.243202i	$0.0781978\pi$
$229$	21.5327	+	17.1717i	1.42292	+	1.13474i	0.452944	+	0.891539i	$0.350374\pi$
$230$	−3.83280	+	16.7926i	−0.252727	+	1.10727i
$231$		0			0
$232$	19.3442	+	84.7523i	1.27001	+	5.56426i
$233$	−1.29428	+	2.68760i	−0.0847912	+	0.176071i	−0.939053	−	0.343772i	$-0.888295\pi$
$233$	−1.29428	+	2.68760i	−0.0847912	+	0.176071i	0.854262	+	0.519843i	$0.174010\pi$
$234$		0			0
$235$	−0.0113551	+	0.0142389i	−0.000740728	+	0.000928844i
$236$	14.8372	−	65.0059i	0.965818	−	4.23152i
$237$		0			0
$238$	−33.5190	+	18.6183i	−2.17272	+	1.20684i
$239$	2.54905	+	2.03280i	0.164884	+	0.131491i	0.702456	−	0.711727i	$-0.252087\pi$
$239$	2.54905	+	2.03280i	0.164884	+	0.131491i	−0.537572	+	0.843218i	$0.680658\pi$
$240$		0			0
$241$	10.5951	+	22.0010i	0.682493	+	1.41721i	0.897685	+	0.440639i	$0.145248\pi$
$241$	10.5951	+	22.0010i	0.682493	+	1.41721i	−0.215192	+	0.976572i	$0.569038\pi$
$242$	−2.46868	+	1.96871i	−0.158693	+	0.126553i
$243$		0			0
$244$			17.9521i			1.14926i
$245$	−20.7643	+	13.1703i	−1.32658	+	0.841420i
$246$		0			0
$247$	−1.24327	−	5.44713i	−0.0791075	−	0.346592i
$248$	−4.06033	−	5.09149i	−0.257831	−	0.323310i
$249$		0			0
$250$	17.3633	−	13.8467i	1.09815	−	0.875745i
$251$	−4.13288	+	5.18247i	−0.260865	+	0.327115i	−0.894965	−	0.446137i	$-0.852800\pi$
$251$	−4.13288	+	5.18247i	−0.260865	+	0.327115i	0.634100	+	0.773251i	$0.281371\pi$
$252$		0			0
$253$	−3.54655	−	4.44724i	−0.222970	−	0.279595i
$254$	−8.76014	−	1.99944i	−0.549660	−	0.125456i
$255$		0			0
$256$	−5.27164	−	23.0965i	−0.329477	−	1.44353i
$257$	−18.6150	−	8.96453i	−1.16117	−	0.559192i	−0.248802	−	0.968554i	$-0.580037\pi$
$257$	−18.6150	−	8.96453i	−1.16117	−	0.559192i	−0.912372	+	0.409362i	$0.865751\pi$
$258$		0			0
$259$	15.0000	−	4.35591i	0.932052	−	0.270663i
$260$	22.5678	+	5.15096i	1.39960	+	0.319449i
$261$		0			0
$262$	−6.04141	+	12.5451i	−0.373240	+	0.775040i
$263$		−	19.4869i		−	1.20161i	−0.799394	−	0.600807i	$-0.794846\pi$
$263$		−	19.4869i		−	1.20161i	0.799394	−	0.600807i	$-0.205154\pi$
$264$		0			0
$265$	−0.155948	+	0.323829i	−0.00957980	+	0.0198927i
$266$	−26.2785	−	18.5619i	−1.61124	−	1.13810i
$267$		0			0
$268$	48.3927	−	23.3047i	2.95606	−	1.42356i
$269$	6.07099	−	26.5987i	0.370155	−	1.62175i	−0.356183	−	0.934416i	$-0.615922\pi$
$269$	6.07099	−	26.5987i	0.370155	−	1.62175i	0.726338	−	0.687338i	$-0.241221\pi$
$270$		0			0
$271$	−6.29293	−	13.0674i	−0.382268	−	0.793788i	−0.999973	−	0.00737801i	$-0.997651\pi$
$271$	−6.29293	−	13.0674i	−0.382268	−	0.793788i	0.617704	−	0.786410i	$-0.288063\pi$
$272$	65.4207	−	31.5049i	3.96671	−	1.91027i
$273$		0			0
$274$	17.7836	+	8.56415i	1.07435	+	0.517379i
$275$			23.0120i			1.38768i
$276$		0			0
$277$	−24.4446	−	11.7719i	−1.46873	−	0.707304i	−0.482999	−	0.875621i	$-0.660453\pi$
$277$	−24.4446	−	11.7719i	−1.46873	−	0.707304i	−0.985733	+	0.168316i	$0.946167\pi$
$278$	18.7423	−	23.5020i	1.12409	−	1.40956i
$279$		0			0
$280$	72.6049	−	40.3287i	4.33898	−	2.41010i
$281$	7.65615	−	1.74747i	0.456728	−	0.104245i	0.0120336	−	0.999928i	$-0.496169\pi$
$281$	7.65615	−	1.74747i	0.456728	−	0.104245i	0.444694	+	0.895682i	$0.353312\pi$
$282$		0			0
$283$	3.08816	−	0.704852i	0.183572	−	0.0418991i	−0.129747	−	0.991547i	$-0.541416\pi$
$283$	3.08816	−	0.704852i	0.183572	−	0.0418991i	0.313319	+	0.949648i	$0.398559\pi$
$284$	−26.9074	−	21.4579i	−1.59666	−	1.27329i
$285$		0			0
$286$	−8.22947	+	6.56278i	−0.486618	+	0.388065i
$287$	−2.28331	−	0.382966i	−0.134779	−	0.0226058i
$288$		0			0
$289$	7.32360	+	9.18350i	0.430800	+	0.540206i
$290$	83.2157	−	40.0746i	4.88659	−	2.35326i
$291$		0			0
$292$	−32.5135	+	7.42100i	−1.90271	+	0.434281i
$293$	−9.07462			−0.530145			−0.265072	−	0.964229i	$-0.585396\pi$
$293$	−9.07462			−0.530145			−0.265072	+	0.964229i	$0.585396\pi$
$294$		0			0
$295$	−44.1408			−2.56998
$296$	−51.4355	+	11.7398i	−2.98963	+	0.682363i
$297$		0			0
$298$	34.7430	−	16.7314i	2.01261	−	0.969221i
$299$	1.40471	+	1.76145i	0.0812363	+	0.101867i
$300$		0			0
$301$	−0.881426	−	15.1219i	−0.0508045	−	0.871613i
$302$	8.64953	−	6.89777i	0.497725	−	0.396922i
$303$		0			0
$304$	47.6351	+	37.9877i	2.73206	+	2.17875i
$305$	11.5864	−	2.64451i	0.663433	−	0.151424i
$306$		0			0
$307$	16.9589	−	3.87076i	0.967895	−	0.220916i	0.290778	−	0.956791i	$-0.406086\pi$
$307$	16.9589	−	3.87076i	0.967895	−	0.220916i	0.677117	+	0.735875i	$0.263229\pi$
$308$	−7.28145	+	43.4132i	−0.414899	+	2.47370i
$309$		0			0
$310$	−4.31397	+	5.40955i	−0.245017	+	0.307242i
$311$	6.97174	+	3.35741i	0.395331	+	0.190381i	0.620978	−	0.783828i	$-0.286735\pi$
$311$	6.97174	+	3.35741i	0.395331	+	0.190381i	−0.225647	+	0.974209i	$0.572450\pi$
$312$		0			0
$313$		−	20.5396i		−	1.16097i	−0.814272	−	0.580483i	$-0.802864\pi$
$313$		−	20.5396i		−	1.16097i	0.814272	−	0.580483i	$-0.197136\pi$
$314$	32.0170	+	15.4186i	1.80683	+	0.870122i
$315$		0			0
$316$	−11.1288	+	5.35936i	−0.626045	+	0.301487i
$317$	13.7561	+	28.5648i	0.772620	+	1.60436i	0.796494	+	0.604647i	$0.206686\pi$
$317$	13.7561	+	28.5648i	0.772620	+	1.60436i	−0.0238740	+	0.999715i	$0.507600\pi$
$318$		0			0
$319$	−6.78732	+	29.7372i	−0.380017	+	1.66496i
$320$	−74.5341	+	35.8937i	−4.16658	+	2.00652i
$321$		0			0
$322$	12.7947	+	2.14598i	0.713019	+	0.119591i
$323$	−10.4655	+	21.7319i	−0.582318	+	1.20920i
$324$		0			0
$325$		−	9.11454i		−	0.505584i
$326$	10.8418	−	22.5132i	0.600471	−	1.24689i
$327$		0			0
$328$	7.62396	+	1.74012i	0.420963	+	0.0960820i
$329$	0.0112042	+	0.00791411i	0.000617708	+	0.000436319i
$330$		0			0
$331$	−21.9684	−	10.5794i	−1.20749	−	0.581498i	−0.281691	−	0.959505i	$-0.590895\pi$
$331$	−21.9684	−	10.5794i	−1.20749	−	0.581498i	−0.925803	+	0.378007i	$0.876610\pi$
$332$	−18.4666	−	80.9073i	−1.01348	−	4.44036i
$333$		0			0
$334$	−19.2314	−	4.38944i	−1.05229	−	0.240179i
$335$	−22.1697	−	27.7999i	−1.21126	−	1.51887i
$336$		0			0
$337$	14.5455	−	18.2395i	0.792345	−	0.993569i	−0.207538	−	0.978227i	$-0.566545\pi$
$337$	14.5455	−	18.2395i	0.792345	−	0.993569i	0.999882	−	0.0153417i	$-0.00488362\pi$
$338$	−24.2132	+	19.3094i	−1.31702	+	1.05029i
$339$		0			0
$340$	−62.3074	−	78.1310i	−3.37909	−	4.23725i
$341$	−0.508453	−	2.22768i	−0.0275343	−	0.120636i
$342$		0			0
$343$	10.8131	+	15.0359i	0.583852	+	0.811860i
$344$			51.1638i			2.75857i
$345$		0			0
$346$	18.6286	−	14.8558i	1.00148	−	0.798654i
$347$	2.35773	+	4.89589i	0.126570	+	0.262825i	0.954619	−	0.297831i	$-0.0962633\pi$
$347$	2.35773	+	4.89589i	0.126570	+	0.262825i	−0.828049	+	0.560656i	$0.810549\pi$
$348$		0			0
$349$	25.4218	+	20.2732i	1.36080	+	1.08520i	0.987523	+	0.157477i	$0.0503361\pi$
$349$	25.4218	+	20.2732i	1.36080	+	1.08520i	0.373273	+	0.927721i	$0.378235\pi$
$350$	−35.0559	−	39.0604i	−1.87382	−	2.08787i
$351$		0			0
$352$	13.0710	−	57.2679i	0.696688	−	3.05239i
$353$	−19.3191	+	24.2254i	−1.02825	+	1.28939i	−0.0718269	+	0.997417i	$0.522883\pi$
$353$	−19.3191	+	24.2254i	−1.02825	+	1.28939i	−0.956427	+	0.291972i	$0.905689\pi$
$354$		0			0
$355$	−9.88533	+	20.5271i	−0.524659	+	1.08947i
$356$	3.15787	+	13.8355i	0.167367	+	0.733282i
$357$		0			0
$358$	7.09820	−	31.0993i	0.375152	−	1.64365i
$359$	21.3785	+	17.0488i	1.12832	+	0.899802i	0.995816	−	0.0913813i	$-0.0291282\pi$
$359$	21.3785	+	17.0488i	1.12832	+	0.899802i	0.132500	+	0.991183i	$0.457700\pi$
$360$		0			0
$361$	−1.23935			−0.0652291
$362$	33.4291			1.75699
$363$		0			0
$364$	2.88402	−	17.1950i	0.151163	−	0.901262i
$365$	9.57910	+	19.8912i	0.501393	+	1.04115i
$366$		0			0
$367$	8.91784	+	2.03544i	0.465507	+	0.106249i	0.448840	−	0.893612i	$-0.351837\pi$
$367$	8.91784	+	2.03544i	0.465507	+	0.106249i	0.0166673	+	0.999861i	$0.494694\pi$
$368$	−23.9523	−	5.46696i	−1.24860	−	0.284985i
$369$		0			0
$370$	24.3209	+	50.5029i	1.26438	+	2.62552i
$371$	0.250329	+	0.103068i	0.0129964	+	0.00535101i
$372$		0			0
$373$	30.9204			1.60100			0.800498	−	0.599335i	$-0.204568\pi$
$373$	30.9204			1.60100			0.800498	+	0.599335i	$0.204568\pi$
$374$	45.4414			2.34972
$375$		0			0
$376$	−0.0362247	−	0.0288882i	−0.00186815	−	0.00148980i
$377$	2.68830	−	11.7782i	0.138455	−	0.606609i
$378$		0			0
$379$	2.70581	+	11.8549i	0.138988	+	0.608947i	0.995658	+	0.0930825i	$0.0296720\pi$
$379$	2.70581	+	11.8549i	0.138988	+	0.608947i	−0.856670	+	0.515864i	$0.827471\pi$
$380$	36.3825	−	75.5490i	1.86638	−	3.87558i
$381$		0			0
$382$	−26.6450	+	33.4118i	−1.36328	+	1.70949i
$383$	−1.20812	+	5.29312i	−0.0617321	+	0.270466i	−0.996369	−	0.0851368i	$-0.972867\pi$
$383$	−1.20812	+	5.29312i	−0.0617321	+	0.270466i	0.934637	+	0.355603i	$0.115724\pi$
$384$		0			0
$385$	29.0918	−	1.69570i	1.48265	−	0.0864208i
$386$	12.7811	+	10.1926i	0.650539	+	0.518788i
$387$		0			0
$388$	4.02606	+	8.36021i	0.204392	+	0.424425i
$389$	4.16534	−	3.32175i	0.211191	−	0.168419i	−0.512181	−	0.858877i	$-0.671162\pi$
$389$	4.16534	−	3.32175i	0.211191	−	0.168419i	0.723372	+	0.690458i	$0.242591\pi$
$390$		0			0
$391$		−	9.72634i		−	0.491882i
$392$	−33.5061	−	52.8257i	−1.69232	−	2.66810i
$393$		0			0
$394$	−9.26986	−	40.6139i	−0.467009	−	2.04610i
$395$	5.09834	+	6.39311i	0.256525	+	0.321672i
$396$		0			0
$397$	−2.56810	+	2.04799i	−0.128889	+	0.102786i	−0.685813	−	0.727778i	$-0.740553\pi$
$397$	−2.56810	+	2.04799i	−0.128889	+	0.102786i	0.556924	+	0.830564i	$0.311982\pi$
$398$	−25.1745	+	31.5679i	−1.26188	+	1.58235i
$399$		0			0
$400$	61.9702	+	77.7082i	3.09851	+	3.88541i
$401$	1.25904	+	0.287367i	0.0628734	+	0.0143504i	0.253842	−	0.967246i	$-0.418306\pi$
$401$	1.25904	+	0.287367i	0.0628734	+	0.0143504i	−0.190969	+	0.981596i	$0.561163\pi$
$402$		0			0
$403$	0.201387	+	0.882333i	0.0100318	+	0.0439521i
$404$	−21.0151	−	10.1204i	−1.04554	−	0.503507i
$405$		0			0
$406$	−33.7801	−	60.8152i	−1.67648	−	3.01821i
$407$	−18.0473	−	4.11917i	−0.894569	−	0.204180i
$408$		0			0
$409$	−12.3196	+	25.5820i	−0.609167	+	1.26495i	0.337071	+	0.941479i	$0.390564\pi$
$409$	−12.3196	+	25.5820i	−0.609167	+	1.26495i	−0.946239	+	0.323470i	$0.895151\pi$
$410$		−	8.30854i		−	0.410329i
$411$		0			0
$412$	−38.6853	+	80.3308i	−1.90589	+	3.95761i
$413$	1.93460	+	33.1904i	0.0951954	+	1.63319i
$414$		0			0
$415$	−49.4977	+	23.8368i	−2.42974	+	1.17010i
$416$	−5.17713	+	22.6825i	−0.253830	+	1.11210i
$417$		0			0
$418$	16.5437	+	34.3534i	0.809180	+	1.68028i
$419$	−11.9371	+	5.74859i	−0.583164	+	0.280837i	−0.702116	−	0.712063i	$-0.747761\pi$
$419$	−11.9371	+	5.74859i	−0.583164	+	0.280837i	0.118951	+	0.992900i	$0.462047\pi$
$420$		0			0
$421$	3.67785	+	1.77116i	0.179247	+	0.0863210i	0.521355	−	0.853340i	$-0.325427\pi$
$421$	3.67785	+	1.77116i	0.179247	+	0.0863210i	−0.342108	+	0.939661i	$0.611141\pi$
$422$		−	6.60745i		−	0.321646i
$423$		0			0
$424$	−0.823842	−	0.396742i	−0.0400093	−	0.0192675i
$425$	−24.5334	+	30.7639i	−1.19004	+	1.49227i
$426$		0			0
$427$	−2.49627	−	8.59613i	−0.120803	−	0.415996i
$428$	−9.80552	+	2.23805i	−0.473968	+	0.108180i
$429$		0			0
$430$	52.9971	−	12.0962i	2.55575	−	0.583332i
$431$	−0.882205	−	0.703535i	−0.0424943	−	0.0338881i	0.602012	−	0.798487i	$-0.294366\pi$
$431$	−0.882205	−	0.703535i	−0.0424943	−	0.0338881i	−0.644507	+	0.764599i	$0.722937\pi$
$432$		0			0
$433$	−5.17948	+	4.13050i	−0.248910	+	0.198499i	−0.739995	−	0.672613i	$-0.765172\pi$
$433$	−5.17948	+	4.13050i	−0.248910	+	0.198499i	0.491085	+	0.871112i	$0.336601\pi$
$434$	4.25663	+	3.00668i	0.204325	+	0.144325i
$435$		0			0
$436$	19.1320	+	23.9908i	0.916257	+	1.14895i
$437$	7.35306	−	3.54105i	0.351744	−	0.169391i
$438$		0			0
$439$	23.4431	−	5.35073i	1.11888	−	0.255376i	0.377199	−	0.926132i	$-0.376887\pi$
$439$	23.4431	−	5.35073i	1.11888	−	0.255376i	0.741678	+	0.670756i	$0.234030\pi$
$440$	−98.4297			−4.69245
$441$		0			0
$442$	−17.9983			−0.856091
$443$	17.1026	−	3.90356i	0.812569	−	0.185464i	0.204007	−	0.978970i	$-0.434604\pi$
$443$	17.1026	−	3.90356i	0.812569	−	0.185464i	0.608563	+	0.793506i	$0.291746\pi$
$444$		0			0
$445$	8.46434	−	4.07621i	0.401248	−	0.193231i
$446$	−30.8675	−	38.7066i	−1.46162	−	1.83281i
$447$		0			0
$448$	30.2559	+	54.4706i	1.42946	+	2.57349i
$449$	7.48598	−	5.96987i	0.353285	−	0.281735i	−0.430725	−	0.902483i	$-0.641742\pi$
$449$	7.48598	−	5.96987i	0.353285	−	0.281735i	0.784010	+	0.620748i	$0.213171\pi$
$450$		0			0
$451$	2.14521	+	1.71075i	0.101014	+	0.0805560i
$452$	−99.1916	+	22.6398i	−4.66558	+	1.06489i
$453$		0			0
$454$	−58.9140	+	13.4467i	−2.76497	+	0.631087i
$455$	−11.5226	+	0.671627i	−0.540187	+	0.0314864i
$456$		0			0
$457$	−10.6012	+	13.2935i	−0.495904	+	0.621844i	−0.965300	−	0.261144i	$-0.915900\pi$
$457$	−10.6012	+	13.2935i	−0.495904	+	0.621844i	0.469396	+	0.882988i	$0.344472\pi$
$458$	67.0717	+	32.3000i	3.13406	+	1.50928i
$459$		0			0
$460$			33.8128i			1.57653i
$461$	13.7485	+	6.62093i	0.640332	+	0.308368i	0.725730	−	0.687979i	$-0.241502\pi$
$461$	13.7485	+	6.62093i	0.640332	+	0.308368i	−0.0853983	+	0.996347i	$0.527216\pi$
$462$		0			0
$463$	−11.2570	+	5.42110i	−0.523159	+	0.251940i	−0.676774	−	0.736191i	$-0.736623\pi$
$463$	−11.2570	+	5.42110i	−0.523159	+	0.251940i	0.153615	+	0.988131i	$0.450908\pi$
$464$	57.1609	+	118.696i	2.65363	+	5.51032i
$465$		0			0
$466$	−1.79420	+	7.86091i	−0.0831147	+	0.364149i
$467$	34.3243	−	16.5297i	1.58834	−	0.764905i	0.589267	−	0.807938i	$-0.299417\pi$
$467$	34.3243	−	16.5297i	1.58834	−	0.764905i	0.999074	+	0.0430337i	$0.0137023\pi$
$468$		0			0
$469$	−19.9317	+	17.8883i	−0.920360	+	0.826003i
$470$	−0.0213590	+	0.0443525i	−0.000985218	+	0.00204583i
$471$		0			0
$472$		−	112.297i		−	5.16889i
$473$	−7.78906	+	16.1741i	−0.358141	+	0.743688i
$474$		0			0
$475$	−32.1891	−	7.34695i	−1.47694	−	0.337101i
$476$	−56.0176	+	50.2746i	−2.56756	+	2.30433i
$477$		0			0
$478$	7.93998	+	3.82369i	0.363166	+	0.174892i
$479$	1.27909	+	5.60405i	0.0584430	+	0.256055i	0.995707	−	0.0925662i	$-0.0295070\pi$
$479$	1.27909	+	5.60405i	0.0584430	+	0.256055i	−0.937264	+	0.348622i	$0.886650\pi$
$480$		0			0
$481$	7.14810	+	1.63151i	0.325926	+	0.0743904i
$482$	41.1535	+	51.6049i	1.87449	+	2.35054i
$483$		0			0
$484$	−3.86471	+	4.84620i	−0.175669	+	0.220282i
$485$	4.80264	−	3.82998i	0.218077	−	0.173910i
$486$		0			0
$487$	−1.62317	−	2.03539i	−0.0735530	−	0.0922325i	0.743694	−	0.668520i	$-0.233072\pi$
$487$	−1.62317	−	2.03539i	−0.0735530	−	0.0922325i	−0.817247	+	0.576288i	$0.804501\pi$
$488$	6.72781	+	29.4765i	0.304554	+	1.33434i
$489$		0			0
$490$	−46.7969	+	47.1958i	−2.11407	+	2.13209i
$491$		−	17.1387i		−	0.773461i	−0.922193	−	0.386730i	$-0.873604\pi$
$491$		−	17.1387i		−	0.773461i	0.922193	−	0.386730i	$-0.126396\pi$
$492$		0			0
$493$	−40.7768	+	32.5184i	−1.83650	+	1.46456i
$494$	−6.55259	−	13.6066i	−0.294815	−	0.612190i
$495$		0			0
$496$	−7.71599	−	6.15330i	−0.346458	−	0.276291i
$497$	15.8680	+	6.53333i	0.711778	+	0.293060i
$498$		0			0
$499$	4.12628	−	18.0784i	0.184717	−	0.809300i	−0.794626	−	0.607099i	$-0.792333\pi$
$499$	4.12628	−	18.0784i	0.184717	−	0.809300i	0.979344	−	0.202201i	$-0.0648096\pi$
$500$	27.1821	−	34.0853i	1.21562	−	1.52434i
$501$		0			0
$502$	−7.77395	+	16.1428i	−0.346968	+	0.720487i
$503$	−7.38991	−	32.3773i	−0.329500	−	1.44363i	−0.820086	−	0.572241i	$-0.806074\pi$
$503$	−7.38991	−	32.3773i	−0.329500	−	1.44363i	0.490586	−	0.871393i	$-0.336783\pi$
$504$		0			0
$505$	−3.43600	+	15.0541i	−0.152900	+	0.669899i
$506$	−12.0208	−	9.58630i	−0.534391	−	0.426163i
$507$		0			0
$508$	−17.6390			−0.782605
$509$	−20.6242			−0.914150			−0.457075	−	0.889428i	$-0.651103\pi$
$509$	−20.6242			−0.914150			−0.457075	+	0.889428i	$0.651103\pi$
$510$		0			0
$511$	14.5368	−	8.07452i	0.643069	−	0.357196i
$512$	−5.05680	−	10.5006i	−0.223481	−	0.464063i
$513$		0			0
$514$	−54.4467	−	12.4271i	−2.40154	−	0.548136i
$515$	57.5446	+	13.1342i	2.53572	+	0.578761i
$516$		0			0
$517$	−0.00705365	−	0.0146470i	−0.000310219	−	0.000644176i
$518$	36.9083	−	20.5008i	1.62166	−	0.900755i
$519$		0			0
$520$	38.9857			1.70964
$521$	−6.17881			−0.270699			−0.135349	−	0.990798i	$-0.543216\pi$
$521$	−6.17881			−0.270699			−0.135349	+	0.990798i	$0.543216\pi$
$522$		0			0
$523$	−18.3534	−	14.6364i	−0.802538	−	0.640003i	0.133837	−	0.991003i	$-0.457270\pi$
$523$	−18.3534	−	14.6364i	−0.802538	−	0.640003i	−0.936375	+	0.351000i	$0.885842\pi$
$524$	−6.08235	+	26.6485i	−0.265709	+	1.16415i
$525$		0			0
$526$	−11.7208	−	51.3523i	−0.511052	−	2.23907i
$527$	1.69522	−	3.52016i	0.0738450	−	0.153341i
$528$		0			0
$529$	12.2884	−	15.4092i	0.534278	−	0.669964i
$530$	−0.216183	+	0.947160i	−0.00939039	+	0.0411420i
$531$		0			0
$532$	−58.4015	−	24.0456i	−2.53202	−	1.04251i
$533$	−0.849668	−	0.677588i	−0.0368032	−	0.0293496i
$534$		0			0
$535$	2.88889	+	5.99885i	0.124898	+	0.259353i
$536$	70.7248	−	56.4011i	3.05485	−	2.43616i
$537$		0			0
$538$		−	73.7451i		−	3.17938i
$539$	−2.55006	−	21.8004i	−0.109839	−	0.939009i
$540$		0			0
$541$	−6.89116	−	30.1921i	−0.296274	−	1.29806i	−0.875628	−	0.482985i	$-0.839552\pi$
$541$	−6.89116	−	30.1921i	−0.296274	−	1.29806i	0.579354	−	0.815076i	$-0.303305\pi$
$542$	−24.4429	−	30.6505i	−1.04991	−	1.31655i
$543$		0			0
$544$	78.5280	−	62.6240i	3.36686	−	2.68498i
$545$	12.6655	−	15.8820i	0.542528	−	0.680309i
$546$		0			0
$547$	20.5234	+	25.7355i	0.877518	+	1.10037i	0.994237	+	0.107207i	$0.0341909\pi$
$547$	20.5234	+	25.7355i	0.877518	+	1.10037i	−0.116719	+	0.993165i	$0.537238\pi$
$548$	37.7763	+	8.62219i	1.61372	+	0.368322i
$549$		0			0
$550$	13.8411	+	60.6418i	0.590186	+	2.58578i
$551$	−39.4292	−	18.9881i	−1.67974	−	0.808921i
$552$		0			0
$553$	4.58367	−	4.11374i	0.194917	−	0.174934i
$554$	−71.4973	−	16.3188i	−3.03763	−	0.693319i
$555$		0			0
$556$	25.6036	−	53.1665i	1.08584	−	2.25476i
$557$			17.3289i			0.734250i	0.930172	+	0.367125i	$0.119658\pi$
$557$			17.3289i			0.734250i	−0.930172	+	0.367125i	$0.880342\pi$
$558$		0			0
$559$	3.08507	−	6.40621i	0.130484	−	0.270954i
$560$	93.6720	−	84.0687i	3.95837	−	3.55255i
$561$		0			0
$562$	19.1246	−	9.20993i	0.806723	−	0.388497i
$563$	−7.42851	+	32.5464i	−0.313074	+	1.37167i	0.536367	+	0.843985i	$0.319796\pi$
$563$	−7.42851	+	32.5464i	−0.313074	+	1.37167i	−0.849441	+	0.527683i	$0.823061\pi$
$564$		0			0
$565$	29.2237	+	60.6837i	1.22945	+	2.55298i
$566$	7.71403	−	3.71488i	0.324245	−	0.156148i
$567$		0			0
$568$	−52.2223	−	25.1489i	−2.19120	−	1.05523i
$569$		−	14.0612i		−	0.589474i	−0.955578	−	0.294737i	$-0.904768\pi$
$569$		−	14.0612i		−	0.589474i	0.955578	−	0.294737i	$-0.0952321\pi$
$570$		0			0
$571$	−15.7023	−	7.56183i	−0.657121	−	0.316453i	0.0754439	−	0.997150i	$-0.475963\pi$
$571$	−15.7023	−	7.56183i	−0.657121	−	0.316453i	−0.732565	+	0.680697i	$0.761677\pi$
$572$	−12.8832	+	16.1550i	−0.538673	+	0.675475i
$573$		0			0
$574$	−6.24736	+	0.364146i	−0.260760	+	0.0151992i
$575$	12.9799	−	2.96257i	0.541298	−	0.123548i
$576$		0			0
$577$	−44.1122	+	10.0683i	−1.83642	+	0.419150i	−0.993000	−	0.118111i	$-0.962316\pi$
$577$	−44.1122	+	10.0683i	−1.83642	+	0.419150i	−0.843416	+	0.537261i	$0.819459\pi$
$578$	24.8229	+	19.7956i	1.03250	+	0.823389i
$579$		0			0
$580$	141.757	−	113.047i	5.88614	−	4.69404i
$581$	20.0928	+	36.1736i	0.833589	+	1.50073i
$582$		0			0
$583$	−0.200038	−	0.250840i	−0.00828472	−	0.0103887i
$584$	−50.6045	+	24.3699i	−2.09403	+	1.00843i
$585$		0			0
$586$	−23.9136	+	5.45813i	−0.987863	+	0.225473i
$587$	37.6421			1.55366			0.776828	−	0.629713i	$-0.216827\pi$
$587$	37.6421			1.55366			0.776828	+	0.629713i	$0.216827\pi$
$588$		0			0
$589$	3.27840			0.135084
$590$	−116.321	+	26.5495i	−4.78885	+	1.09302i
$591$		0			0
$592$	−72.0356	+	34.6905i	−2.96064	+	1.42577i
$593$	−21.6218	−	27.1129i	−0.887902	−	1.11339i	−0.992904	−	0.118922i	$-0.962056\pi$
$593$	−21.6218	−	27.1129i	−0.887902	−	1.11339i	0.105002	−	0.994472i	$-0.466515\pi$
$594$		0			0
$595$	40.6994	+	28.7481i	1.66851	+	1.17856i
$596$	59.1843	−	47.1979i	2.42428	−	1.93330i
$597$		0			0
$598$	4.76118	+	3.79691i	0.194699	+	0.155267i
$599$	22.4762	−	5.13004i	0.918351	−	0.209608i	0.262880	−	0.964828i	$-0.415328\pi$
$599$	22.4762	−	5.13004i	0.918351	−	0.209608i	0.655470	+	0.755221i	$0.272470\pi$
$600$		0			0
$601$	−2.75476	+	0.628756i	−0.112369	+	0.0256475i	−0.278336	−	0.960484i	$-0.589783\pi$
$601$	−2.75476	+	0.628756i	−0.112369	+	0.0256475i	0.165967	+	0.986131i	$0.446926\pi$
$602$	−11.4182	−	39.3195i	−0.465370	−	1.60254i
$603$		0			0
$604$	13.5408	−	16.9796i	0.550968	−	0.690892i
$605$	3.69707	+	1.78041i	0.150307	+	0.0723841i
$606$		0			0
$607$		−	9.72550i		−	0.394746i	−0.980328	−	0.197373i	$-0.936759\pi$
$607$		−	9.72550i		−	0.394746i	0.980328	−	0.197373i	$-0.0632410\pi$
$608$	75.9329	+	36.5673i	3.07948	+	1.48300i
$609$		0			0
$610$	28.9420	−	13.9377i	1.17183	−	0.564323i
$611$	0.00279379	+	0.00580136i	0.000113025	+	0.000234698i
$612$		0			0
$613$	4.17707	−	18.3010i	0.168710	−	0.739169i	−0.817804	−	0.575496i	$-0.804809\pi$
$613$	4.17707	−	18.3010i	0.168710	−	0.739169i	0.986515	−	0.163672i	$-0.0523340\pi$
$614$	42.3623	−	20.4006i	1.70960	−	0.823301i
$615$		0			0
$616$	4.31397	+	74.0113i	0.173815	+	2.98200i
$617$	−10.1337	+	21.0429i	−0.407968	+	0.847154i	0.591206	+	0.806520i	$0.298652\pi$
$617$	−10.1337	+	21.0429i	−0.407968	+	0.847154i	−0.999174	+	0.0406334i	$0.987062\pi$
$618$		0			0
$619$		−	11.6938i		−	0.470013i	−0.971994	−	0.235007i	$-0.924489\pi$
$619$		−	11.6938i		−	0.470013i	0.971994	−	0.235007i	$-0.0755112\pi$
$620$	−5.89328	+	12.2375i	−0.236680	+	0.491471i
$621$		0			0
$622$	20.3915	+	4.65422i	0.817623	+	0.186617i
$623$	−3.43596	−	6.18586i	−0.137659	−	0.247831i
$624$		0			0
$625$	7.05810	+	3.39900i	0.282324	+	0.135960i
$626$	−12.3540	−	54.1264i	−0.493765	−	2.16332i
$627$		0			0
$628$	68.0111	+	15.5231i	2.71394	+	0.619439i
$629$	−19.7352	−	24.7471i	−0.786893	−	0.986732i
$630$		0			0
$631$	−12.9979	+	16.2989i	−0.517440	+	0.648849i	−0.970063	−	0.242853i	$-0.921917\pi$
$631$	−12.9979	+	16.2989i	−0.517440	+	0.648849i	0.452623	+	0.891702i	$0.350488\pi$
$632$	−16.2645	+	12.9705i	−0.646967	+	0.515939i
$633$		0			0
$634$	53.4313	+	67.0008i	2.12203	+	2.66094i
$635$	2.59839	+	11.3843i	0.103114	+	0.451772i
$636$		0			0
$637$	1.01002	+	8.63463i	0.0400185	+	0.342117i
$638$			82.4465i			3.26409i
$639$		0			0
$640$	−71.9272	+	57.3600i	−2.84317	+	2.26735i
$641$	6.08793	+	12.6417i	0.240459	+	0.499318i	0.985917	−	0.167234i	$-0.0534836\pi$
$641$	6.08793	+	12.6417i	0.240459	+	0.499318i	−0.745458	+	0.666552i	$0.767769\pi$
$642$		0			0
$643$	−17.9294	−	14.2982i	−0.707066	−	0.563867i	0.202572	−	0.979267i	$-0.435070\pi$
$643$	−17.9294	−	14.2982i	−0.707066	−	0.563867i	−0.909638	+	0.415401i	$0.863641\pi$
$644$	25.4245	−	1.48194i	1.00187	−	0.0583967i
$645$		0			0
$646$	−14.5079	+	63.5631i	−0.570804	+	2.50086i
$647$	16.9506	−	21.2554i	0.666398	−	0.835637i	−0.327625	−	0.944808i	$-0.606248\pi$
$647$	16.9506	−	21.2554i	0.666398	−	0.835637i	0.994023	+	0.109171i	$0.0348196\pi$
$648$		0			0
$649$	17.0958	−	35.4999i	0.671070	−	1.39349i
$650$	−5.48214	−	24.0188i	−0.215027	−	0.942096i
$651$		0			0
$652$	10.9153	−	47.8229i	0.427474	−	1.87289i
$653$	−10.8570	−	8.65819i	−0.424868	−	0.338821i	0.387599	−	0.921828i	$-0.373305\pi$
$653$	−10.8570	−	8.65819i	−0.424868	−	0.338821i	−0.812467	+	0.583007i	$0.801876\pi$
$654$		0			0
$655$	18.0951			0.707034
$656$	11.8510			0.462704
$657$		0			0
$658$	0.0342857	+	0.0141164i	0.00133659	+	0.000550315i
$659$	−14.2048	−	29.4967i	−0.553342	−	1.14903i	−0.970702	−	0.240286i	$-0.922759\pi$
$659$	−14.2048	−	29.4967i	−0.553342	−	1.14903i	0.417360	−	0.908741i	$-0.362955\pi$
$660$		0			0
$661$	32.5106	+	7.42032i	1.26451	+	0.288617i	0.801640	−	0.597807i	$-0.203961\pi$
$661$	32.5106	+	7.42032i	1.26451	+	0.288617i	0.462874	+	0.886424i	$0.346818\pi$
$662$	−64.2549	−	14.6658i	−2.49734	−	0.570001i
$663$		0			0
$664$	−60.6424	−	125.925i	−2.35338	−	4.88685i
$665$	−6.91606	+	41.2347i	−0.268193	+	1.59901i
$666$		0			0
$667$	17.6470			0.683294
$668$	−38.7234			−1.49825
$669$		0			0
$670$	−75.1429	−	59.9245i	−2.90302	−	2.31508i
$671$	−2.36060	+	10.3425i	−0.0911299	+	0.399266i
$672$		0			0
$673$	3.27509	+	14.3491i	0.126245	+	0.553117i	0.998002	+	0.0631781i	$0.0201236\pi$
$673$	3.27509	+	14.3491i	0.126245	+	0.553117i	−0.871757	+	0.489938i	$0.837019\pi$
$674$	27.3601	−	56.8138i	1.05387	−	2.18839i
$675$		0			0
$676$	−37.9056	+	47.5322i	−1.45791	+	1.82816i
$677$	−9.65530	+	42.3026i	−0.371083	+	1.62582i	0.352659	+	0.935752i	$0.385278\pi$
$677$	−9.65530	+	42.3026i	−0.371083	+	1.62582i	−0.723742	+	0.690071i	$0.757579\pi$
$678$		0			0
$679$	−3.09033	−	3.44335i	−0.118596	−	0.132144i
$680$	−131.587	−	104.937i	−5.04612	−	4.02414i
$681$		0			0
$682$	−2.67977	−	5.56461i	−0.102614	−	0.213080i
$683$	−17.2471	+	13.7541i	−0.659942	+	0.526286i	−0.895210	−	0.445644i	$-0.852975\pi$
$683$	−17.2471	+	13.7541i	−0.659942	+	0.526286i	0.235268	+	0.971931i	$0.424403\pi$
$684$		0			0
$685$		−	25.6511i		−	0.980080i
$686$	37.5385	+	33.1191i	1.43323	+	1.26449i
$687$		0			0
$688$	17.2536	+	75.5932i	0.657789	+	2.88196i
$689$	0.0792304	+	0.0993518i	0.00301844	+	0.00378500i
$690$		0			0
$691$	−11.2474	+	8.96948i	−0.427870	+	0.341215i	−0.813629	−	0.581385i	$-0.802511\pi$
$691$	−11.2474	+	8.96948i	−0.427870	+	0.341215i	0.385759	+	0.922600i	$0.373940\pi$
$692$	29.1630	−	36.5693i	1.10861	−	1.39016i
$693$		0			0
$694$	9.15789	+	11.4836i	0.347629	+	0.435913i
$695$	−38.0856	−	8.69279i	−1.44467	−	0.329736i
$696$		0			0
$697$	1.04400	+	4.57406i	0.0395443	+	0.173255i
$698$	79.1857	+	38.1338i	2.99722	+	1.44339i
$699$		0			0
$700$	−84.1543	−	59.4426i	−3.18073	−	2.24672i
$701$	−6.84716	−	1.56282i	−0.258614	−	0.0590269i	0.0912481	−	0.995828i	$-0.470914\pi$
$701$	−6.84716	−	1.56282i	−0.258614	−	0.0590269i	−0.349862	+	0.936801i	$0.613772\pi$
$702$		0			0
$703$	11.5237	−	23.9293i	0.434626	−	0.902510i
$704$		−	73.8452i		−	2.78314i
$705$		0			0
$706$	−36.3393	+	75.4593i	−1.36765	+	2.83995i
$707$	11.4701	+	1.92381i	0.431377	+	0.0723524i
$708$		0			0
$709$	−32.6847	+	15.7401i	−1.22750	+	0.591133i	−0.931391	−	0.364020i	$-0.881404\pi$
$709$	−32.6847	+	15.7401i	−1.22750	+	0.591133i	−0.296110	+	0.955154i	$0.595690\pi$
$710$	−13.7036	+	60.0392i	−0.514285	+	2.25323i
$711$		0			0
$712$	10.3701	+	21.5338i	0.388638	+	0.807015i
$713$	−1.19106	+	0.573583i	−0.0446054	+	0.0214809i
$714$		0			0
$715$	12.3243	+	5.93509i	0.460904	+	0.221960i
$716$		−	62.6200i		−	2.34022i
$717$		0			0
$718$	66.5915	+	32.0688i	2.48517	+	1.19680i
$719$	3.38138	−	4.24012i	0.126104	−	0.158130i	−0.714771	−	0.699358i	$-0.753469\pi$
$719$	3.38138	−	4.24012i	0.126104	−	0.158130i	0.840876	+	0.541229i	$0.182041\pi$
$720$		0			0
$721$	7.35380	−	43.8446i	0.273870	−	1.63286i
$722$	−3.26597	+	0.745437i	−0.121547	+	0.0277423i
$723$		0			0
$724$	63.9783	−	14.6026i	2.37773	−	0.542702i
$725$	−55.8164	−	44.5121i	−2.07297	−	1.65314i
$726$		0			0
$727$	−4.70481	+	3.75196i	−0.174492	+	0.139152i	−0.706841	−	0.707372i	$-0.749881\pi$
$727$	−4.70481	+	3.75196i	−0.174492	+	0.139152i	0.532350	+	0.846525i	$0.321309\pi$
$728$	−1.70866	−	29.3142i	−0.0633273	−	1.08646i
$729$		0			0
$730$	37.2071	+	46.6562i	1.37709	+	1.72682i
$731$	−27.6563	+	13.3186i	−1.02291	+	0.492605i
$732$		0			0
$733$	−4.19578	+	0.957660i	−0.154975	+	0.0353720i	−0.299304	−	0.954158i	$-0.596755\pi$
$733$	−4.19578	+	0.957660i	−0.154975	+	0.0353720i	0.144330	+	0.989530i	$0.453897\pi$
$734$	24.7247			0.912607
$735$		0			0
$736$	−33.9845			−1.25269
$737$	30.9442	−	7.06282i	1.13984	−	0.260162i
$738$		0			0
$739$	41.9649	−	20.2092i	1.54370	−	0.743409i	0.548042	−	0.836451i	$-0.315373\pi$
$739$	41.9649	−	20.2092i	1.54370	−	0.743409i	0.995662	+	0.0930420i	$0.0296591\pi$
$740$	68.6075	+	86.0311i	2.52206	+	3.16257i
$741$		0			0
$742$	0.721664	+	0.121041i	0.0264931	+	0.00444354i
$743$	−10.8408	+	8.64523i	−0.397709	+	0.317163i	−0.801840	−	0.597539i	$-0.796145\pi$
$743$	−10.8408	+	8.64523i	−0.397709	+	0.317163i	0.404131	+	0.914701i	$0.367574\pi$
$744$		0			0
$745$	−39.1802	−	31.2452i	−1.43545	−	1.14473i
$746$	81.4821	−	18.5978i	2.98327	−	0.680912i
$747$		0			0
$748$	86.9681	−	19.8499i	3.17987	−	0.725784i
$749$	4.38405	−	2.43514i	0.160190	−	0.0889780i
$750$		0			0
$751$	−19.1159	+	23.9705i	−0.697548	+	0.874697i	−0.996838	−	0.0794651i	$-0.974679\pi$
$751$	−19.1159	+	23.9705i	−0.697548	+	0.874697i	0.299290	+	0.954162i	$0.403250\pi$
$752$	−0.0632628	−	0.0304658i	−0.00230696	−	0.00111097i
$753$		0			0
$754$		−	32.6552i		−	1.18923i
$755$	−12.9534	−	6.23805i	−0.471424	−	0.227026i
$756$		0			0
$757$	20.4583	−	9.85218i	0.743568	−	0.358083i	−0.0234364	−	0.999725i	$-0.507461\pi$
$757$	20.4583	−	9.85218i	0.743568	−	0.358083i	0.767004	+	0.641642i	$0.221746\pi$
$758$	14.2608	+	29.6129i	0.517976	+	1.07559i
$759$		0			0
$760$	31.4252	−	137.683i	1.13991	−	4.99428i
$761$	7.96253	−	3.83455i	0.288642	−	0.139002i	−0.283960	−	0.958836i	$-0.591648\pi$
$761$	7.96253	−	3.83455i	0.288642	−	0.139002i	0.572602	+	0.819834i	$0.305934\pi$
$762$		0			0
$763$	−12.4971	−	8.82735i	−0.452425	−	0.319571i
$764$	−36.3995	+	75.5843i	−1.31689	+	2.73454i
$765$		0			0
$766$			14.6752i			0.530237i
$767$	−6.77127	+	14.0607i	−0.244496	+	0.507702i
$768$		0			0
$769$	15.2531	+	3.48143i	0.550042	+	0.125544i	0.488505	−	0.872561i	$-0.337542\pi$
$769$	15.2531	+	3.48143i	0.550042	+	0.125544i	0.0615375	+	0.998105i	$0.480400\pi$
$770$	75.6433	−	21.9664i	2.72600	−	0.791615i
$771$		0			0
$772$	28.9134	+	13.9240i	1.04062	+	0.501135i
$773$	−1.36859	−	5.99619i	−0.0492248	−	0.215668i	0.944334	−	0.328990i	$-0.106708\pi$
$773$	−1.36859	−	5.99619i	−0.0492248	−	0.215668i	−0.993558	+	0.113322i	$0.963851\pi$
$774$		0			0
$775$	5.21403	+	1.19007i	0.187293	+	0.0427485i
$776$	9.74372	+	12.2182i	0.349779	+	0.438609i
$777$		0			0
$778$	8.97865	−	11.2589i	0.321900	−	0.403650i
$779$	−3.07788	+	2.45452i	−0.110276	+	0.0879424i
$780$		0			0
$781$	−12.6801	−	15.9004i	−0.453731	−	0.568961i
$782$	−5.85012	−	25.6311i	−0.209200	−	0.916565i
$783$		0			0
$784$	−67.3184	−	66.7494i	−2.40423	−	2.38391i
$785$		−	46.1814i		−	1.64828i
$786$		0			0
$787$	34.1159	−	27.2065i	1.21610	−	0.969807i	0.216120	−	0.976367i	$-0.430660\pi$
$787$	34.1159	−	27.2065i	1.21610	−	0.969807i	0.999978	+	0.00656016i	$0.00208818\pi$
$788$	−35.4823	−	73.6797i	−1.26400	−	2.62473i
$789$		0			0
$790$	17.2805	+	13.7808i	0.614814	+	0.490297i
$791$	44.3486	−	24.6336i	1.57685	−	0.875869i
$792$		0			0
$793$	0.934979	−	4.09641i	0.0332021	−	0.145468i
$794$	−5.53569	+	6.94154i	−0.196454	+	0.246346i
$795$		0			0
$796$	−34.3907	+	71.4130i	−1.21895	+	2.53117i
$797$	3.01336	+	13.2024i	0.106739	+	0.467653i	0.999842	+	0.0178004i	$0.00566635\pi$
$797$	3.01336	+	13.2024i	0.106739	+	0.467653i	−0.893103	+	0.449853i	$0.851477\pi$
$798$		0			0
$799$	0.00618563	−	0.0271010i	0.000218832	−	0.000958765i
$800$	107.491	+	85.7213i	3.80039	+	3.03071i
$801$		0			0
$802$	3.49069			0.123261
$803$	−19.7073			−0.695457
$804$		0			0
$805$	−4.70173	−	16.1908i	−0.165714	−	0.570651i
$806$	1.06140	+	2.20401i	0.0373861	+	0.0776330i
$807$		0			0
$808$	−38.2986	−	8.74141i	−1.34734	−	0.307522i
$809$	8.06091	+	1.83985i	0.283406	+	0.0646857i	0.361861	−	0.932232i	$-0.382141\pi$
$809$	8.06091	+	1.83985i	0.283406	+	0.0646857i	−0.0784547	+	0.996918i	$0.524999\pi$
$810$		0			0
$811$	9.15314	+	19.0067i	0.321410	+	0.667415i	0.997595	−	0.0693172i	$-0.0220821\pi$
$811$	9.15314	+	19.0067i	0.321410	+	0.667415i	−0.676184	+	0.736732i	$0.736368\pi$
$812$	−91.2156	−	101.635i	−3.20104	−	3.56670i
$813$		0			0
$814$	−50.0361			−1.75376
$815$	−32.4730			−1.13748
$816$		0			0
$817$	−20.1375	−	16.0591i	−0.704523	−	0.561838i
$818$	−17.0781	+	74.8242i	−0.597123	+	2.61617i
$819$		0			0
$820$	−3.62937	−	15.9013i	−0.126743	−	0.555298i
$821$	5.49162	−	11.4035i	0.191659	−	0.397984i	−0.782889	−	0.622161i	$-0.786255\pi$
$821$	5.49162	−	11.4035i	0.191659	−	0.397984i	0.974549	+	0.224177i	$0.0719693\pi$
$822$		0			0
$823$	6.46427	−	8.10594i	0.225330	−	0.282555i	−0.656296	−	0.754504i	$-0.727878\pi$
$823$	6.46427	−	8.10594i	0.225330	−	0.282555i	0.881626	+	0.471948i	$0.156449\pi$
$824$	−33.4142	+	146.397i	−1.16404	+	5.09999i
$825$		0			0
$826$	25.0612	+	86.3004i	0.871990	+	3.00278i
$827$	−11.9366	−	9.51916i	−0.415078	−	0.331013i	0.393583	−	0.919289i	$-0.371236\pi$
$827$	−11.9366	−	9.51916i	−0.415078	−	0.331013i	−0.808660	+	0.588276i	$0.799807\pi$
$828$		0			0
$829$	9.57598	+	19.8847i	0.332588	+	0.690625i	0.998462	−	0.0554385i	$-0.0176557\pi$
$829$	9.57598	+	19.8847i	0.332588	+	0.690625i	−0.665875	+	0.746064i	$0.731941\pi$
$830$	−116.100	+	92.5868i	−4.02989	+	3.21373i
$831$		0			0
$832$			29.2484i			1.01400i
$833$	19.8325	−	31.8627i	0.687156	−	1.10398i
$834$		0			0
$835$	5.70433	+	24.9923i	0.197406	+	0.864894i
$836$	46.6686	+	58.5206i	1.61407	+	2.02398i
$837$		0			0
$838$	−27.9992	+	22.3286i	−0.967217	+	0.771330i
$839$	33.6883	−	42.2438i	1.16305	−	1.45842i	0.299540	−	0.954084i	$-0.403167\pi$
$839$	33.6883	−	42.2438i	1.16305	−	1.45842i	0.863509	−	0.504333i	$-0.168262\pi$
$840$		0			0
$841$	−40.9185	−	51.3102i	−1.41098	−	1.76932i
$842$	10.7573	+	2.45527i	0.370719	+	0.0846143i
$843$		0			0
$844$	−2.88629	−	12.6457i	−0.0993503	−	0.435282i
$845$	36.2614	+	17.4626i	1.24743	+	0.600730i
$846$		0			0
$847$	1.17670	−	2.85793i	0.0404318	−	0.0981998i
$848$	−1.35100	−	0.308356i	−0.0463934	−	0.0105890i
$849$		0			0
$850$	−46.1472	+	95.8257i	−1.58284	+	3.28680i
$851$			10.7098i			0.367127i
$852$		0			0
$853$	−2.16990	+	4.50584i	−0.0742958	+	0.154277i	−0.934809	−	0.355152i	$-0.884429\pi$
$853$	−2.16990	+	4.50584i	−0.0742958	+	0.154277i	0.860513	+	0.509429i	$0.170143\pi$
$854$	−11.7486	−	21.1513i	−0.402027	−	0.723781i
$855$		0			0
$856$	−15.2615	+	7.34953i	−0.521626	+	0.251202i
$857$	3.44342	−	15.0866i	0.117625	−	0.515348i	−0.881447	−	0.472282i	$-0.843430\pi$
$857$	3.44342	−	15.0866i	0.117625	−	0.515348i	0.999072	−	0.0430658i	$-0.0137125\pi$
$858$		0			0
$859$	−14.8238	−	30.7818i	−0.505780	−	1.05026i	−0.984998	−	0.172567i	$-0.944794\pi$
$859$	−14.8238	−	30.7818i	−0.505780	−	1.05026i	0.479218	−	0.877696i	$-0.340920\pi$
$860$	96.1446	−	46.3008i	3.27850	−	1.57884i
$861$		0			0
$862$	−2.74796	−	1.32335i	−0.0935960	−	0.0450735i
$863$			1.12739i			0.0383769i	0.999816	+	0.0191884i	$0.00610824\pi$
$863$			1.12739i			0.0383769i	−0.999816	+	0.0191884i	$0.993892\pi$
$864$		0			0
$865$	−27.8980	−	13.4350i	−0.948560	−	0.456803i
$866$	−11.1647	+	14.0001i	−0.379392	+	0.475742i
$867$		0			0
$868$	9.45994	+	3.89494i	0.321091	+	0.132203i
$869$	−7.11621	+	1.62423i	−0.241401	+	0.0550982i
$870$		0			0
$871$	−12.2563	+	2.79742i	−0.415289	+	0.0947869i
$872$	40.4048	+	32.2217i	1.36828	+	1.09117i
$873$		0			0
$874$	17.2471	−	13.7541i	0.583392	−	0.465239i
$875$	−8.27620	+	20.1011i	−0.279786	+	0.679540i
$876$		0			0
$877$	−25.0121	−	31.3642i	−0.844599	−	1.05909i	−0.997487	−	0.0708500i	$-0.977429\pi$
$877$	−25.0121	−	31.3642i	−0.844599	−	1.05909i	0.152888	−	0.988244i	$-0.451143\pi$
$878$	58.5594	−	28.2007i	1.97628	−	0.951728i
$879$		0			0
$880$	−145.427	+	33.1928i	−4.90235	+	1.11893i
$881$	−35.6341			−1.20054			−0.600271	−	0.799796i	$-0.704941\pi$
$881$	−35.6341			−1.20054			−0.600271	+	0.799796i	$0.704941\pi$
$882$		0			0
$883$	−30.0559			−1.01146			−0.505731	−	0.862691i	$-0.668777\pi$
$883$	−30.0559			−1.01146			−0.505731	+	0.862691i	$0.668777\pi$
$884$	−34.4460	+	7.86209i	−1.15855	+	0.264431i
$885$		0			0
$886$	42.7213	−	20.5735i	1.43525	−	0.691179i
$887$	15.1261	+	18.9676i	0.507886	+	0.636869i	0.967988	−	0.250997i	$-0.0807584\pi$
$887$	15.1261	+	18.9676i	0.507886	+	0.636869i	−0.460101	+	0.887866i	$0.652187\pi$
$888$		0			0
$889$	8.44622	−	2.45274i	0.283277	−	0.0822622i
$890$	19.8537	−	15.8328i	0.665497	−	0.530716i
$891$		0			0
$892$	−75.9838	−	60.5951i	−2.54413	−	2.02887i
$893$	0.0227402	−	0.00519030i	0.000760971	−	0.000173687i
$894$		0			0
$895$	−40.4153	+	9.22453i	−1.35093	+	0.308342i
$896$	46.2826	+	51.5696i	1.54619	+	1.72282i
$897$		0			0
$898$	16.1365	−	20.2345i	0.538482	−	0.675235i
$899$	6.38680	+	3.07572i	0.213012	+	0.102581i
$900$		0			0
$901$		−	0.548600i		−	0.0182765i
$902$	6.68207	+	3.21792i	0.222489	+	0.107145i
$903$		0			0
$904$	−154.383	+	74.3471i	−5.13471	+	2.47275i
$905$	−18.8492	−	39.1408i	−0.626569	−	1.30108i
$906$		0			0
$907$	−7.93461	+	34.7638i	−0.263465	+	1.15431i	0.654000	+	0.756495i	$0.273090\pi$
$907$	−7.93461	+	34.7638i	−0.263465	+	1.15431i	−0.917464	+	0.397819i	$0.869767\pi$
$908$	−106.879	+	51.4701i	−3.54690	+	1.70810i
$909$		0			0
$910$	−29.9606	+	8.70039i	−0.993183	+	0.288415i
$911$	15.1636	−	31.4876i	0.502393	−	1.04323i	−0.483421	−	0.875388i	$-0.660606\pi$
$911$	15.1636	−	31.4876i	0.502393	−	1.04323i	0.985814	−	0.167842i	$-0.0536798\pi$
$912$		0			0
$913$		−	49.0401i		−	1.62299i
$914$	−19.9409	+	41.4077i	−0.659586	+	1.36964i
$915$		0			0
$916$	142.475	+	32.5189i	4.70750	+	1.07446i
$917$	−0.793070	−	13.6061i	−0.0261895	−	0.449312i
$918$		0			0
$919$	49.4045	+	23.7919i	1.62970	+	0.784824i	0.999968	+	0.00801425i	$0.00255104\pi$
$919$	49.4045	+	23.7919i	1.62970	+	0.784824i	0.629736	+	0.776810i	$0.283163\pi$
$920$	12.6718	+	55.5190i	0.417778	+	1.83041i
$921$		0			0
$922$	40.2127	+	9.17828i	1.32433	+	0.302271i
$923$	5.02231	+	6.29778i	0.165311	+	0.207294i
$924$		0			0
$925$	27.0140	−	33.8745i	0.888215	−	1.11379i
$926$	−26.4041	+	21.0566i	−0.867694	+	0.691963i
$927$		0			0
$928$	113.622	+	142.477i	3.72982	+	4.67704i
$929$	−4.80395	−	21.0475i	−0.157613	−	0.690546i	−0.990547	−	0.137174i	$-0.956198\pi$
$929$	−4.80395	−	21.0475i	−0.157613	−	0.690546i	0.832934	−	0.553372i	$-0.186659\pi$
$930$		0			0
$931$	31.3084	+	3.39310i	1.02609	+	0.111204i
$932$			15.8284i			0.518475i
$933$		0			0
$934$	80.5100	−	64.2046i	2.63437	−	2.10084i
$935$	−25.6224	−	53.2056i	−0.837943	−	1.74001i
$936$		0			0
$937$	−6.14450	−	4.90008i	−0.200732	−	0.160079i	0.517965	−	0.855402i	$-0.326690\pi$
$937$	−6.14450	−	4.90008i	−0.200732	−	0.160079i	−0.718697	+	0.695323i	$0.755261\pi$
$938$	−41.7651	+	59.1279i	−1.36368	+	1.93059i
$939$		0			0
$940$	−0.0215038	+	0.0942142i	−0.000701376	+	0.00307293i
$941$	13.0795	−	16.4012i	0.426381	−	0.534665i	−0.521516	−	0.853241i	$-0.674633\pi$
$941$	13.0795	−	16.4012i	0.426381	−	0.534665i	0.947897	+	0.318576i	$0.103205\pi$
$942$		0			0
$943$	0.688768	−	1.43024i	0.0224294	−	0.0465751i
$944$	−37.8692	−	165.916i	−1.23254	−	5.40010i
$945$		0			0
$946$	−10.7976	+	47.3074i	−0.351060	+	1.53810i
$947$	15.9042	+	12.6832i	0.516817	+	0.412148i	0.846858	−	0.531819i	$-0.178491\pi$
$947$	15.9042	+	12.6832i	0.516817	+	0.412148i	−0.330041	+	0.943966i	$0.607063\pi$
$948$		0			0
$949$	7.80563			0.253381
$950$	−89.2444			−2.89547
$951$		0			0
$952$	−73.1370	+	103.542i	−2.37039	+	3.35581i
$953$	1.65405	+	3.43467i	0.0535800	+	0.111260i	0.926040	−	0.377426i	$-0.123191\pi$
$953$	1.65405	+	3.43467i	0.0535800	+	0.111260i	−0.872460	+	0.488686i	$0.837476\pi$
$954$		0			0
$955$	54.1445	+	12.3581i	1.75207	+	0.399900i
$956$	16.8662	+	3.84960i	0.545492	+	0.124505i
$957$		0			0
$958$	6.74136	+	13.9986i	0.217803	+	0.452273i
$959$	−19.2876	+	1.12424i	−0.622830	+	0.0363035i
$960$		0			0
$961$	30.4690			0.982870
$962$	19.8181			0.638963
$963$		0			0
$964$	101.304	+	80.7873i	3.26278	+	2.60198i
$965$	4.72738	−	20.7120i	0.152180	−	0.666743i
$966$		0			0
$967$	3.81379	+	16.7093i	0.122643	+	0.537336i	0.998499	+	0.0547631i	$0.0174404\pi$
$967$	3.81379	+	16.7093i	0.122643	+	0.537336i	−0.875856	+	0.482572i	$0.839702\pi$
$968$	−4.52949	+	9.40558i	−0.145583	+	0.302307i
$969$		0			0
$970$	10.3524	−	12.9815i	0.332396	−	0.416811i
$971$	0.151070	−	0.661883i	0.00484808	−	0.0212408i	−0.972446	−	0.233128i	$-0.925104\pi$
$971$	0.151070	−	0.661883i	0.00484808	−	0.0212408i	0.977294	+	0.211887i	$0.0679610\pi$
$972$		0			0
$973$	−4.86708	+	29.0183i	−0.156031	+	0.930285i
$974$	−5.50165	−	4.38742i	−0.176284	−	0.140582i
$975$		0			0
$976$	19.8803	+	41.2819i	0.636353	+	1.32140i
$977$	7.42087	−	5.91795i	0.237415	−	0.189332i	−0.497554	−	0.867433i	$-0.665768\pi$
$977$	7.42087	−	5.91795i	0.237415	−	0.189332i	0.734969	+	0.678101i	$0.237197\pi$
$978$		0			0
$979$			8.38610i			0.268021i
$980$	−68.9460	+	110.768i	−2.20240	+	3.53835i
$981$		0			0
$982$	−10.3085	−	45.1644i	−0.328957	−	1.44125i
$983$	−33.0858	−	41.4883i	−1.05527	−	1.32327i	−0.944169	−	0.329463i	$-0.893132\pi$
$983$	−33.0858	−	41.4883i	−1.05527	−	1.32327i	−0.111105	−	0.993809i	$-0.535439\pi$
$984$		0			0
$985$	−42.3264	+	33.7541i	−1.34863	+	1.07550i
$986$	−87.8970	+	110.219i	−2.79921	+	3.51010i
$987$		0			0
$988$	−18.4844	−	23.1787i	−0.588066	−	0.737412i
$989$	10.1257	+	2.31114i	0.321980	+	0.0734898i
$990$		0			0
$991$	−8.95540	−	39.2362i	−0.284478	−	1.24638i	−0.891986	−	0.452064i	$-0.850688\pi$
$991$	−8.95540	−	39.2362i	−0.284478	−	1.24638i	0.607508	−	0.794314i	$-0.292169\pi$
$992$	−12.2997	−	5.92322i	−0.390516	−	0.188063i
$993$		0			0
$994$	45.7453	+	7.67260i	1.45095	+	0.243360i
$995$	51.1564	+	11.6761i	1.62177	+	0.370158i
$996$		0			0
$997$	−11.9437	+	24.8013i	−0.378260	+	0.785465i	0.621737	+	0.783226i	$0.286427\pi$
$997$	−11.9437	+	24.8013i	−0.378260	+	0.785465i	−0.999997	+	0.00223954i	$0.999287\pi$
$998$		−	50.1224i		−	1.58660i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.62.20	yes	120
3.2	odd	2	inner	441.2.w.a.62.1	✓	120
49.34	odd	14	inner	441.2.w.a.377.1	yes	120
147.83	even	14	inner	441.2.w.a.377.20	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.1	✓	120	3.2	odd	2	inner
441.2.w.a.62.20	yes	120	1.1	even	1	trivial
441.2.w.a.377.1	yes	120	49.34	odd	14	inner
441.2.w.a.377.20	yes	120	147.83	even	14	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(2.63522 - 0.601472i) q^{2} +(4.78069 - 2.30226i) q^{4} +(-2.19013 - 2.74633i) q^{5} +(-1.96904 + 1.76717i) q^{7} +(6.98686 - 5.57183i) q^{8} +(-7.42332 - 5.91990i) q^{10} +(3.05696 - 0.697731i) q^{11} +(-1.21079 + 0.276355i) q^{13} +(-4.12595 + 5.84121i) q^{14} +(8.44394 - 10.5884i) q^{16} +(4.83058 + 2.32629i) q^{17} +4.49882i q^{19} +(-16.7931 - 8.08712i) q^{20} +(7.63610 - 3.67735i) q^{22} +(-0.787106 - 1.63444i) q^{23} +(-1.63309 + 7.15501i) q^{25} +(-3.02448 + 1.45651i) q^{26} +(-5.34487 + 12.9815i) q^{28} +(-4.22069 + 8.76436i) q^{29} -0.728724i q^{31} +(8.12821 - 16.8784i) q^{32} +(14.1289 + 3.22482i) q^{34} +(9.16569 + 1.53731i) q^{35} +(-5.31902 - 2.56150i) q^{37} +(2.70591 + 11.8554i) q^{38} +(-30.6042 - 6.98521i) q^{40} +(0.545593 + 0.684152i) q^{41} +(-3.56964 + 4.47618i) q^{43} +(13.0080 - 10.3735i) q^{44} +(-3.05727 - 3.83370i) q^{46} +(-0.00115370 - 0.00505470i) q^{47} +(0.754221 - 6.95925i) q^{49} +19.8373i q^{50} +(-5.15217 + 4.10872i) q^{52} +(-0.0443955 - 0.0921883i) q^{53} +(-8.61134 - 6.86731i) q^{55} +(-3.91101 + 23.3181i) q^{56} +(-5.85094 + 25.6347i) q^{58} +(7.83482 - 9.82456i) q^{59} +(-1.46794 + 3.04820i) q^{61} +(-0.438307 - 1.92035i) q^{62} +(5.24054 - 22.9603i) q^{64} +(3.41075 + 2.71998i) q^{65} +10.1225 q^{67} +28.4492 q^{68} +(25.0783 - 1.46176i) q^{70} +(-2.81417 - 5.84369i) q^{71} +(-6.12750 - 1.39856i) q^{73} +(-15.5575 - 3.55089i) q^{74} +(10.3574 + 21.5074i) q^{76} +(-4.78626 + 6.77602i) q^{77} -2.32787 q^{79} -47.5725 q^{80} +(1.84926 + 1.47473i) q^{82} +(3.48021 - 15.2478i) q^{83} +(-4.19084 - 18.3613i) q^{85} +(-6.71448 + 13.9428i) q^{86} +(17.4709 - 21.9078i) q^{88} +(-0.595133 + 2.60745i) q^{89} +(1.89573 - 2.68383i) q^{91} +(-7.52581 - 6.00164i) q^{92} +(-0.00608053 - 0.0126263i) q^{94} +(12.3553 - 9.85299i) q^{95} +1.74875i q^{97} +(-2.19826 - 18.7928i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70}+ \cdots - 112 q^{94}+O(q^{100}) \) 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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