LMFDB - Embedded newform 224.2.p.a.159.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(31,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("224.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.p (of order $6$, degree $2$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.2353561680715186176.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 2 x^{14} + 41 x^{12} - 92 x^{11} + 66 x^{10} - 104 x^{9} + 291 x^{8} - 388 x^{7} + \cdots + 4 $ x^16 - 4x^15 + 2x^14 + 41x^12 - 92x^11 + 66x^10 - 104x^9 + 291x^8 - 388x^7 + 366x^6 - 344x^5 + 286x^4 - 184x^3 + 84x^2 - 24x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			159.4
Root			$0.224274 + 0.447866i$ of defining polynomial
Character	$\chi$	$=$	224.159
Dual form			224.2.p.a.31.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0913671 - 0.158252i) q^{3} +(-3.08101 - 1.77882i) q^{5} +(-2.64485 - 0.0690906i) q^{7} +(1.48330 - 2.56916i) q^{9} +O(q^{10})$	\(q+(-0.0913671 - 0.158252i) q^{3} +(-3.08101 - 1.77882i) q^{5} +(-2.64485 - 0.0690906i) q^{7} +(1.48330 - 2.56916i) q^{9} +(-4.74455 + 2.73927i) q^{11} -2.70791i q^{13} +0.650103i q^{15} +(-0.845123 + 0.487932i) q^{17} +(2.73622 - 4.73927i) q^{19} +(0.230718 + 0.424866i) q^{21} +(3.90744 + 2.25596i) q^{23} +(3.82843 + 6.63103i) q^{25} -1.09030 q^{27} -2.96661 q^{29} +(-3.27092 - 5.66540i) q^{31} +(0.866990 + 0.500557i) q^{33} +(8.02591 + 4.91759i) q^{35} +(0.597709 - 1.03526i) q^{37} +(-0.428534 + 0.247414i) q^{39} -2.70791i q^{41} -1.02384i q^{43} +(-9.14016 + 5.27707i) q^{45} +(-2.01878 + 3.49662i) q^{47} +(6.99045 + 0.365468i) q^{49} +(0.154433 + 0.0891618i) q^{51} +(3.42614 + 5.93424i) q^{53} +19.4907 q^{55} -1.00000 q^{57} +(-2.79928 - 4.84850i) q^{59} +(7.53093 + 4.34798i) q^{61} +(-4.10062 + 6.69255i) q^{63} +(-4.81690 + 8.34312i) q^{65} +(3.42934 - 1.97993i) q^{67} -0.824482i q^{69} -13.3002i q^{71} +(-8.29504 + 4.78914i) q^{73} +(0.699584 - 1.21172i) q^{75} +(12.7379 - 6.91714i) q^{77} +(-3.35924 - 1.93946i) q^{79} +(-4.35029 - 7.53493i) q^{81} -2.24331 q^{83} +3.47178 q^{85} +(0.271050 + 0.469473i) q^{87} +(-12.3523 - 7.13159i) q^{89} +(-0.187091 + 7.16203i) q^{91} +(-0.597709 + 1.03526i) q^{93} +(-16.8606 + 9.73449i) q^{95} -10.7412i q^{97} +16.2527i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^9	$ 16 q - 8 q^{9} - 24 q^{21} + 16 q^{25} + 16 q^{29} + 24 q^{33} - 8 q^{37} - 24 q^{45} - 32 q^{49} - 8 q^{53} - 16 q^{57} - 24 q^{61} + 8 q^{65} - 24 q^{73} + 64 q^{77} - 48 q^{81} - 16 q^{85} - 72 q^{89} + 8 q^{93}+O(q^{100}) $ 16 * q - 8 * q^9 - 24 * q^21 + 16 * q^25 + 16 * q^29 + 24 * q^33 - 8 * q^37 - 24 * q^45 - 32 * q^49 - 8 * q^53 - 16 * q^57 - 24 * q^61 + 8 * q^65 - 24 * q^73 + 64 * q^77 - 48 * q^81 - 16 * q^85 - 72 * q^89 + 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.0913671	−	0.158252i	−0.0527508	−	0.0913671i	0.838444	−	0.544987i	$-0.183466\pi$
$3$	−0.0913671	−	0.158252i	−0.0527508	−	0.0913671i	−0.891195	+	0.453620i	$0.850132\pi$
$4$		0			0
$5$	−3.08101	−	1.77882i	−1.37787	−	0.795514i	−0.385968	−	0.922512i	$-0.626132\pi$
$5$	−3.08101	−	1.77882i	−1.37787	−	0.795514i	−0.991903	+	0.126998i	$0.959466\pi$
$6$		0			0
$7$	−2.64485	−	0.0690906i	−0.999659	−	0.0261138i
$7$	−2.64485	−	0.0690906i	−0.999659	−	0.0261138i
$8$		0			0
$9$	1.48330	−	2.56916i	0.494435	−	0.856386i
$10$		0			0
$11$	−4.74455	+	2.73927i	−1.43053	+	0.825920i	−0.997161	−	0.0752949i	$-0.976010\pi$
$11$	−4.74455	+	2.73927i	−1.43053	+	0.825920i	−0.433373	+	0.901214i	$0.642677\pi$
$12$		0			0
$13$		−	2.70791i		−	0.751040i	−0.926814	−	0.375520i	$-0.877464\pi$
$13$		−	2.70791i		−	0.751040i	0.926814	−	0.375520i	$-0.122536\pi$
$14$		0			0
$15$			0.650103i			0.167856i
$16$		0			0
$17$	−0.845123	+	0.487932i	−0.204972	+	0.118341i	−0.598973	−	0.800769i	$-0.704424\pi$
$17$	−0.845123	+	0.487932i	−0.204972	+	0.118341i	0.394000	+	0.919110i	$0.371091\pi$
$18$		0			0
$19$	2.73622	−	4.73927i	0.627731	−	1.08726i	−0.360275	−	0.932846i	$-0.617317\pi$
$19$	2.73622	−	4.73927i	0.627731	−	1.08726i	0.988006	−	0.154416i	$-0.0493496\pi$
$20$		0			0
$21$	0.230718	+	0.424866i	0.0503469	+	0.0927134i
$22$		0			0
$23$	3.90744	+	2.25596i	0.814757	+	0.470400i	0.848605	−	0.529027i	$-0.177443\pi$
$23$	3.90744	+	2.25596i	0.814757	+	0.470400i	−0.0338478	+	0.999427i	$0.510776\pi$
$24$		0			0
$25$	3.82843	+	6.63103i	0.765685	+	1.32621i
$26$		0			0
$27$	−1.09030			−0.209829
$28$		0			0
$29$	−2.96661			−0.550885			−0.275443	−	0.961318i	$-0.588824\pi$
$29$	−2.96661			−0.550885			−0.275443	+	0.961318i	$0.588824\pi$
$30$		0			0
$31$	−3.27092	−	5.66540i	−0.587475	−	1.01754i	−0.994562	−	0.104147i	$-0.966789\pi$
$31$	−3.27092	−	5.66540i	−0.587475	−	1.01754i	0.407087	−	0.913389i	$-0.366545\pi$
$32$		0			0
$33$	0.866990	+	0.500557i	0.150924	+	0.0871358i
$34$		0			0
$35$	8.02591	+	4.91759i	1.35663	+	0.831224i
$36$		0			0
$37$	0.597709	−	1.03526i	0.0982627	−	0.170196i	−0.812703	−	0.582678i	$-0.802005\pi$
$37$	0.597709	−	1.03526i	0.0982627	−	0.170196i	0.910966	+	0.412482i	$0.135338\pi$
$38$		0			0
$39$	−0.428534	+	0.247414i	−0.0686204	+	0.0396180i
$40$		0			0
$41$		−	2.70791i		−	0.422905i	−0.977388	−	0.211453i	$-0.932181\pi$
$41$		−	2.70791i		−	0.422905i	0.977388	−	0.211453i	$-0.0678194\pi$
$42$		0			0
$43$		−	1.02384i		−	0.156135i	−0.996948	−	0.0780674i	$-0.975125\pi$
$43$		−	1.02384i		−	0.156135i	0.996948	−	0.0780674i	$-0.0248749\pi$
$44$		0			0
$45$	−9.14016	+	5.27707i	−1.36253	+	0.786660i
$46$		0			0
$47$	−2.01878	+	3.49662i	−0.294469	+	0.510035i	−0.974861	−	0.222813i	$-0.928476\pi$
$47$	−2.01878	+	3.49662i	−0.294469	+	0.510035i	0.680392	+	0.732848i	$0.261809\pi$
$48$		0			0
$49$	6.99045	+	0.365468i	0.998636	+	0.0522097i
$50$		0			0
$51$	0.154433	+	0.0891618i	0.0216249	+	0.0124852i
$52$		0			0
$53$	3.42614	+	5.93424i	0.470616	+	0.815131i	0.999435	−	0.0336037i	$-0.0106984\pi$
$53$	3.42614	+	5.93424i	0.470616	+	0.815131i	−0.528819	+	0.848734i	$0.677365\pi$
$54$		0			0
$55$	19.4907			2.62812
$56$		0			0
$57$	−1.00000			−0.132453
$58$		0			0
$59$	−2.79928	−	4.84850i	−0.364435	−	0.631221i	0.624250	−	0.781225i	$-0.285405\pi$
$59$	−2.79928	−	4.84850i	−0.364435	−	0.631221i	−0.988685	+	0.150004i	$0.952071\pi$
$60$		0			0
$61$	7.53093	+	4.34798i	0.964236	+	0.556702i	0.897474	−	0.441067i	$-0.145400\pi$
$61$	7.53093	+	4.34798i	0.964236	+	0.556702i	0.0667620	+	0.997769i	$0.478733\pi$
$62$		0			0
$63$	−4.10062	+	6.69255i	−0.516630	+	0.843182i
$64$		0			0
$65$	−4.81690	+	8.34312i	−0.597463	+	1.03484i
$66$		0			0
$67$	3.42934	−	1.97993i	0.418960	−	0.241887i	−0.275672	−	0.961252i	$-0.588900\pi$
$67$	3.42934	−	1.97993i	0.418960	−	0.241887i	0.694632	+	0.719365i	$0.255567\pi$
$68$		0			0
$69$		−	0.824482i		−	0.0992560i
$70$		0			0
$71$		−	13.3002i		−	1.57844i	−0.614108	−	0.789222i	$-0.710484\pi$
$71$		−	13.3002i		−	1.57844i	0.614108	−	0.789222i	$-0.289516\pi$
$72$		0			0
$73$	−8.29504	+	4.78914i	−0.970860	+	0.560527i	−0.899498	−	0.436924i	$-0.856068\pi$
$73$	−8.29504	+	4.78914i	−0.970860	+	0.560527i	−0.0713620	+	0.997450i	$0.522735\pi$
$74$		0			0
$75$	0.699584	−	1.21172i	0.0807810	−	0.139917i
$76$		0			0
$77$	12.7379	−	6.91714i	1.45161	−	0.788281i
$78$		0			0
$79$	−3.35924	−	1.93946i	−0.377944	−	0.218206i	0.298980	−	0.954260i	$-0.403354\pi$
$79$	−3.35924	−	1.93946i	−0.377944	−	0.218206i	−0.676923	+	0.736054i	$0.736687\pi$
$80$		0			0
$81$	−4.35029	−	7.53493i	−0.483366	−	0.837215i
$82$		0			0
$83$	−2.24331			−0.246235			−0.123118	−	0.992392i	$-0.539289\pi$
$83$	−2.24331			−0.246235			−0.123118	+	0.992392i	$0.539289\pi$
$84$		0			0
$85$	3.47178			0.376567
$86$		0			0
$87$	0.271050	+	0.469473i	0.0290596	+	0.0503328i
$88$		0			0
$89$	−12.3523	−	7.13159i	−1.30934	−	0.755947i	−0.327353	−	0.944902i	$-0.606156\pi$
$89$	−12.3523	−	7.13159i	−1.30934	−	0.755947i	−0.981986	+	0.188956i	$0.939490\pi$
$90$		0			0
$91$	−0.187091	+	7.16203i	−0.0196125	+	0.750784i
$92$		0			0
$93$	−0.597709	+	1.03526i	−0.0619795	+	0.107352i
$94$		0			0
$95$	−16.8606	+	9.73449i	−1.72986	+	0.998738i
$96$		0			0
$97$		−	10.7412i		−	1.09061i	−0.838239	−	0.545304i	$-0.816414\pi$
$97$		−	10.7412i		−	1.09061i	0.838239	−	0.545304i	$-0.183586\pi$
$98$		0			0
$99$			16.2527i			1.63345i
$100$		0			0
$101$	7.39077	−	4.26706i	0.735409	−	0.424588i	−0.0849888	−	0.996382i	$-0.527085\pi$
$101$	7.39077	−	4.26706i	0.735409	−	0.424588i	0.820398	+	0.571793i	$0.193752\pi$
$102$		0			0
$103$	−2.08184	+	3.60586i	−0.205130	+	0.355296i	−0.950174	−	0.311720i	$-0.899095\pi$
$103$	−2.08184	+	3.60586i	−0.205130	+	0.355296i	0.745044	+	0.667015i	$0.232428\pi$
$104$		0			0
$105$	0.0449160	−	1.71943i	0.00438335	−	0.167799i
$106$		0			0
$107$	−7.08264	−	4.08916i	−0.684704	−	0.395314i	0.116921	−	0.993141i	$-0.462698\pi$
$107$	−7.08264	−	4.08916i	−0.684704	−	0.395314i	−0.801625	+	0.597827i	$0.796031\pi$
$108$		0			0
$109$	2.74741	+	4.75866i	0.263155	+	0.455797i	0.967078	−	0.254478i	$-0.0819038\pi$
$109$	2.74741	+	4.75866i	0.263155	+	0.455797i	−0.703924	+	0.710275i	$0.748570\pi$
$110$		0			0
$111$	−0.218444			−0.0207337
$112$		0			0
$113$	−11.3574			−1.06842			−0.534209	−	0.845352i	$-0.679391\pi$
$113$	−11.3574			−1.06842			−0.534209	+	0.845352i	$0.679391\pi$
$114$		0			0
$115$	−8.02591	−	13.9013i	−0.748420	−	1.29630i
$116$		0			0
$117$	−6.95706	−	4.01666i	−0.643181	−	0.371340i
$118$		0			0
$119$	2.26893	−	1.23212i	0.207993	−	0.112948i
$120$		0			0
$121$	9.50715	−	16.4669i	0.864286	−	1.49699i
$122$		0			0
$123$	−0.428534	+	0.247414i	−0.0386396	+	0.0223086i
$124$		0			0
$125$		−	9.45215i		−	0.845426i
$126$		0			0
$127$		−	14.2899i		−	1.26802i	−0.773325	−	0.634010i	$-0.781408\pi$
$127$		−	14.2899i		−	1.26802i	0.773325	−	0.634010i	$-0.218592\pi$
$128$		0			0
$129$	−0.162026	+	0.0935457i	−0.0142656	+	0.00823624i
$130$		0			0
$131$	6.50272	−	11.2630i	0.568145	−	0.984057i	−0.428604	−	0.903492i	$-0.640994\pi$
$131$	6.50272	−	11.2630i	0.568145	−	0.984057i	0.996749	−	0.0805641i	$-0.0256722\pi$
$132$		0			0
$133$	−7.56432	+	12.3456i	−0.655909	+	1.07050i
$134$		0			0
$135$	3.35924	+	1.93946i	0.289117	+	0.166922i
$136$		0			0
$137$	7.31690	+	12.6732i	0.625125	+	1.08275i	0.988517	+	0.151112i	$0.0482854\pi$
$137$	7.31690	+	12.6732i	0.625125	+	1.08275i	−0.363391	+	0.931637i	$0.618381\pi$
$138$		0			0
$139$	−11.3608			−0.963613			−0.481807	−	0.876278i	$-0.660019\pi$
$139$	−11.3608			−0.963613			−0.481807	+	0.876278i	$0.660019\pi$
$140$		0			0
$141$	0.737799			0.0621339
$142$		0			0
$143$	7.41770	+	12.8478i	0.620299	+	1.07439i
$144$		0			0
$145$	9.14016	+	5.27707i	0.759049	+	0.438237i
$146$		0			0
$147$	−0.580861	−	1.13965i	−0.0479086	−	0.0939965i
$148$		0			0
$149$	5.08101	−	8.80057i	0.416253	−	0.720971i	−0.579306	−	0.815110i	$-0.696676\pi$
$149$	5.08101	−	8.80057i	0.416253	−	0.720971i	0.995559	+	0.0941390i	$0.0300098\pi$
$150$		0			0
$151$	−8.37788	+	4.83697i	−0.681783	+	0.393627i	−0.800526	−	0.599298i	$-0.795447\pi$
$151$	−8.37788	+	4.83697i	−0.681783	+	0.393627i	0.118744	+	0.992925i	$0.462113\pi$
$152$		0			0
$153$			2.89501i			0.234047i
$154$		0			0
$155$			23.2736i			1.86938i
$156$		0			0
$157$	−2.94085	+	1.69790i	−0.234706	+	0.135507i	−0.612741	−	0.790284i	$-0.709933\pi$
$157$	−2.94085	+	1.69790i	−0.234706	+	0.135507i	0.378035	+	0.925791i	$0.376600\pi$
$158$		0			0
$159$	0.626072	−	1.08439i	0.0496507	−	0.0859976i
$160$		0			0
$161$	−10.1787	−	6.23664i	−0.802196	−	0.491516i
$162$		0			0
$163$	17.8174	+	10.2869i	1.39557	+	0.805731i	0.993924	−	0.110065i	$-0.0351060\pi$
$163$	17.8174	+	10.2869i	1.39557	+	0.805731i	0.401643	+	0.915796i	$0.368439\pi$
$164$		0			0
$165$	−1.78081	−	3.08445i	−0.138636	−	0.240124i
$166$		0			0
$167$	−2.01269			−0.155746			−0.0778732	−	0.996963i	$-0.524813\pi$
$167$	−2.01269			−0.155746			−0.0778732	+	0.996963i	$0.524813\pi$
$168$		0			0
$169$	5.66720			0.435938
$170$		0			0
$171$	−8.11728	−	14.0595i	−0.620744	−	1.07516i
$172$		0			0
$173$	−8.00191	−	4.61990i	−0.608374	−	0.351245i	0.163955	−	0.986468i	$-0.447575\pi$
$173$	−8.00191	−	4.61990i	−0.608374	−	0.351245i	−0.772329	+	0.635223i	$0.780908\pi$
$174$		0			0
$175$	−9.66747	−	17.8026i	−0.730792	−	1.34575i
$176$		0			0
$177$	−0.511524	+	0.885986i	−0.0384485	+	0.0665948i
$178$		0			0
$179$	3.37920	−	1.95098i	0.252573	−	0.145823i	−0.368369	−	0.929680i	$-0.620084\pi$
$179$	3.37920	−	1.95098i	0.252573	−	0.145823i	0.620942	+	0.783857i	$0.286750\pi$
$180$		0			0
$181$			12.8227i			0.953104i	0.879146	+	0.476552i	$0.158114\pi$
$181$			12.8227i			0.953104i	−0.879146	+	0.476552i	$0.841886\pi$
$182$		0			0
$183$		−	1.58905i		−	0.117466i
$184$		0			0
$185$	−3.68310	+	2.12644i	−0.270787	+	0.156339i
$186$		0			0
$187$	2.67315	−	4.63003i	0.195480	−	0.338581i
$188$		0			0
$189$	2.88369	+	0.0753296i	0.209757	+	0.00547942i
$190$		0			0
$191$	8.03941	+	4.64156i	0.581711	+	0.335851i	0.761813	−	0.647797i	$-0.224309\pi$
$191$	8.03941	+	4.64156i	0.581711	+	0.335851i	−0.180102	+	0.983648i	$0.557643\pi$
$192$		0			0
$193$	−1.78789	−	3.09671i	−0.128695	−	0.222906i	0.794476	−	0.607295i	$-0.207745\pi$
$193$	−1.78789	−	3.09671i	−0.128695	−	0.222906i	−0.923171	+	0.384389i	$0.874412\pi$
$194$		0			0
$195$	1.76042			0.126067
$196$		0			0
$197$	6.41388			0.456970			0.228485	−	0.973547i	$-0.426623\pi$
$197$	6.41388			0.456970			0.228485	+	0.973547i	$0.426623\pi$
$198$		0			0
$199$	7.28322	+	12.6149i	0.516294	+	0.894248i	0.999821	+	0.0189182i	$0.00602220\pi$
$199$	7.28322	+	12.6149i	0.516294	+	0.894248i	−0.483527	+	0.875329i	$0.660644\pi$
$200$		0			0
$201$	−0.626657	−	0.361801i	−0.0442010	−	0.0255194i
$202$		0			0
$203$	7.84623	+	0.204965i	0.550697	+	0.0143857i
$204$		0			0
$205$	−4.81690	+	8.34312i	−0.336427	+	0.582709i
$206$		0			0
$207$	11.5918	−	6.69255i	0.805689	−	0.465165i
$208$		0			0
$209$			29.9809i			2.07382i
$210$		0			0
$211$		−	16.3376i		−	1.12472i	−0.826891	−	0.562362i	$-0.809893\pi$
$211$		−	16.3376i		−	1.12472i	0.826891	−	0.562362i	$-0.190107\pi$
$212$		0			0
$213$	−2.10479	+	1.21520i	−0.144218	+	0.0832642i
$214$		0			0
$215$	−1.82124	+	3.15448i	−0.124207	+	0.215134i
$216$		0			0
$217$	8.25967	+	15.2101i	0.560703	+	1.03253i
$218$		0			0
$219$	1.51579	+	0.875139i	0.102427	+	0.0591364i
$220$		0			0
$221$	1.32128	+	2.28852i	0.0888788	+	0.153943i
$222$		0			0
$223$	24.8100			1.66140			0.830700	−	0.556721i	$-0.187941\pi$
$223$	24.8100			1.66140			0.830700	+	0.556721i	$0.187941\pi$
$224$		0			0
$225$	22.7149			1.51433
$226$		0			0
$227$	10.9166	+	18.9080i	0.724558	+	1.25497i	0.959156	+	0.282878i	$0.0912893\pi$
$227$	10.9166	+	18.9080i	0.724558	+	1.25497i	−0.234598	+	0.972092i	$0.575377\pi$
$228$		0			0
$229$	3.87605	+	2.23784i	0.256136	+	0.147880i	0.622571	−	0.782563i	$-0.286088\pi$
$229$	3.87605	+	2.23784i	0.256136	+	0.147880i	−0.366434	+	0.930444i	$0.619422\pi$
$230$		0			0
$231$	−2.25848	−	1.38380i	−0.148597	−	0.0910473i
$232$		0			0
$233$	−7.64016	+	13.2331i	−0.500523	+	0.866932i	0.499476	+	0.866327i	$0.333526\pi$
$233$	−7.64016	+	13.2331i	−0.500523	+	0.866932i	−1.00000		0.000604495i	$0.999808\pi$
$234$		0			0
$235$	12.4398	−	7.18210i	0.811480	−	0.468508i
$236$		0			0
$237$			0.708810i			0.0460421i
$238$		0			0
$239$		−	8.13818i		−	0.526415i	−0.964739	−	0.263208i	$-0.915220\pi$
$239$		−	8.13818i		−	0.526415i	0.964739	−	0.263208i	$-0.0847804\pi$
$240$		0			0
$241$	24.5143	−	14.1533i	1.57910	−	0.911697i	0.584120	−	0.811667i	$-0.301440\pi$
$241$	24.5143	−	14.1533i	1.57910	−	0.911697i	0.994984	−	0.100029i	$-0.0318937\pi$
$242$		0			0
$243$	−2.43040	+	4.20958i	−0.155910	+	0.270045i
$244$		0			0
$245$	−20.8876	−	13.5608i	−1.33446	−	0.866367i
$246$		0			0
$247$	−12.8335	−	7.40944i	−0.816578	−	0.471451i
$248$		0			0
$249$	0.204965	+	0.355009i	0.0129891	+	0.0224978i
$250$		0			0
$251$	−9.19315			−0.580267			−0.290133	−	0.956986i	$-0.593700\pi$
$251$	−9.19315			−0.580267			−0.290133	+	0.956986i	$0.593700\pi$
$252$		0			0
$253$	−24.7187			−1.55405
$254$		0			0
$255$	−0.317206	−	0.549417i	−0.0198642	−	0.0344059i
$256$		0			0
$257$	14.0547	+	8.11449i	0.876708	+	0.506168i	0.869572	−	0.493807i	$-0.164395\pi$
$257$	14.0547	+	8.11449i	0.876708	+	0.506168i	0.00713657	+	0.999975i	$0.497728\pi$
$258$		0			0
$259$	−1.65238	+	2.69682i	−0.102674	+	0.167572i
$260$		0			0
$261$	−4.40038	+	7.62169i	−0.272377	+	0.471770i
$262$		0			0
$263$	16.9598	−	9.79173i	1.04578	−	0.603784i	0.124318	−	0.992242i	$-0.460326\pi$
$263$	16.9598	−	9.79173i	1.04578	−	0.603784i	0.921466	+	0.388459i	$0.126992\pi$
$264$		0			0
$265$		−	24.3780i		−	1.49753i
$266$		0			0
$267$			2.60637i			0.159507i
$268$		0			0
$269$	1.74939	−	1.01001i	0.106662	−	0.0615815i	−0.445720	−	0.895172i	$-0.647052\pi$
$269$	1.74939	−	1.01001i	0.106662	−	0.0615815i	0.552382	+	0.833591i	$0.313719\pi$
$270$		0			0
$271$	−12.8231	+	22.2102i	−0.778947	+	1.34918i	0.153603	+	0.988133i	$0.450912\pi$
$271$	−12.8231	+	22.2102i	−0.778947	+	1.34918i	−0.932549	+	0.361042i	$0.882421\pi$
$272$		0			0
$273$	1.15050	−	0.624766i	0.0696315	−	0.0378125i
$274$		0			0
$275$	−36.3283	−	20.9742i	−2.19068	−	1.26479i
$276$		0			0
$277$	−15.5882	−	26.9995i	−0.936602	−	1.62224i	−0.771752	−	0.635923i	$-0.780619\pi$
$277$	−15.5882	−	26.9995i	−0.936602	−	1.62224i	−0.164850	−	0.986319i	$-0.552714\pi$
$278$		0			0
$279$	−19.4071			−1.16187
$280$		0			0
$281$	−1.97695			−0.117935			−0.0589675	−	0.998260i	$-0.518781\pi$
$281$	−1.97695			−0.117935			−0.0589675	+	0.998260i	$0.518781\pi$
$282$		0			0
$283$	13.8116	+	23.9223i	0.821013	+	1.42204i	0.904929	+	0.425563i	$0.139924\pi$
$283$	13.8116	+	23.9223i	0.821013	+	1.42204i	−0.0839164	+	0.996473i	$0.526743\pi$
$284$		0			0
$285$	3.08101	+	1.77882i	0.182503	+	0.105368i
$286$		0			0
$287$	−0.187091	+	7.16203i	−0.0110437	+	0.422761i
$288$		0			0
$289$	−8.02384	+	13.8977i	−0.471991	+	0.817512i
$290$		0			0
$291$	−1.69983	+	0.981395i	−0.0996456	+	0.0575304i
$292$		0			0
$293$			10.5289i			0.615105i	0.951531	+	0.307552i	$0.0995099\pi$
$293$			10.5289i			0.615105i	−0.951531	+	0.307552i	$0.900490\pi$
$294$		0			0
$295$			19.9177i			1.15965i
$296$		0			0
$297$	5.17299	−	2.98663i	0.300167	−	0.173302i
$298$		0			0
$299$	6.10895	−	10.5810i	0.353290	−	0.611916i
$300$		0			0
$301$	−0.0707380	+	2.70791i	−0.00407727	+	0.156082i
$302$		0			0
$303$	−1.35055	−	0.779738i	−0.0775868	−	0.0447948i
$304$		0			0
$305$	−15.4686	−	26.7924i	−0.885729	−	1.53413i
$306$		0			0
$307$	−27.0533			−1.54401			−0.772007	−	0.635615i	$-0.780747\pi$
$307$	−27.0533			−1.54401			−0.772007	+	0.635615i	$0.780747\pi$
$308$		0			0
$309$	0.760847			0.0432831
$310$		0			0
$311$	−12.6926	−	21.9842i	−0.719731	−	1.24661i	−0.961106	−	0.276179i	$-0.910932\pi$
$311$	−12.6926	−	21.9842i	−0.719731	−	1.24661i	0.241376	−	0.970432i	$-0.422401\pi$
$312$		0			0
$313$	3.98528	+	2.30090i	0.225261	+	0.130055i	0.608384	−	0.793643i	$-0.291818\pi$
$313$	3.98528	+	2.30090i	0.225261	+	0.130055i	−0.383123	+	0.923697i	$0.625151\pi$
$314$		0			0
$315$	24.5389	−	13.3256i	1.38261	−	0.750810i
$316$		0			0
$317$	3.76928	−	6.52859i	0.211704	−	0.366682i	−0.740544	−	0.672008i	$-0.765432\pi$
$317$	3.76928	−	6.52859i	0.211704	−	0.366682i	0.952248	+	0.305326i	$0.0987654\pi$
$318$		0			0
$319$	14.0752	−	8.12633i	0.788061	−	0.454987i
$320$		0			0
$321$			1.49446i			0.0834125i
$322$		0			0
$323$			5.34035i			0.297145i
$324$		0			0
$325$	17.9563	−	10.3671i	0.996034	−	0.575061i
$326$		0			0
$327$	0.502046	−	0.869570i	0.0277632	−	0.0480873i
$328$		0			0
$329$	5.58094	−	9.10857i	0.307687	−	0.502171i
$330$		0			0
$331$	2.40246	+	1.38706i	0.132051	+	0.0762398i	0.564570	−	0.825385i	$-0.309042\pi$
$331$	2.40246	+	1.38706i	0.132051	+	0.0762398i	−0.432519	+	0.901625i	$0.642375\pi$
$332$		0			0
$333$	−1.77317	−	3.07122i	−0.0971690	−	0.168302i
$334$		0			0
$335$	−14.0878			−0.769697
$336$		0			0
$337$	−25.2716			−1.37663			−0.688315	−	0.725412i	$-0.741649\pi$
$337$	−25.2716			−1.37663			−0.688315	+	0.725412i	$0.741649\pi$
$338$		0			0
$339$	1.03770	+	1.79734i	0.0563599	+	0.0976182i
$340$		0			0
$341$	31.0381	+	17.9198i	1.68081	+	0.970414i
$342$		0			0
$343$	−18.4634	−	1.44958i	−0.996932	−	0.0782701i
$344$		0			0
$345$	−1.46661	+	2.54024i	−0.0789595	+	0.136762i
$346$		0			0
$347$	9.42472	−	5.44137i	0.505946	−	0.292108i	−0.225220	−	0.974308i	$-0.572310\pi$
$347$	9.42472	−	5.44137i	0.505946	−	0.292108i	0.731165	+	0.682200i	$0.238977\pi$
$348$		0			0
$349$		−	20.6437i		−	1.10503i	−0.833503	−	0.552516i	$-0.813668\pi$
$349$		−	20.6437i		−	1.10503i	0.833503	−	0.552516i	$-0.186332\pi$
$350$		0			0
$351$			2.95245i			0.157590i
$352$		0			0
$353$	1.57831	−	0.911236i	0.0840048	−	0.0485002i	−0.457409	−	0.889256i	$-0.651223\pi$
$353$	1.57831	−	0.911236i	0.0840048	−	0.0485002i	0.541414	+	0.840756i	$0.317889\pi$
$354$		0			0
$355$	−23.6587	+	40.9781i	−1.25567	+	2.17489i
$356$		0			0
$357$	−0.402291	−	0.246489i	−0.0212915	−	0.0130456i
$358$		0			0
$359$	2.04403	+	1.18012i	0.107880	+	0.0622843i	0.552969	−	0.833202i	$-0.313495\pi$
$359$	2.04403	+	1.18012i	0.107880	+	0.0622843i	−0.445089	+	0.895486i	$0.646828\pi$
$360$		0			0
$361$	−5.47376	−	9.48083i	−0.288092	−	0.498991i
$362$		0			0
$363$	−3.47456			−0.182367
$364$		0			0
$365$	34.0761			1.78363
$366$		0			0
$367$	3.27738	+	5.67660i	0.171078	+	0.296316i	0.938797	−	0.344471i	$-0.111942\pi$
$367$	3.27738	+	5.67660i	0.171078	+	0.296316i	−0.767719	+	0.640787i	$0.778608\pi$
$368$		0			0
$369$	−6.95706	−	4.01666i	−0.362170	−	0.209099i
$370$		0			0
$371$	−8.65161	−	15.9319i	−0.449169	−	0.827142i
$372$		0			0
$373$	−0.426136	+	0.738089i	−0.0220645	+	0.0382168i	−0.876847	−	0.480770i	$-0.840357\pi$
$373$	−0.426136	+	0.738089i	−0.0220645	+	0.0382168i	0.854782	+	0.518987i	$0.173691\pi$
$374$		0			0
$375$	−1.49583	+	0.863615i	−0.0772441	+	0.0445969i
$376$		0			0
$377$			8.03332i			0.413737i
$378$		0			0
$379$		−	24.3954i		−	1.25311i	−0.779377	−	0.626555i	$-0.784464\pi$
$379$		−	24.3954i		−	1.25311i	0.779377	−	0.626555i	$-0.215536\pi$
$380$		0			0
$381$	−2.26140	+	1.30562i	−0.115855	+	0.0668891i
$382$		0			0
$383$	0.411624	−	0.712954i	0.0210330	−	0.0364303i	−0.855317	−	0.518105i	$-0.826638\pi$
$383$	0.411624	−	0.712954i	0.0210330	−	0.0364303i	0.876350	+	0.481674i	$0.159971\pi$
$384$		0			0
$385$	−51.5499	−	1.34662i	−2.62723	−	0.0686302i
$386$		0			0
$387$	−2.63042	−	1.51867i	−0.133712	−	0.0771985i
$388$		0			0
$389$	−11.0476	−	19.1350i	−0.560137	−	0.970185i	−0.997484	−	0.0708924i	$-0.977415\pi$
$389$	−11.0476	−	19.1350i	−0.560137	−	0.970185i	0.437347	−	0.899293i	$-0.355918\pi$
$390$		0			0
$391$	−4.40302			−0.222670
$392$		0			0
$393$	−2.37654			−0.119880
$394$		0			0
$395$	6.89990	+	11.9510i	0.347172	+	0.601319i
$396$		0			0
$397$	−21.8196	−	12.5976i	−1.09509	−	0.632253i	−0.160166	−	0.987090i	$-0.551203\pi$
$397$	−21.8196	−	12.5976i	−1.09509	−	0.632253i	−0.934928	+	0.354837i	$0.884536\pi$
$398$		0			0
$399$	2.64485	+	0.0690906i	0.132408	+	0.00345885i
$400$		0			0
$401$	18.8260	−	32.6076i	0.940127	−	1.62835i	0.174901	−	0.984586i	$-0.444039\pi$
$401$	18.8260	−	32.6076i	0.940127	−	1.62835i	0.765226	−	0.643762i	$-0.222627\pi$
$402$		0			0
$403$	−15.3414	+	8.85738i	−0.764211	+	0.441217i
$404$		0			0
$405$			30.9536i			1.53810i
$406$		0			0
$407$			6.54913i			0.324628i
$408$		0			0
$409$	−7.93641	+	4.58209i	−0.392430	+	0.226570i	−0.683213	−	0.730220i	$-0.739418\pi$
$409$	−7.93641	+	4.58209i	−0.392430	+	0.226570i	0.290782	+	0.956789i	$0.406084\pi$
$410$		0			0
$411$	1.33705	−	2.31583i	0.0659517	−	0.114232i
$412$		0			0
$413$	7.06869	+	13.0170i	0.347828	+	0.640522i
$414$		0			0
$415$	6.91167	+	3.99045i	0.339280	+	0.195884i
$416$		0			0
$417$	1.03801	+	1.79788i	0.0508314	+	0.0880425i
$418$		0			0
$419$	10.9867			0.536733			0.268367	−	0.963317i	$-0.413516\pi$
$419$	10.9867			0.536733			0.268367	+	0.963317i	$0.413516\pi$
$420$		0			0
$421$	−6.99361			−0.340848			−0.170424	−	0.985371i	$-0.554514\pi$
$421$	−6.99361			−0.340848			−0.170424	+	0.985371i	$0.554514\pi$
$422$		0			0
$423$	5.98892	+	10.3731i	0.291191	+	0.504358i
$424$		0			0
$425$	−6.47098	−	3.73602i	−0.313889	−	0.181224i
$426$		0			0
$427$	−19.6178	−	12.0201i	−0.949370	−	0.581692i
$428$		0			0
$429$	1.35547	−	2.34774i	0.0654425	−	0.113350i
$430$		0			0
$431$	22.4275	−	12.9485i	1.08029	−	0.623708i	0.149318	−	0.988789i	$-0.452292\pi$
$431$	22.4275	−	12.9485i	1.08029	−	0.623708i	0.930976	+	0.365081i	$0.118959\pi$
$432$		0			0
$433$			33.4629i			1.60812i	0.594545	+	0.804062i	$0.297332\pi$
$433$			33.4629i			1.60812i	−0.594545	+	0.804062i	$0.702668\pi$
$434$		0			0
$435$		−	1.92860i		−	0.0924694i
$436$		0			0
$437$	21.3832	−	12.3456i	1.02290	−	0.590570i
$438$		0			0
$439$	−0.355022	+	0.614916i	−0.0169443	+	0.0293483i	−0.874373	−	0.485254i	$-0.838727\pi$
$439$	−0.355022	+	0.614916i	−0.0169443	+	0.0293483i	0.857429	+	0.514602i	$0.172060\pi$
$440$		0			0
$441$	11.3079	−	17.4175i	0.538472	−	0.829404i
$442$		0			0
$443$	15.5990	+	9.00608i	0.741130	+	0.427892i	0.822480	−	0.568794i	$-0.192590\pi$
$443$	15.5990	+	9.00608i	0.741130	+	0.427892i	−0.0813498	+	0.996686i	$0.525923\pi$
$444$		0			0
$445$	25.3717	+	43.9450i	1.20273	+	2.08319i
$446$		0			0
$447$	−1.85695			−0.0878307
$448$		0			0
$449$	31.2048			1.47264			0.736322	−	0.676631i	$-0.236561\pi$
$449$	31.2048			1.47264			0.736322	+	0.676631i	$0.236561\pi$
$450$		0			0
$451$	7.41770	+	12.8478i	0.349286	+	0.604981i
$452$		0			0
$453$	1.53093	+	0.883880i	0.0719291	+	0.0415283i
$454$		0			0
$455$	13.3164	−	21.7335i	0.624283	−	1.01888i
$456$		0			0
$457$	−4.99562	+	8.65268i	−0.233685	+	0.404755i	−0.958890	−	0.283779i	$-0.908412\pi$
$457$	−4.99562	+	8.65268i	−0.233685	+	0.404755i	0.725204	+	0.688534i	$0.241745\pi$
$458$		0			0
$459$	0.921440	−	0.531994i	0.0430091	−	0.0248313i
$460$		0			0
$461$			21.5729i			1.00475i	0.864650	+	0.502375i	$0.167540\pi$
$461$			21.5729i			1.00475i	−0.864650	+	0.502375i	$0.832460\pi$
$462$		0			0
$463$			14.6998i			0.683157i	0.939853	+	0.341579i	$0.110962\pi$
$463$			14.6998i			0.683157i	−0.939853	+	0.341579i	$0.889038\pi$
$464$		0			0
$465$	3.68310	−	2.12644i	0.170800	−	0.0986112i
$466$		0			0
$467$	17.5215	−	30.3481i	0.810797	−	1.40434i	−0.101510	−	0.994835i	$-0.532367\pi$
$467$	17.5215	−	30.3481i	0.810797	−	1.40434i	0.912307	−	0.409507i	$-0.134299\pi$
$468$		0			0
$469$	−9.20687	+	4.99968i	−0.425134	+	0.230864i
$470$		0			0
$471$	0.537394	+	0.310265i	0.0247618	+	0.0142962i
$472$		0			0
$473$	2.80458	+	4.85768i	0.128955	+	0.223356i
$474$		0			0
$475$	41.9016			1.92258
$476$		0			0
$477$	20.3280			0.930755
$478$		0			0
$479$	0.291956	+	0.505682i	0.0133398	+	0.0231052i	0.872618	−	0.488403i	$-0.162420\pi$
$479$	0.291956	+	0.505682i	0.0133398	+	0.0231052i	−0.859278	+	0.511508i	$0.829087\pi$
$480$		0			0
$481$	−2.80340	−	1.61854i	−0.127824	−	0.0737993i
$482$		0			0
$483$	−0.0569639	+	2.18063i	−0.00259195	+	0.0992221i
$484$		0			0
$485$	−19.1068	+	33.0939i	−0.867594	+	1.50272i
$486$		0			0
$487$	−24.0977	+	13.9128i	−1.09197	+	0.630450i	−0.934101	−	0.357010i	$-0.883796\pi$
$487$	−24.0977	+	13.9128i	−1.09197	+	0.630450i	−0.157871	+	0.987460i	$0.550463\pi$
$488$		0			0
$489$		−	3.75953i		−	0.170012i
$490$		0			0
$491$			4.25265i			0.191920i	0.995385	+	0.0959598i	$0.0305920\pi$
$491$			4.25265i			0.191920i	−0.995385	+	0.0959598i	$0.969408\pi$
$492$		0			0
$493$	2.50715	−	1.44750i	0.112916	−	0.0651923i
$494$		0			0
$495$	28.9106	−	50.0746i	1.29944	−	2.25069i
$496$		0			0
$497$	−0.918919	+	35.1770i	−0.0412191	+	1.57791i
$498$		0			0
$499$	17.8174	+	10.2869i	0.797617	+	0.460504i	0.842637	−	0.538482i	$-0.181002\pi$
$499$	17.8174	+	10.2869i	0.797617	+	0.460504i	−0.0450203	+	0.998986i	$0.514335\pi$
$500$		0			0
$501$	0.183893	+	0.318513i	0.00821575	+	0.0142301i
$502$		0			0
$503$	−29.2966			−1.30627			−0.653136	−	0.757241i	$-0.726547\pi$
$503$	−29.2966			−1.30627			−0.653136	+	0.757241i	$0.726547\pi$
$504$		0			0
$505$	−30.3614			−1.35106
$506$		0			0
$507$	−0.517795	−	0.896847i	−0.0229961	−	0.0398304i
$508$		0			0
$509$	−15.6673	−	9.04550i	−0.694439	−	0.400935i	0.110834	−	0.993839i	$-0.464648\pi$
$509$	−15.6673	−	9.04550i	−0.694439	−	0.400935i	−0.805273	+	0.592904i	$0.797981\pi$
$510$		0			0
$511$	22.2700	−	12.0934i	0.985167	−	0.534983i
$512$		0			0
$513$	−2.98330	+	5.16723i	−0.131716	+	0.228139i
$514$		0			0
$515$	12.8284	−	7.40646i	0.565286	−	0.326368i
$516$		0			0
$517$		−	22.1199i		−	0.972831i
$518$		0			0
$519$			1.68843i			0.0741138i
$520$		0			0
$521$	−23.8279	+	13.7570i	−1.04392	+	0.602706i	−0.920941	−	0.389703i	$-0.872578\pi$
$521$	−23.8279	+	13.7570i	−1.04392	+	0.602706i	−0.122977	+	0.992409i	$0.539244\pi$
$522$		0			0
$523$	−7.63084	+	13.2170i	−0.333673	+	0.577939i	−0.983229	−	0.182375i	$-0.941622\pi$
$523$	−7.63084	+	13.2170i	−0.333673	+	0.577939i	0.649556	+	0.760314i	$0.274955\pi$
$524$		0			0
$525$	−1.93401	+	3.15647i	−0.0844072	+	0.137760i
$526$		0			0
$527$	5.52866	+	3.19197i	0.240832	+	0.139045i
$528$		0			0
$529$	−1.32128	−	2.28852i	−0.0574469	−	0.0995009i
$530$		0			0
$531$	−16.6087			−0.720758
$532$		0			0
$533$	−7.33280			−0.317619
$534$		0			0
$535$	14.5478	+	25.1975i	0.628956	+	1.08938i
$536$		0			0
$537$	−0.617495	−	0.356511i	−0.0266469	−	0.0153846i
$538$		0			0
$539$	−34.1676	+	17.4147i	−1.47170	+	0.750105i
$540$		0			0
$541$	19.8999	−	34.4676i	0.855563	−	1.48188i	−0.0205583	−	0.999789i	$-0.506544\pi$
$541$	19.8999	−	34.4676i	0.855563	−	1.48188i	0.876122	−	0.482090i	$-0.160122\pi$
$542$		0			0
$543$	2.02922	−	1.17157i	0.0870823	−	0.0502770i
$544$		0			0
$545$		−	19.5487i		−	0.837373i
$546$		0			0
$547$		−	3.19462i		−	0.136592i	−0.997665	−	0.0682961i	$-0.978244\pi$
$547$		−	3.19462i		−	0.136592i	0.997665	−	0.0682961i	$-0.0217563\pi$
$548$		0			0
$549$	22.3413	−	12.8988i	0.953504	−	0.550506i
$550$		0			0
$551$	−8.11728	+	14.0595i	−0.345808	+	0.598957i
$552$		0			0
$553$	8.75068	+	5.36166i	0.372117	+	0.228001i
$554$		0			0
$555$	0.673027	+	0.388573i	0.0285684	+	0.0164940i
$556$		0			0
$557$	−1.94283	−	3.36508i	−0.0823204	−	0.142583i	0.821926	−	0.569595i	$-0.192900\pi$
$557$	−1.94283	−	3.36508i	−0.0823204	−	0.142583i	−0.904246	+	0.427011i	$0.859566\pi$
$558$		0			0
$559$	−2.77248			−0.117264
$560$		0			0
$561$	−0.976951			−0.0412469
$562$		0			0
$563$	−20.5297	−	35.5585i	−0.865223	−	1.49861i	−0.866826	−	0.498611i	$-0.833843\pi$
$563$	−20.5297	−	35.5585i	−0.865223	−	1.49861i	0.00160270	−	0.999999i	$-0.499490\pi$
$564$		0			0
$565$	34.9924	+	20.2029i	1.47214	+	0.849942i
$566$		0			0
$567$	10.9853	+	20.2293i	0.461338	+	0.849552i
$568$		0			0
$569$	−3.75265	+	6.49979i	−0.157319	+	0.272485i	−0.933901	−	0.357531i	$-0.883619\pi$
$569$	−3.75265	+	6.49979i	−0.157319	+	0.272485i	0.776582	+	0.630017i	$0.216952\pi$
$570$		0			0
$571$	−5.60161	+	3.23409i	−0.234420	+	0.135343i	−0.612610	−	0.790386i	$-0.709880\pi$
$571$	−5.60161	+	3.23409i	−0.234420	+	0.135343i	0.378189	+	0.925728i	$0.376547\pi$
$572$		0			0
$573$		−	1.69634i		−	0.0708657i
$574$		0			0
$575$			34.5471i			1.44071i
$576$		0			0
$577$	32.9335	−	19.0141i	1.37104	−	0.791569i	0.379979	−	0.924995i	$-0.375931\pi$
$577$	32.9335	−	19.0141i	1.37104	−	0.791569i	0.991059	+	0.133426i	$0.0425979\pi$
$578$		0			0
$579$	−0.326708	+	0.565875i	−0.0135775	+	0.0235169i
$580$		0			0
$581$	5.93322	+	0.154992i	0.246151	+	0.00643013i
$582$		0			0
$583$	−32.5109	−	18.7702i	−1.34646	−	0.777382i
$584$		0			0
$585$	14.2899	+	24.7508i	0.590813	+	1.02332i
$586$		0			0
$587$	27.0533			1.11661			0.558305	−	0.829636i	$-0.311452\pi$
$587$	27.0533			1.11661			0.558305	+	0.829636i	$0.311452\pi$
$588$		0			0
$589$	−35.7998			−1.47510
$590$		0			0
$591$	−0.586018	−	1.01501i	−0.0241055	−	0.0417520i
$592$		0			0
$593$	−15.3923	−	8.88672i	−0.632084	−	0.364934i	0.149475	−	0.988766i	$-0.452242\pi$
$593$	−15.3923	−	8.88672i	−0.632084	−	0.364934i	−0.781559	+	0.623832i	$0.785575\pi$
$594$		0			0
$595$	−9.18233	−	0.239867i	−0.376439	−	0.00983360i
$596$		0			0
$597$	1.33089	−	2.30518i	0.0544698	−	0.0943445i
$598$		0			0
$599$	12.1418	−	7.01006i	0.496100	−	0.286423i	−0.231002	−	0.972953i	$-0.574200\pi$
$599$	12.1418	−	7.01006i	0.496100	−	0.286423i	0.727101	+	0.686530i	$0.240867\pi$
$600$		0			0
$601$		−	26.0595i		−	1.06299i	−0.847061	−	0.531495i	$-0.821630\pi$
$601$		−	26.0595i		−	1.06299i	0.847061	−	0.531495i	$-0.178370\pi$
$602$		0			0
$603$		−	11.7473i		−	0.478389i
$604$		0			0
$605$	−58.5833	+	33.8231i	−2.38175	+	1.37510i
$606$		0			0
$607$	10.0120	−	17.3413i	0.406376	−	0.703864i	−0.588105	−	0.808785i	$-0.700126\pi$
$607$	10.0120	−	17.3413i	0.406376	−	0.703864i	0.994481	+	0.104921i	$0.0334590\pi$
$608$		0			0
$609$	−0.684451	−	1.26041i	−0.0277353	−	0.0510745i
$610$		0			0
$611$	9.46856	+	5.46668i	0.383057	+	0.221158i
$612$		0			0
$613$	−13.7244	−	23.7713i	−0.554322	−	0.960114i	−0.997956	−	0.0639057i	$-0.979644\pi$
$613$	−13.7244	−	23.7713i	−0.554322	−	0.960114i	0.443634	−	0.896208i	$-0.353689\pi$
$614$		0			0
$615$	1.76042			0.0709872
$616$		0			0
$617$	24.6235			0.991303			0.495652	−	0.868521i	$-0.334929\pi$
$617$	24.6235			0.991303			0.495652	+	0.868521i	$0.334929\pi$
$618$		0			0
$619$	−7.17095	−	12.4205i	−0.288225	−	0.499220i	0.685161	−	0.728391i	$-0.259732\pi$
$619$	−7.17095	−	12.4205i	−0.288225	−	0.499220i	−0.973386	+	0.229171i	$0.926398\pi$
$620$		0			0
$621$	−4.26029	−	2.45968i	−0.170960	−	0.0987036i
$622$		0			0
$623$	32.1772	+	19.7154i	1.28915	+	0.789881i
$624$		0			0
$625$	2.32843	−	4.03295i	0.0931371	−	0.161318i
$626$		0			0
$627$	4.74455	−	2.73927i	0.189479	−	0.109396i
$628$		0			0
$629$			1.16656i			0.0465140i
$630$		0			0
$631$		−	30.2517i		−	1.20430i	−0.798383	−	0.602150i	$-0.794311\pi$
$631$		−	30.2517i		−	1.20430i	0.798383	−	0.602150i	$-0.205689\pi$
$632$		0			0
$633$	−2.58546	+	1.49271i	−0.102763	+	0.0593301i
$634$		0			0
$635$	−25.4191	+	44.0273i	−1.00873	+	1.74717i
$636$		0			0
$637$	0.989657	−	18.9296i	0.0392116	−	0.750016i
$638$		0			0
$639$	−34.1703	−	19.7283i	−1.35176	−	0.780438i
$640$		0			0
$641$	−3.08612	−	5.34531i	−0.121894	−	0.211127i	0.798620	−	0.601835i	$-0.205564\pi$
$641$	−3.08612	−	5.34531i	−0.121894	−	0.211127i	−0.920515	+	0.390708i	$0.872230\pi$
$642$		0			0
$643$	28.7674			1.13448			0.567238	−	0.823554i	$-0.308012\pi$
$643$	28.7674			1.13448			0.567238	+	0.823554i	$0.308012\pi$
$644$		0			0
$645$	0.665605			0.0262082
$646$		0			0
$647$	−24.0534	−	41.6618i	−0.945638	−	1.63789i	−0.754469	−	0.656335i	$-0.772106\pi$
$647$	−24.0534	−	41.6618i	−0.945638	−	1.63789i	−0.191168	−	0.981557i	$-0.561228\pi$
$648$		0			0
$649$	26.5626	+	15.3360i	1.04268	+	0.601989i
$650$		0			0
$651$	1.65238	−	2.69682i	0.0647617	−	0.105697i
$652$		0			0
$653$	8.04960	−	13.9423i	0.315005	−	0.545605i	−0.664433	−	0.747347i	$-0.731327\pi$
$653$	8.04960	−	13.9423i	0.315005	−	0.545605i	0.979439	+	0.201743i	$0.0646604\pi$
$654$		0			0
$655$	−40.0699	+	23.1344i	−1.56566	+	0.903935i
$656$		0			0
$657$			28.4150i			1.10858i
$658$		0			0
$659$			1.60357i			0.0624663i	0.999512	+	0.0312332i	$0.00994344\pi$
$659$			1.60357i			0.0624663i	−0.999512	+	0.0312332i	$0.990057\pi$
$660$		0			0
$661$	−38.8217	+	22.4137i	−1.50999	+	0.871793i	−0.510058	+	0.860140i	$0.670376\pi$
$661$	−38.8217	+	22.4137i	−1.50999	+	0.871793i	−0.999932	+	0.0116530i	$0.996291\pi$
$662$		0			0
$663$	0.241443	−	0.418191i	0.00937685	−	0.0162412i
$664$		0			0
$665$	45.2664	−	24.5814i	1.75536	−	0.953224i
$666$		0			0
$667$	−11.5918	−	6.69255i	−0.448838	−	0.259137i
$668$		0			0
$669$	−2.26682	−	3.92624i	−0.0876401	−	0.151797i
$670$		0			0
$671$	−47.6411			−1.83916
$672$		0			0
$673$	15.2430			0.587573			0.293787	−	0.955871i	$-0.405084\pi$
$673$	15.2430			0.587573			0.293787	+	0.955871i	$0.405084\pi$
$674$		0			0
$675$	−4.17414	−	7.22983i	−0.160663	−	0.278276i
$676$		0			0
$677$	−32.6846	−	18.8705i	−1.25617	−	0.725250i	−0.283843	−	0.958871i	$-0.591609\pi$
$677$	−32.6846	−	18.8705i	−1.25617	−	0.725250i	−0.972328	+	0.233620i	$0.924943\pi$
$678$		0			0
$679$	−0.742118	+	28.4090i	−0.0284799	+	1.09024i
$680$		0			0
$681$	1.99483	−	3.45514i	0.0764420	−	0.132401i
$682$		0			0
$683$	−7.72997	+	4.46290i	−0.295779	+	0.170768i	−0.640545	−	0.767920i	$-0.721292\pi$
$683$	−7.72997	+	4.46290i	−0.295779	+	0.170768i	0.344766	+	0.938689i	$0.387958\pi$
$684$		0			0
$685$		−	52.0619i		−	1.98918i
$686$		0			0
$687$		−	0.817858i		−	0.0312032i
$688$		0			0
$689$	16.0694	−	9.27768i	0.612196	−	0.353452i
$690$		0			0
$691$	−21.4076	+	37.0791i	−0.814385	+	1.41056i	0.0953835	+	0.995441i	$0.469592\pi$
$691$	−21.4076	+	37.0791i	−0.814385	+	1.41056i	−0.909769	+	0.415116i	$0.863741\pi$
$692$		0			0
$693$	1.12290	−	42.9858i	0.0426556	−	1.63290i
$694$		0			0
$695$	35.0029	+	20.2089i	1.32773	+	0.766568i
$696$		0			0
$697$	1.32128	+	2.28852i	0.0500470	+	0.0866839i
$698$		0			0
$699$	2.79224			0.105612
$700$		0			0
$701$	−13.3137			−0.502852			−0.251426	−	0.967877i	$-0.580899\pi$
$701$	−13.3137			−0.502852			−0.251426	+	0.967877i	$0.580899\pi$
$702$		0			0
$703$	−3.27092	−	5.66540i	−0.123365	−	0.213675i
$704$		0			0
$705$	−2.27317	−	1.31241i	−0.0856125	−	0.0494284i
$706$		0			0
$707$	−19.8423	+	10.7751i	−0.746246	+	0.405239i
$708$		0			0
$709$	−16.3689	+	28.3518i	−0.614747	+	1.06477i	0.375682	+	0.926749i	$0.377409\pi$
$709$	−16.3689	+	28.3518i	−0.614747	+	1.06477i	−0.990429	+	0.138024i	$0.955925\pi$
$710$		0			0
$711$	−9.96554	+	5.75361i	−0.373737	+	0.215777i
$712$		0			0
$713$		−	29.5163i		−	1.10539i
$714$		0			0
$715$		−	52.7791i		−	1.97383i
$716$		0			0
$717$	−1.28789	+	0.743562i	−0.0480970	+	0.0277688i
$718$		0			0
$719$	−10.7348	+	18.5932i	−0.400339	+	0.693408i	−0.993767	−	0.111480i	$-0.964441\pi$
$719$	−10.7348	+	18.5932i	−0.400339	+	0.693408i	0.593428	+	0.804887i	$0.297774\pi$
$720$		0			0
$721$	5.75529	−	9.39311i	0.214338	−	0.349818i
$722$		0			0
$723$	−4.47960	−	2.58630i	−0.166598	−	0.0961854i
$724$		0			0
$725$	−11.3574	−	19.6717i	−0.421805	−	0.730587i
$726$		0			0
$727$	31.7591			1.17788			0.588940	−	0.808177i	$-0.299545\pi$
$727$	31.7591			1.17788			0.588940	+	0.808177i	$0.299545\pi$
$728$		0			0
$729$	−25.2135			−0.933835
$730$		0			0
$731$	0.499567	+	0.865275i	0.0184771	+	0.0320033i
$732$		0			0
$733$	5.26411	+	3.03924i	0.194434	+	0.112257i	0.594057	−	0.804423i	$-0.297525\pi$
$733$	5.26411	+	3.03924i	0.194434	+	0.112257i	−0.399622	+	0.916680i	$0.630859\pi$
$734$		0			0
$735$	−0.237592	+	4.54452i	−0.00876372	+	0.167627i
$736$		0			0
$737$	−10.8471	+	18.7877i	−0.399558	+	0.692055i
$738$		0			0
$739$	−26.1304	+	15.0864i	−0.961221	+	0.554961i	−0.896548	−	0.442946i	$-0.853933\pi$
$739$	−26.1304	+	15.0864i	−0.961221	+	0.554961i	−0.0646721	+	0.997907i	$0.520600\pi$
$740$		0			0
$741$			2.70791i			0.0994777i
$742$		0			0
$743$			2.49181i			0.0914155i	0.998955	+	0.0457078i	$0.0145543\pi$
$743$			2.49181i			0.0914155i	−0.998955	+	0.0457078i	$0.985446\pi$
$744$		0			0
$745$	−31.3093	+	18.0765i	−1.14709	+	0.662270i
$746$		0			0
$747$	−3.32751	+	5.76342i	−0.121747	+	0.210872i
$748$		0			0
$749$	18.4500	+	11.3046i	0.674148	+	0.413060i
$750$		0			0
$751$	13.3002	+	7.67890i	0.485333	+	0.280207i	0.722636	−	0.691228i	$-0.242930\pi$
$751$	13.3002	+	7.67890i	0.485333	+	0.280207i	−0.237303	+	0.971436i	$0.576264\pi$
$752$		0			0
$753$	0.839951	+	1.45484i	0.0306095	+	0.0530173i
$754$		0			0
$755$	34.4165			1.25254
$756$		0			0
$757$	−5.45255			−0.198176			−0.0990881	−	0.995079i	$-0.531593\pi$
$757$	−5.45255			−0.198176			−0.0990881	+	0.995079i	$0.531593\pi$
$758$		0			0
$759$	2.25848	+	3.91179i	0.0819775	+	0.141989i
$760$		0			0
$761$	16.3439	+	9.43616i	0.592466	+	0.342060i	0.766072	−	0.642755i	$-0.222209\pi$
$761$	16.3439	+	9.43616i	0.592466	+	0.342060i	−0.173606	+	0.984815i	$0.555542\pi$
$762$		0			0
$763$	−6.93772	−	12.7758i	−0.251162	−	0.462514i
$764$		0			0
$765$	5.14971	−	8.91955i	0.186188	−	0.322487i
$766$		0			0
$767$	−13.1293	+	7.58022i	−0.474072	+	0.273706i
$768$		0			0
$769$		−	9.05295i		−	0.326458i	−0.986588	−	0.163229i	$-0.947809\pi$
$769$		−	9.05295i		−	0.326458i	0.986588	−	0.163229i	$-0.0521909\pi$
$770$		0			0
$771$		−	2.96559i		−	0.106803i
$772$		0			0
$773$	15.9665	−	9.21829i	0.574277	−	0.331559i	−0.184579	−	0.982818i	$-0.559092\pi$
$773$	15.9665	−	9.21829i	0.574277	−	0.331559i	0.758856	+	0.651259i	$0.225759\pi$
$774$		0			0
$775$	25.0450	−	43.3792i	0.899642	−	1.55823i
$776$		0			0
$777$	0.577750	+	0.0150924i	0.0207267	+	0.000541436i
$778$		0			0
$779$	−12.8335	−	7.40944i	−0.459809	−	0.265471i
$780$		0			0
$781$	36.4328	+	63.1035i	1.30367	+	2.25802i
$782$		0			0
$783$	3.23450			0.115592
$784$		0			0
$785$	12.0811			0.431192
$786$		0			0
$787$	17.5424	+	30.3843i	0.625318	+	1.08308i	0.988479	+	0.151356i	$0.0483640\pi$
$787$	17.5424	+	30.3843i	0.625318	+	1.08308i	−0.363162	+	0.931726i	$0.618303\pi$
$788$		0			0
$789$	−3.09913	−	1.78928i	−0.110332	−	0.0637002i
$790$		0			0
$791$	30.0387	+	0.784692i	1.06805	+	0.0279004i
$792$		0			0
$793$	11.7740	−	20.3931i	0.418106	−	0.724180i
$794$		0			0
$795$	−3.85787	+	2.22734i	−0.136825	+	0.0789957i
$796$		0			0
$797$			9.81203i			0.347560i	0.984785	+	0.173780i	$0.0555981\pi$
$797$			9.81203i			0.347560i	−0.984785	+	0.173780i	$0.944402\pi$
$798$		0			0
$799$		−	3.94010i		−	0.139391i
$800$		0			0
$801$	−36.6444	+	21.1566i	−1.29476	+	0.747533i
$802$		0			0
$803$	26.2375	−	45.4446i	0.925900	−	1.60371i
$804$		0			0
$805$	20.2669	+	37.3213i	0.714314	+	1.31540i
$806$		0			0
$807$	−0.319673	−	0.184564i	−0.0112530	−	0.00649695i
$808$		0			0
$809$	14.4095	+	24.9580i	0.506611	+	0.877477i	0.999971	+	0.00765101i	$0.00243542\pi$
$809$	14.4095	+	24.9580i	0.506611	+	0.877477i	−0.493359	+	0.869826i	$0.664231\pi$
$810$		0			0
$811$	13.4492			0.472264			0.236132	−	0.971721i	$-0.424120\pi$
$811$	13.4492			0.472264			0.236132	+	0.971721i	$0.424120\pi$
$812$		0			0
$813$	4.68643			0.164360
$814$		0			0
$815$	−36.5971	−	63.3881i	−1.28194	−	2.22039i
$816$		0			0
$817$	−4.85227	−	2.80146i	−0.169760	−	0.0980107i
$818$		0			0
$819$	18.1229	+	11.1041i	0.633264	+	0.388010i
$820$		0			0
$821$	0.356579	−	0.617613i	0.0124447	−	0.0215548i	−0.859736	−	0.510739i	$-0.829372\pi$
$821$	0.356579	−	0.617613i	0.0124447	−	0.0215548i	0.872181	+	0.489184i	$0.162705\pi$
$822$		0			0
$823$	36.9518	−	21.3341i	1.28806	−	0.743660i	0.309750	−	0.950818i	$-0.399755\pi$
$823$	36.9518	−	21.3341i	1.28806	−	0.743660i	0.978308	+	0.207158i	$0.0664213\pi$
$824$		0			0
$825$			7.66539i			0.266875i
$826$		0			0
$827$			9.85293i			0.342620i	0.985217	+	0.171310i	$0.0548000\pi$
$827$			9.85293i			0.342620i	−0.985217	+	0.171310i	$0.945200\pi$
$828$		0			0
$829$	23.0486	−	13.3071i	0.800509	−	0.462174i	−0.0431399	−	0.999069i	$-0.513736\pi$
$829$	23.0486	−	13.3071i	0.800509	−	0.462174i	0.843649	+	0.536895i	$0.180403\pi$
$830$		0			0
$831$	−2.84849	+	4.93373i	−0.0988130	+	0.171149i
$832$		0			0
$833$	−6.08612	+	3.10200i	−0.210871	+	0.107478i
$834$		0			0
$835$	6.20112	+	3.58022i	0.214599	+	0.123899i
$836$		0			0
$837$	3.56629	+	6.17700i	0.123269	+	0.213508i
$838$		0			0
$839$	20.6975			0.714559			0.357279	−	0.933998i	$-0.383704\pi$
$839$	20.6975			0.714559			0.357279	+	0.933998i	$0.383704\pi$
$840$		0			0
$841$	−20.1992			−0.696525
$842$		0			0
$843$	0.180628	+	0.312857i	0.00622117	+	0.0107754i
$844$		0			0
$845$	−17.4607	−	10.0809i	−0.600667	−	0.346795i
$846$		0			0
$847$	−26.2827	+	42.8955i	−0.903084	+	1.47391i
$848$		0			0
$849$	2.52384	−	4.37143i	0.0866181	−	0.150027i
$850$		0			0
$851$	4.67102	−	2.69682i	0.160121	−	0.0924457i
$852$		0			0
$853$		−	3.45628i		−	0.118341i	−0.998248	−	0.0591704i	$-0.981154\pi$
$853$		−	3.45628i		−	0.118341i	0.998248	−	0.0591704i	$-0.0188455\pi$
$854$		0			0
$855$			57.7568i			1.97524i
$856$		0			0
$857$	−26.2513	+	15.1562i	−0.896727	+	0.517726i	−0.876137	−	0.482062i	$-0.839888\pi$
$857$	−26.2513	+	15.1562i	−0.896727	+	0.517726i	−0.0205904	+	0.999788i	$0.506555\pi$
$858$		0			0
$859$	15.6058	−	27.0301i	0.532463	−	0.922254i	−0.466818	−	0.884353i	$-0.654600\pi$
$859$	15.6058	−	27.0301i	0.532463	−	0.922254i	0.999282	−	0.0379004i	$-0.0120670\pi$
$860$		0			0
$861$	1.15050	−	0.624766i	0.0392090	−	0.0212920i
$862$		0			0
$863$	6.77035	+	3.90886i	0.230465	+	0.133059i	0.610787	−	0.791795i	$-0.290853\pi$
$863$	6.77035	+	3.90886i	0.230465	+	0.133059i	−0.380321	+	0.924854i	$0.624187\pi$
$864$		0			0
$865$	16.4360	+	28.4680i	0.558840	+	0.967940i
$866$		0			0
$867$	2.93246			0.0995916
$868$		0			0
$869$	21.2507			0.720882
$870$		0			0
$871$	−5.36148	−	9.28635i	−0.181667	−	0.314656i
$872$		0			0
$873$	−27.5959	−	15.9325i	−0.933981	−	0.539234i
$874$		0			0
$875$	−0.653054	+	24.9995i	−0.0220773	+	0.845138i
$876$		0			0
$877$	−8.49490	+	14.7136i	−0.286852	+	0.496843i	−0.973057	−	0.230566i	$-0.925942\pi$
$877$	−8.49490	+	14.7136i	−0.286852	+	0.496843i	0.686204	+	0.727409i	$0.259276\pi$
$878$		0			0
$879$	1.66622	−	0.961994i	0.0562003	−	0.0324473i
$880$		0			0
$881$		−	5.82308i		−	0.196185i	−0.995177	−	0.0980923i	$-0.968726\pi$
$881$		−	5.82308i		−	0.196185i	0.995177	−	0.0980923i	$-0.0312741\pi$
$882$		0			0
$883$		−	27.2143i		−	0.915835i	−0.888995	−	0.457918i	$-0.848595\pi$
$883$		−	27.2143i		−	0.915835i	0.888995	−	0.457918i	$-0.151405\pi$
$884$		0			0
$885$	3.15203	−	1.81982i	0.105954	−	0.0611727i
$886$		0			0
$887$	25.4991	−	44.1658i	0.856177	−	1.48294i	−0.0193723	−	0.999812i	$-0.506167\pi$
$887$	25.4991	−	44.1658i	0.856177	−	1.48294i	0.875549	−	0.483129i	$-0.160500\pi$
$888$		0			0
$889$	−0.987295	+	37.7945i	−0.0331128	+	1.26759i
$890$		0			0
$891$	41.2804	+	23.8332i	1.38294	+	0.798443i
$892$		0			0
$893$	11.0476	+	19.1350i	0.369695	+	0.640330i
$894$		0			0
$895$	−13.8818			−0.464017
$896$		0			0
$897$	−2.23263			−0.0745453
$898$		0			0
$899$	9.70354	+	16.8070i	0.323631	+	0.560546i
$900$		0			0
$901$	−5.79101	−	3.34344i	−0.192927	−	0.111386i
$902$		0			0
$903$	0.434997	−	0.236220i	0.0144758	−	0.00786090i
$904$		0			0
$905$	22.8093	−	39.5069i	0.758208	−	1.31325i
$906$		0			0
$907$	−41.0523	+	23.7016i	−1.36312	+	0.786998i	−0.990038	−	0.140801i	$-0.955032\pi$
$907$	−41.0523	+	23.7016i	−1.36312	+	0.786998i	−0.373082	+	0.927798i	$0.621699\pi$
$908$		0			0
$909$		−	25.3174i		−	0.839725i
$910$		0			0
$911$			37.4430i			1.24054i	0.784388	+	0.620271i	$0.212977\pi$
$911$			37.4430i			1.24054i	−0.784388	+	0.620271i	$0.787023\pi$
$912$		0			0
$913$	10.6435	−	6.14502i	0.352248	−	0.203371i
$914$		0			0
$915$	−2.82664	+	4.89588i	−0.0934458	+	0.161853i
$916$		0			0
$917$	−17.9769	+	29.3398i	−0.593649	+	0.968885i
$918$		0			0
$919$	12.3207	+	7.11334i	0.406421	+	0.234647i	0.689251	−	0.724523i	$-0.257940\pi$
$919$	12.3207	+	7.11334i	0.406421	+	0.234647i	−0.282830	+	0.959170i	$0.591273\pi$
$920$		0			0
$921$	2.47178	+	4.28125i	0.0814479	+	0.141072i
$922$		0			0
$923$	−36.0158			−1.18548
$924$		0			0
$925$	9.15314			0.300953
$926$		0			0
$927$	6.17601	+	10.6972i	0.202847	+	0.351341i
$928$		0			0
$929$	−2.03283	−	1.17366i	−0.0666951	−	0.0385065i	0.466282	−	0.884636i	$-0.345593\pi$
$929$	−2.03283	−	1.17366i	−0.0666951	−	0.0385065i	−0.532977	+	0.846130i	$0.678927\pi$
$930$		0			0
$931$	20.8594	−	32.1296i	0.683641	−	1.05301i
$932$		0			0
$933$	−2.31937	+	4.01727i	−0.0759327	+	0.131519i
$934$		0			0
$935$	−16.4720	+	9.51013i	−0.538693	+	0.311014i
$936$		0			0
$937$		−	7.80691i		−	0.255041i	−0.991836	−	0.127520i	$-0.959298\pi$
$937$		−	7.80691i		−	0.255041i	0.991836	−	0.127520i	$-0.0407018\pi$
$938$		0			0
$939$		−	0.840907i		−	0.0274420i
$940$		0			0
$941$	−42.5730	+	24.5795i	−1.38784	+	0.801270i	−0.993072	−	0.117510i	$-0.962509\pi$
$941$	−42.5730	+	24.5795i	−1.38784	+	0.801270i	−0.394769	+	0.918780i	$0.629175\pi$
$942$		0			0
$943$	6.10895	−	10.5810i	0.198935	−	0.344565i
$944$		0			0
$945$	−8.75068	−	5.36166i	−0.284660	−	0.174415i
$946$		0			0
$947$	8.10205	+	4.67772i	0.263281	+	0.152006i	0.625830	−	0.779959i	$-0.284760\pi$
$947$	8.10205	+	4.67772i	0.263281	+	0.152006i	−0.362549	+	0.931965i	$0.618094\pi$
$948$		0			0
$949$	12.9686	+	22.4622i	0.420978	+	0.729155i
$950$		0			0
$951$	−1.37755			−0.0446702
$952$		0			0
$953$	19.2700			0.624216			0.312108	−	0.950047i	$-0.398965\pi$
$953$	19.2700			0.624216			0.312108	+	0.950047i	$0.398965\pi$
$954$		0			0
$955$	−16.5130	−	28.6014i	−0.534349	−	0.925519i
$956$		0			0
$957$	−2.57202	−	1.48496i	−0.0831416	−	0.0480018i
$958$		0			0
$959$	−18.4765	−	34.0244i	−0.596637	−	1.09870i
$960$		0			0
$961$	−5.89785	+	10.2154i	−0.190253	+	0.329528i
$962$		0			0
$963$	−21.0114	+	12.1309i	−0.677083	+	0.390914i
$964$		0			0
$965$			12.7213i			0.409514i
$966$		0			0
$967$			3.48146i			0.111956i	0.998432	+	0.0559782i	$0.0178277\pi$
$967$			3.48146i			0.111956i	−0.998432	+	0.0559782i	$0.982172\pi$
$968$		0			0
$969$	0.845123	−	0.487932i	0.0271493	−	0.0156746i
$970$		0			0
$971$	8.35357	−	14.4688i	0.268079	−	0.464326i	−0.700287	−	0.713861i	$-0.746945\pi$
$971$	8.35357	−	14.4688i	0.268079	−	0.464326i	0.968366	+	0.249536i	$0.0802779\pi$
$972$		0			0
$973$	30.0477	+	0.784926i	0.963285	+	0.0251636i
$974$		0			0
$975$	−3.28122	−	1.89441i	−0.105083	−	0.0606698i
$976$		0			0
$977$	−10.1787	−	17.6301i	−0.325646	−	0.564036i	0.655997	−	0.754764i	$-0.272248\pi$
$977$	−10.1787	−	17.6301i	−0.325646	−	0.564036i	−0.981643	+	0.190728i	$0.938915\pi$
$978$		0			0
$979$	78.1412			2.49740
$980$		0			0
$981$	16.3010			0.520451
$982$		0			0
$983$	−8.22215	−	14.2412i	−0.262246	−	0.454223i	0.704593	−	0.709612i	$-0.251130\pi$
$983$	−8.22215	−	14.2412i	−0.262246	−	0.454223i	−0.966838	+	0.255389i	$0.917796\pi$
$984$		0			0
$985$	−19.7613	−	11.4092i	−0.629646	−	0.363526i
$986$		0			0
$987$	−1.95137	−	0.0509749i	−0.0621127	−	0.00162255i
$988$		0			0
$989$	2.30975	−	4.00061i	0.0734459	−	0.127212i
$990$		0			0
$991$	31.5177	−	18.1967i	1.00119	−	0.578038i	0.0925907	−	0.995704i	$-0.470485\pi$
$991$	31.5177	−	18.1967i	1.00119	−	0.578038i	0.908601	+	0.417666i	$0.137152\pi$
$992$		0			0
$993$		−	0.506927i		−	0.0160868i
$994$		0			0
$995$		−	51.8223i		−	1.64288i
$996$		0			0
$997$	31.4872	−	18.1791i	0.997209	−	0.575739i	0.0897879	−	0.995961i	$-0.471381\pi$
$997$	31.4872	−	18.1791i	0.997209	−	0.575739i	0.907421	+	0.420222i	$0.138048\pi$
$998$		0			0
$999$	−0.651684	+	1.12875i	−0.0206184	+	0.0357120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.p.a.159.4	yes	16
3.2	odd	2		2016.2.cs.b.1279.7		16
4.3	odd	2	inner	224.2.p.a.159.5	yes	16
7.2	even	3		1568.2.f.b.1567.10		16
7.3	odd	6	inner	224.2.p.a.31.5	yes	16
7.4	even	3		1568.2.p.b.31.4		16
7.5	odd	6		1568.2.f.b.1567.7		16
7.6	odd	2		1568.2.p.b.607.5		16
8.3	odd	2		448.2.p.e.383.4		16
8.5	even	2		448.2.p.e.383.5		16
12.11	even	2		2016.2.cs.b.1279.8		16
21.17	even	6		2016.2.cs.b.703.8		16
28.3	even	6	inner	224.2.p.a.31.4	✓	16
28.11	odd	6		1568.2.p.b.31.5		16
28.19	even	6		1568.2.f.b.1567.9		16
28.23	odd	6		1568.2.f.b.1567.8		16
28.27	even	2		1568.2.p.b.607.4		16
56.3	even	6		448.2.p.e.255.5		16
56.5	odd	6		3136.2.f.j.3135.10		16
56.19	even	6		3136.2.f.j.3135.8		16
56.37	even	6		3136.2.f.j.3135.7		16
56.45	odd	6		448.2.p.e.255.4		16
56.51	odd	6		3136.2.f.j.3135.9		16
84.59	odd	6		2016.2.cs.b.703.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.p.a.31.4	✓	16	28.3	even	6	inner
224.2.p.a.31.5	yes	16	7.3	odd	6	inner
224.2.p.a.159.4	yes	16	1.1	even	1	trivial
224.2.p.a.159.5	yes	16	4.3	odd	2	inner
448.2.p.e.255.4		16	56.45	odd	6
448.2.p.e.255.5		16	56.3	even	6
448.2.p.e.383.4		16	8.3	odd	2
448.2.p.e.383.5		16	8.5	even	2
1568.2.f.b.1567.7		16	7.5	odd	6
1568.2.f.b.1567.8		16	28.23	odd	6
1568.2.f.b.1567.9		16	28.19	even	6
1568.2.f.b.1567.10		16	7.2	even	3
1568.2.p.b.31.4		16	7.4	even	3
1568.2.p.b.31.5		16	28.11	odd	6
1568.2.p.b.607.4		16	28.27	even	2
1568.2.p.b.607.5		16	7.6	odd	2
2016.2.cs.b.703.7		16	84.59	odd	6
2016.2.cs.b.703.8		16	21.17	even	6
2016.2.cs.b.1279.7		16	3.2	odd	2
2016.2.cs.b.1279.8		16	12.11	even	2
3136.2.f.j.3135.7		16	56.37	even	6
3136.2.f.j.3135.8		16	56.19	even	6
3136.2.f.j.3135.9		16	56.51	odd	6
3136.2.f.j.3135.10		16	56.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0913671 - 0.158252i) q^{3} +(-3.08101 - 1.77882i) q^{5} +(-2.64485 - 0.0690906i) q^{7} +(1.48330 - 2.56916i) q^{9} +O(q^{10})\)	\(q+(-0.0913671 - 0.158252i) q^{3} +(-3.08101 - 1.77882i) q^{5} +(-2.64485 - 0.0690906i) q^{7} +(1.48330 - 2.56916i) q^{9} +(-4.74455 + 2.73927i) q^{11} -2.70791i q^{13} +0.650103i q^{15} +(-0.845123 + 0.487932i) q^{17} +(2.73622 - 4.73927i) q^{19} +(0.230718 + 0.424866i) q^{21} +(3.90744 + 2.25596i) q^{23} +(3.82843 + 6.63103i) q^{25} -1.09030 q^{27} -2.96661 q^{29} +(-3.27092 - 5.66540i) q^{31} +(0.866990 + 0.500557i) q^{33} +(8.02591 + 4.91759i) q^{35} +(0.597709 - 1.03526i) q^{37} +(-0.428534 + 0.247414i) q^{39} -2.70791i q^{41} -1.02384i q^{43} +(-9.14016 + 5.27707i) q^{45} +(-2.01878 + 3.49662i) q^{47} +(6.99045 + 0.365468i) q^{49} +(0.154433 + 0.0891618i) q^{51} +(3.42614 + 5.93424i) q^{53} +19.4907 q^{55} -1.00000 q^{57} +(-2.79928 - 4.84850i) q^{59} +(7.53093 + 4.34798i) q^{61} +(-4.10062 + 6.69255i) q^{63} +(-4.81690 + 8.34312i) q^{65} +(3.42934 - 1.97993i) q^{67} -0.824482i q^{69} -13.3002i q^{71} +(-8.29504 + 4.78914i) q^{73} +(0.699584 - 1.21172i) q^{75} +(12.7379 - 6.91714i) q^{77} +(-3.35924 - 1.93946i) q^{79} +(-4.35029 - 7.53493i) q^{81} -2.24331 q^{83} +3.47178 q^{85} +(0.271050 + 0.469473i) q^{87} +(-12.3523 - 7.13159i) q^{89} +(-0.187091 + 7.16203i) q^{91} +(-0.597709 + 1.03526i) q^{93} +(-16.8606 + 9.73449i) q^{95} -10.7412i q^{97} +16.2527i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^9	\( 16 q - 8 q^{9} - 24 q^{21} + 16 q^{25} + 16 q^{29} + 24 q^{33} - 8 q^{37} - 24 q^{45} - 32 q^{49} - 8 q^{53} - 16 q^{57} - 24 q^{61} + 8 q^{65} - 24 q^{73} + 64 q^{77} - 48 q^{81} - 16 q^{85} - 72 q^{89} + 8 q^{93}+O(q^{100}) \) 16 * q - 8 * q^9 - 24 * q^21 + 16 * q^25 + 16 * q^29 + 24 * q^33 - 8 * q^37 - 24 * q^45 - 32 * q^49 - 8 * q^53 - 16 * q^57 - 24 * q^61 + 8 * q^65 - 24 * q^73 + 64 * q^77 - 48 * q^81 - 16 * q^85 - 72 * q^89 + 8 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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