LMFDB - Embedded newform 912.3.be.g.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.520060207104.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 44x^{6} + 664x^{4} - 3528x^{2} + 8100 $ x^8 - 44x^6 + 664x^4 - 3528*x^2 + 8100
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$-4.34148 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.g.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(-3.25884 - 5.64448i) q^{5} +11.0157 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(-3.25884 - 5.64448i) q^{5} +11.0157 q^{7} +(1.50000 - 2.59808i) q^{9} +17.2006 q^{11} +(13.2756 + 7.66470i) q^{13} +(9.77652 + 5.64448i) q^{15} +(-12.0992 - 20.9565i) q^{17} +(-16.6917 + 9.07675i) q^{19} +(-16.5236 + 9.53989i) q^{21} +(-12.6821 + 21.9660i) q^{23} +(-8.74007 + 15.1382i) q^{25} +5.19615i q^{27} +(10.6987 + 6.17689i) q^{29} -15.5915i q^{31} +(-25.8010 + 14.8962i) q^{33} +(-35.8985 - 62.1779i) q^{35} +17.7317i q^{37} -26.5513 q^{39} +(43.6462 - 25.1991i) q^{41} +(31.6919 + 54.8920i) q^{43} -19.5530 q^{45} +(35.1267 - 60.8413i) q^{47} +72.3460 q^{49} +(36.2977 + 20.9565i) q^{51} +(-12.8290 - 7.40685i) q^{53} +(-56.0541 - 97.0886i) q^{55} +(17.1768 - 28.0706i) q^{57} +(59.8411 - 34.5493i) q^{59} +(18.6084 - 32.2307i) q^{61} +(16.5236 - 28.6197i) q^{63} -99.9121i q^{65} +(85.3266 + 49.2633i) q^{67} -43.9321i q^{69} +(-37.5466 + 21.6776i) q^{71} +(-48.2593 - 83.5876i) q^{73} -30.2765i q^{75} +189.477 q^{77} +(-40.1472 + 23.1790i) q^{79} +(-4.50000 - 7.79423i) q^{81} -66.5221 q^{83} +(-78.8589 + 136.588i) q^{85} -21.3974 q^{87} +(32.5630 + 18.8002i) q^{89} +(146.241 + 84.4321i) q^{91} +(13.5026 + 23.3872i) q^{93} +(105.629 + 64.6362i) q^{95} +(-5.11583 + 2.95363i) q^{97} +(25.8010 - 44.6886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9}+O(q^{10}) $ 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9	$ 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9} + 8 q^{11} + 24 q^{13} - 12 q^{15} - 20 q^{17} - 24 q^{19} - 36 q^{21} - 40 q^{23} - 88 q^{25} - 48 q^{29} - 12 q^{33} - 32 q^{35} - 48 q^{39} + 60 q^{41} + 116 q^{43} + 24 q^{45} + 68 q^{47} - 120 q^{49} + 60 q^{51} - 168 q^{53} - 232 q^{55} + 84 q^{57} + 156 q^{59} + 72 q^{61} + 36 q^{63} + 108 q^{67} - 444 q^{71} - 68 q^{73} + 296 q^{77} - 420 q^{79} - 36 q^{81} - 424 q^{83} + 40 q^{85} + 96 q^{87} - 420 q^{89} + 228 q^{91} + 84 q^{93} + 272 q^{95} + 156 q^{97} + 12 q^{99}+O(q^{100}) $ 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9 + 8 * q^11 + 24 * q^13 - 12 * q^15 - 20 * q^17 - 24 * q^19 - 36 * q^21 - 40 * q^23 - 88 * q^25 - 48 * q^29 - 12 * q^33 - 32 * q^35 - 48 * q^39 + 60 * q^41 + 116 * q^43 + 24 * q^45 + 68 * q^47 - 120 * q^49 + 60 * q^51 - 168 * q^53 - 232 * q^55 + 84 * q^57 + 156 * q^59 + 72 * q^61 + 36 * q^63 + 108 * q^67 - 444 * q^71 - 68 * q^73 + 296 * q^77 - 420 * q^79 - 36 * q^81 - 424 * q^83 + 40 * q^85 + 96 * q^87 - 420 * q^89 + 228 * q^91 + 84 * q^93 + 272 * q^95 + 156 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$		0			0
$5$	−3.25884	−	5.64448i	−0.651768	−	1.12890i	−0.982694	−	0.185238i	$-0.940694\pi$
$5$	−3.25884	−	5.64448i	−0.651768	−	1.12890i	0.330926	−	0.943657i	$-0.392639\pi$
$6$		0			0
$7$	11.0157			1.57367			0.786837	−	0.617161i	$-0.211717\pi$
$7$	11.0157			1.57367			0.786837	+	0.617161i	$0.211717\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	17.2006			1.56369			0.781847	−	0.623470i	$-0.214278\pi$
$11$	17.2006			1.56369			0.781847	+	0.623470i	$0.214278\pi$
$12$		0			0
$13$	13.2756	+	7.66470i	1.02120	+	0.589592i	0.914452	−	0.404694i	$-0.132622\pi$
$13$	13.2756	+	7.66470i	1.02120	+	0.589592i	0.106751	+	0.994286i	$0.465955\pi$
$14$		0			0
$15$	9.77652	+	5.64448i	0.651768	+	0.376298i
$16$		0			0
$17$	−12.0992	−	20.9565i	−0.711719	−	1.23273i	−0.964211	−	0.265135i	$-0.914583\pi$
$17$	−12.0992	−	20.9565i	−0.711719	−	1.23273i	0.252492	−	0.967599i	$-0.418750\pi$
$18$		0			0
$19$	−16.6917	+	9.07675i	−0.878510	+	0.477723i
$19$	−16.6917	+	9.07675i	−0.878510	+	0.477723i
$20$		0			0
$21$	−16.5236	+	9.53989i	−0.786837	+	0.454281i
$22$		0			0
$23$	−12.6821	+	21.9660i	−0.551395	+	0.955045i	0.446779	+	0.894644i	$0.352571\pi$
$23$	−12.6821	+	21.9660i	−0.551395	+	0.955045i	−0.998174	+	0.0604003i	$0.980762\pi$
$24$		0			0
$25$	−8.74007	+	15.1382i	−0.349603	+	0.605530i
$26$		0			0
$27$			5.19615i			0.192450i
$28$		0			0
$29$	10.6987	+	6.17689i	0.368920	+	0.212996i	0.672987	−	0.739655i	$-0.265011\pi$
$29$	10.6987	+	6.17689i	0.368920	+	0.212996i	−0.304066	+	0.952651i	$0.598345\pi$
$30$		0			0
$31$		−	15.5915i		−	0.502951i	−0.967864	−	0.251475i	$-0.919084\pi$
$31$		−	15.5915i		−	0.502951i	0.967864	−	0.251475i	$-0.0809158\pi$
$32$		0			0
$33$	−25.8010	+	14.8962i	−0.781847	+	0.451400i
$34$		0			0
$35$	−35.8985	−	62.1779i	−1.02567	−	1.77651i
$36$		0			0
$37$			17.7317i			0.479235i	0.970867	+	0.239618i	$0.0770220\pi$
$37$			17.7317i			0.479235i	−0.970867	+	0.239618i	$0.922978\pi$
$38$		0			0
$39$	−26.5513			−0.680802
$40$		0			0
$41$	43.6462	−	25.1991i	1.06454	−	0.614613i	0.137856	−	0.990452i	$-0.455979\pi$
$41$	43.6462	−	25.1991i	1.06454	−	0.614613i	0.926685	+	0.375840i	$0.122646\pi$
$42$		0			0
$43$	31.6919	+	54.8920i	0.737021	+	1.27656i	0.953831	+	0.300345i	$0.0971017\pi$
$43$	31.6919	+	54.8920i	0.737021	+	1.27656i	−0.216809	+	0.976214i	$0.569565\pi$
$44$		0			0
$45$	−19.5530			−0.434512
$46$		0			0
$47$	35.1267	−	60.8413i	0.747377	−	1.29450i	−0.201698	−	0.979448i	$-0.564646\pi$
$47$	35.1267	−	60.8413i	0.747377	−	1.29450i	0.949076	−	0.315048i	$-0.102021\pi$
$48$		0			0
$49$	72.3460			1.47645
$50$		0			0
$51$	36.2977	+	20.9565i	0.711719	+	0.410911i
$52$		0			0
$53$	−12.8290	−	7.40685i	−0.242057	−	0.139752i	0.374065	−	0.927403i	$-0.377964\pi$
$53$	−12.8290	−	7.40685i	−0.242057	−	0.139752i	−0.616122	+	0.787651i	$0.711297\pi$
$54$		0			0
$55$	−56.0541	−	97.0886i	−1.01917	−	1.76525i
$56$		0			0
$57$	17.1768	−	28.0706i	0.301348	−	0.492466i
$58$		0			0
$59$	59.8411	−	34.5493i	1.01426	−	0.585581i	0.101822	−	0.994803i	$-0.467533\pi$
$59$	59.8411	−	34.5493i	1.01426	−	0.585581i	0.912435	+	0.409221i	$0.134200\pi$
$60$		0			0
$61$	18.6084	−	32.2307i	0.305056	−	0.528372i	−0.672218	−	0.740353i	$-0.734658\pi$
$61$	18.6084	−	32.2307i	0.305056	−	0.528372i	0.977274	+	0.211981i	$0.0679916\pi$
$62$		0			0
$63$	16.5236	−	28.6197i	0.262279	−	0.454281i
$64$		0			0
$65$		−	99.9121i		−	1.53711i
$66$		0			0
$67$	85.3266	+	49.2633i	1.27353	+	0.735274i	0.975651	−	0.219330i	$-0.0703870\pi$
$67$	85.3266	+	49.2633i	1.27353	+	0.735274i	0.297880	+	0.954603i	$0.403720\pi$
$68$		0			0
$69$		−	43.9321i		−	0.636697i
$70$		0			0
$71$	−37.5466	+	21.6776i	−0.528826	+	0.305318i	−0.740538	−	0.672014i	$-0.765429\pi$
$71$	−37.5466	+	21.6776i	−0.528826	+	0.305318i	0.211712	+	0.977332i	$0.432096\pi$
$72$		0			0
$73$	−48.2593	−	83.5876i	−0.661087	−	1.14504i	−0.980330	−	0.197363i	$-0.936762\pi$
$73$	−48.2593	−	83.5876i	−0.661087	−	1.14504i	0.319243	−	0.947673i	$-0.396571\pi$
$74$		0			0
$75$		−	30.2765i		−	0.403687i
$76$		0			0
$77$	189.477			2.46075
$78$		0			0
$79$	−40.1472	+	23.1790i	−0.508192	+	0.293405i	−0.732090	−	0.681208i	$-0.761455\pi$
$79$	−40.1472	+	23.1790i	−0.508192	+	0.293405i	0.223898	+	0.974613i	$0.428122\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−66.5221			−0.801471			−0.400735	−	0.916194i	$-0.631245\pi$
$83$	−66.5221			−0.801471			−0.400735	+	0.916194i	$0.631245\pi$
$84$		0			0
$85$	−78.8589	+	136.588i	−0.927752	+	1.60691i
$86$		0			0
$87$	−21.3974			−0.245947
$88$		0			0
$89$	32.5630	+	18.8002i	0.365876	+	0.211239i	0.671655	−	0.740864i	$-0.265584\pi$
$89$	32.5630	+	18.8002i	0.365876	+	0.211239i	−0.305779	+	0.952102i	$0.598917\pi$
$90$		0			0
$91$	146.241	+	84.4321i	1.60704	+	0.927826i
$92$		0			0
$93$	13.5026	+	23.3872i	0.145189	+	0.251475i
$94$		0			0
$95$	105.629	+	64.6362i	1.11188	+	0.680381i
$96$		0			0
$97$	−5.11583	+	2.95363i	−0.0527405	+	0.0304498i	−0.526138	−	0.850399i	$-0.676361\pi$
$97$	−5.11583	+	2.95363i	−0.0527405	+	0.0304498i	0.473398	+	0.880849i	$0.343027\pi$
$98$		0			0
$99$	25.8010	−	44.6886i	0.260616	−	0.451400i
$100$		0			0
$101$	1.64222	−	2.84441i	0.0162596	−	0.0281624i	−0.857781	−	0.514015i	$-0.828158\pi$
$101$	1.64222	−	2.84441i	0.0162596	−	0.0281624i	0.874041	+	0.485853i	$0.161491\pi$
$102$		0			0
$103$		−	125.755i		−	1.22092i	−0.792048	−	0.610459i	$-0.790985\pi$
$103$		−	125.755i		−	1.22092i	0.792048	−	0.610459i	$-0.209015\pi$
$104$		0			0
$105$	107.695	+	62.1779i	1.02567	+	0.592171i
$106$		0			0
$107$		−	37.3840i		−	0.349383i	−0.984623	−	0.174692i	$-0.944107\pi$
$107$		−	37.3840i		−	0.349383i	0.984623	−	0.174692i	$-0.0558929\pi$
$108$		0			0
$109$	84.9719	−	49.0586i	0.779559	−	0.450079i	−0.0567150	−	0.998390i	$-0.518063\pi$
$109$	84.9719	−	49.0586i	0.779559	−	0.450079i	0.836274	+	0.548312i	$0.184729\pi$
$110$		0			0
$111$	−15.3561	−	26.5975i	−0.138343	−	0.239618i
$112$		0			0
$113$		−	11.3889i		−	0.100787i	−0.998729	−	0.0503935i	$-0.983952\pi$
$113$		−	11.3889i		−	0.100787i	0.998729	−	0.0503935i	$-0.0160475\pi$
$114$		0			0
$115$	165.316			1.43753
$116$		0			0
$117$	39.8269	−	22.9941i	0.340401	−	0.196531i
$118$		0			0
$119$	−133.282	−	230.851i	−1.12001	−	1.93992i
$120$		0			0
$121$	174.862			1.44514
$122$		0			0
$123$	−43.6462	+	75.5974i	−0.354847	+	0.614613i
$124$		0			0
$125$	−49.0120			−0.392096
$126$		0			0
$127$	10.7972	+	6.23375i	0.0850171	+	0.0490847i	0.541906	−	0.840439i	$-0.317703\pi$
$127$	10.7972	+	6.23375i	0.0850171	+	0.0490847i	−0.456889	+	0.889524i	$0.651036\pi$
$128$		0			0
$129$	−95.0758	−	54.8920i	−0.737021	−	0.425520i
$130$		0			0
$131$	20.0230	+	34.6809i	0.152847	+	0.264740i	0.932273	−	0.361755i	$-0.117822\pi$
$131$	20.0230	+	34.6809i	0.152847	+	0.264740i	−0.779426	+	0.626495i	$0.784489\pi$
$132$		0			0
$133$	−183.871	+	99.9869i	−1.38249	+	0.751781i
$134$		0			0
$135$	29.3296	−	16.9334i	0.217256	−	0.125433i
$136$		0			0
$137$	54.3561	−	94.1475i	0.396760	−	0.687208i	−0.596564	−	0.802565i	$-0.703468\pi$
$137$	54.3561	−	94.1475i	0.396760	−	0.687208i	0.993324	+	0.115357i	$0.0368013\pi$
$138$		0			0
$139$	−93.3288	+	161.650i	−0.671430	+	1.16295i	0.306069	+	0.952009i	$0.400986\pi$
$139$	−93.3288	+	161.650i	−0.671430	+	1.16295i	−0.977499	+	0.210942i	$0.932347\pi$
$140$		0			0
$141$			121.683i			0.862997i
$142$		0			0
$143$	228.350	+	131.838i	1.59685	+	0.921942i
$144$		0			0
$145$		−	80.5179i		−	0.555296i
$146$		0			0
$147$	−108.519	+	62.6535i	−0.738225	+	0.426214i
$148$		0			0
$149$	−20.0249	−	34.6841i	−0.134395	−	0.232779i	0.790971	−	0.611854i	$-0.209576\pi$
$149$	−20.0249	−	34.6841i	−0.134395	−	0.232779i	−0.925366	+	0.379074i	$0.876242\pi$
$150$		0			0
$151$		−	146.489i		−	0.970125i	−0.874480	−	0.485062i	$-0.838797\pi$
$151$		−	146.489i		−	0.970125i	0.874480	−	0.485062i	$-0.161203\pi$
$152$		0			0
$153$	−72.5954			−0.474480
$154$		0			0
$155$	−88.0057	+	50.8101i	−0.567779	+	0.327807i
$156$		0			0
$157$	−94.1713	−	163.110i	−0.599817	−	1.03891i	−0.992848	−	0.119389i	$-0.961907\pi$
$157$	−94.1713	−	163.110i	−0.599817	−	1.03891i	0.393030	−	0.919526i	$-0.371427\pi$
$158$		0			0
$159$	25.6581			0.161372
$160$		0			0
$161$	−139.702	+	241.972i	−0.867716	+	1.50293i
$162$		0			0
$163$	−37.5376			−0.230292			−0.115146	−	0.993349i	$-0.536734\pi$
$163$	−37.5376			−0.230292			−0.115146	+	0.993349i	$0.536734\pi$
$164$		0			0
$165$	168.162	+	97.0886i	1.01917	+	0.588416i
$166$		0			0
$167$	112.613	+	65.0172i	0.674330	+	0.389324i	0.797715	−	0.603034i	$-0.206042\pi$
$167$	112.613	+	65.0172i	0.674330	+	0.389324i	−0.123385	+	0.992359i	$0.539375\pi$
$168$		0			0
$169$	32.9952	+	57.1494i	0.195238	+	0.338162i
$170$		0			0
$171$	−1.45546	+	56.9814i	−0.00851149	+	0.333225i
$172$		0			0
$173$	85.4823	−	49.3533i	0.494118	−	0.285279i	−0.232163	−	0.972677i	$-0.574580\pi$
$173$	85.4823	−	49.3533i	0.494118	−	0.285279i	0.726281	+	0.687398i	$0.241247\pi$
$174$		0			0
$175$	−96.2781	+	166.759i	−0.550161	+	0.952906i
$176$		0			0
$177$	−59.8411	+	103.648i	−0.338086	+	0.585581i
$178$		0			0
$179$		−	134.153i		−	0.749455i	−0.927135	−	0.374728i	$-0.877736\pi$
$179$		−	134.153i		−	0.749455i	0.927135	−	0.374728i	$-0.122264\pi$
$180$		0			0
$181$	−72.2192	−	41.6958i	−0.399001	−	0.230363i	0.287052	−	0.957915i	$-0.407325\pi$
$181$	−72.2192	−	41.6958i	−0.399001	−	0.230363i	−0.686053	+	0.727552i	$0.740658\pi$
$182$		0			0
$183$			64.4614i			0.352248i
$184$		0			0
$185$	100.086	−	57.7847i	0.541006	−	0.312350i
$186$		0			0
$187$	−208.115	−	360.465i	−1.11291	−	1.92762i
$188$		0			0
$189$			57.2393i			0.302854i
$190$		0			0
$191$	20.6327			0.108024			0.0540122	−	0.998540i	$-0.482799\pi$
$191$	20.6327			0.108024			0.0540122	+	0.998540i	$0.482799\pi$
$192$		0			0
$193$	−29.1581	+	16.8344i	−0.151078	+	0.0872250i	−0.573633	−	0.819112i	$-0.694467\pi$
$193$	−29.1581	+	16.8344i	−0.151078	+	0.0872250i	0.422555	+	0.906337i	$0.361133\pi$
$194$		0			0
$195$	86.5264	+	149.868i	0.443725	+	0.768555i
$196$		0			0
$197$	−63.4364			−0.322012			−0.161006	−	0.986953i	$-0.551474\pi$
$197$	−63.4364			−0.322012			−0.161006	+	0.986953i	$0.551474\pi$
$198$		0			0
$199$	−65.9305	+	114.195i	−0.331309	+	0.573844i	−0.982769	−	0.184839i	$-0.940824\pi$
$199$	−65.9305	+	114.195i	−0.331309	+	0.573844i	0.651460	+	0.758683i	$0.274157\pi$
$200$		0			0
$201$	−170.653			−0.849021
$202$		0			0
$203$	117.854	+	68.0428i	0.580560	+	0.335186i
$204$		0			0
$205$	−284.472	−	164.240i	−1.38767	−	0.801170i
$206$		0			0
$207$	38.0463	+	65.8981i	0.183798	+	0.318348i
$208$		0			0
$209$	−287.108	+	156.126i	−1.37372	+	0.747014i
$210$		0			0
$211$	−160.542	+	92.6892i	−0.760864	+	0.439285i	−0.829606	−	0.558349i	$-0.811435\pi$
$211$	−160.542	+	92.6892i	−0.760864	+	0.439285i	0.0687417	+	0.997634i	$0.478102\pi$
$212$		0			0
$213$	37.5466	−	65.0327i	0.176275	−	0.305318i
$214$		0			0
$215$	206.558	−	357.769i	0.960734	−	1.66404i
$216$		0			0
$217$		−	171.751i		−	0.791481i
$218$		0			0
$219$	144.778	+	83.5876i	0.661087	+	0.381679i
$220$		0			0
$221$		−	370.948i		−	1.67850i
$222$		0			0
$223$	321.092	−	185.382i	1.43987	−	0.831311i	0.442032	−	0.896999i	$-0.354258\pi$
$223$	321.092	−	185.382i	1.43987	−	0.831311i	0.997840	+	0.0656885i	$0.0209244\pi$
$224$		0			0
$225$	26.2202	+	45.4147i	0.116534	+	0.201843i
$226$		0			0
$227$			53.9647i			0.237730i	0.992910	+	0.118865i	$0.0379255\pi$
$227$			53.9647i			0.237730i	−0.992910	+	0.118865i	$0.962074\pi$
$228$		0			0
$229$	152.206			0.664656			0.332328	−	0.943164i	$-0.392166\pi$
$229$	152.206			0.664656			0.332328	+	0.943164i	$0.392166\pi$
$230$		0			0
$231$	−284.216	+	164.092i	−1.23037	+	0.710356i
$232$		0			0
$233$	−49.7795	−	86.2207i	−0.213646	−	0.370046i	0.739207	−	0.673478i	$-0.235201\pi$
$233$	−49.7795	−	86.2207i	−0.213646	−	0.370046i	−0.952853	+	0.303433i	$0.901867\pi$
$234$		0			0
$235$	−457.890			−1.94847
$236$		0			0
$237$	40.1472	−	69.5369i	0.169397	−	0.293405i
$238$		0			0
$239$	−317.932			−1.33026			−0.665130	−	0.746728i	$-0.731624\pi$
$239$	−317.932			−1.33026			−0.665130	+	0.746728i	$0.731624\pi$
$240$		0			0
$241$	392.835	+	226.803i	1.63002	+	0.941093i	0.984085	+	0.177701i	$0.0568659\pi$
$241$	392.835	+	226.803i	1.63002	+	0.941093i	0.645936	+	0.763392i	$0.276467\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		0			0
$245$	−235.764	−	408.355i	−0.962302	−	1.66676i
$246$		0			0
$247$	−291.164	−	7.43713i	−1.17880	−	0.0301098i
$248$		0			0
$249$	99.7831	−	57.6098i	0.400735	−	0.231365i
$250$		0			0
$251$	183.515	−	317.857i	0.731135	−	1.26636i	−0.225264	−	0.974298i	$-0.572324\pi$
$251$	183.515	−	317.857i	0.731135	−	1.26636i	0.956399	−	0.292064i	$-0.0943422\pi$
$252$		0			0
$253$	−218.140	+	377.830i	−0.862214	+	1.49340i
$254$		0			0
$255$		−	273.175i		−	1.07128i
$256$		0			0
$257$	223.689	+	129.147i	0.870385	+	0.502517i	0.867476	−	0.497479i	$-0.165741\pi$
$257$	223.689	+	129.147i	0.870385	+	0.502517i	0.00290887	+	0.999996i	$0.499074\pi$
$258$		0			0
$259$			195.327i			0.754160i
$260$		0			0
$261$	32.0960	−	18.5307i	0.122973	−	0.0709987i
$262$		0			0
$263$	−14.6501	−	25.3747i	−0.0557038	−	0.0964817i	0.836829	−	0.547465i	$-0.184407\pi$
$263$	−14.6501	−	25.3747i	−0.0557038	−	0.0964817i	−0.892533	+	0.450983i	$0.851074\pi$
$264$		0			0
$265$			96.5509i			0.364343i
$266$		0			0
$267$	−65.1259			−0.243917
$268$		0			0
$269$	201.089	−	116.099i	0.747543	−	0.431594i	−0.0772622	−	0.997011i	$-0.524618\pi$
$269$	201.089	−	116.099i	0.747543	−	0.431594i	0.824806	+	0.565416i	$0.191285\pi$
$270$		0			0
$271$	17.7278	+	30.7054i	0.0654162	+	0.113304i	0.896879	−	0.442277i	$-0.145829\pi$
$271$	17.7278	+	30.7054i	0.0654162	+	0.113304i	−0.831462	+	0.555581i	$0.812496\pi$
$272$		0			0
$273$	−292.482			−1.07136
$274$		0			0
$275$	−150.335	+	260.388i	−0.546672	+	0.946864i
$276$		0			0
$277$	196.290			0.708628			0.354314	−	0.935127i	$-0.384714\pi$
$277$	196.290			0.708628			0.354314	+	0.935127i	$0.384714\pi$
$278$		0			0
$279$	−40.5078	−	23.3872i	−0.145189	−	0.0838251i
$280$		0			0
$281$	249.290	+	143.928i	0.887154	+	0.512199i	0.873011	−	0.487701i	$-0.162165\pi$
$281$	249.290	+	143.928i	0.887154	+	0.512199i	0.0141434	+	0.999900i	$0.495498\pi$
$282$		0			0
$283$	220.315	+	381.596i	0.778497	+	1.34840i	0.932808	+	0.360374i	$0.117351\pi$
$283$	220.315	+	381.596i	0.778497	+	1.34840i	−0.154311	+	0.988022i	$0.549316\pi$
$284$		0			0
$285$	−214.420	−	5.47689i	−0.752351	−	0.0192171i
$286$		0			0
$287$	480.794	−	277.586i	1.67524	−	0.967200i
$288$		0			0
$289$	−148.283	+	256.833i	−0.513089	+	0.888697i
$290$		0			0
$291$	5.11583	−	8.86088i	0.0175802	−	0.0304498i
$292$		0			0
$293$			445.635i			1.52094i	0.649373	+	0.760470i	$0.275031\pi$
$293$			445.635i			1.52094i	−0.649373	+	0.760470i	$0.724969\pi$
$294$		0			0
$295$	−390.025	−	225.181i	−1.32212	−	0.763326i
$296$		0			0
$297$			89.3772i			0.300933i
$298$		0			0
$299$	−336.726	+	194.409i	−1.12617	+	0.650197i
$300$		0			0
$301$	349.109	+	604.675i	1.15983	+	2.00889i
$302$		0			0
$303$			5.68881i			0.0187750i
$304$		0			0
$305$	−242.567			−0.795302
$306$		0			0
$307$	−364.933	+	210.694i	−1.18871	+	0.686299i	−0.958012	−	0.286727i	$-0.907433\pi$
$307$	−364.933	+	210.694i	−1.18871	+	0.686299i	−0.230693	+	0.973027i	$0.574099\pi$
$308$		0			0
$309$	108.907	+	188.632i	0.352449	+	0.610459i
$310$		0			0
$311$	−297.933			−0.957984			−0.478992	−	0.877819i	$-0.658998\pi$
$311$	−297.933			−0.957984			−0.478992	+	0.877819i	$0.658998\pi$
$312$		0			0
$313$	−247.773	+	429.156i	−0.791608	+	1.37111i	0.133363	+	0.991067i	$0.457422\pi$
$313$	−247.773	+	429.156i	−0.791608	+	1.37111i	−0.924971	+	0.380038i	$0.875911\pi$
$314$		0			0
$315$	−215.391			−0.683780
$316$		0			0
$317$	−295.099	−	170.375i	−0.930910	−	0.537461i	−0.0438110	−	0.999040i	$-0.513950\pi$
$317$	−295.099	−	170.375i	−0.930910	−	0.537461i	−0.887099	+	0.461578i	$0.847283\pi$
$318$		0			0
$319$	184.024	+	106.246i	0.576878	+	0.333061i
$320$		0			0
$321$	32.3755	+	56.0760i	0.100858	+	0.174692i
$322$		0			0
$323$	392.173	+	239.978i	1.21416	+	0.742965i
$324$		0			0
$325$	−232.060	+	133.980i	−0.714031	+	0.412246i
$326$		0			0
$327$	−84.9719	+	147.176i	−0.259853	+	0.450079i
$328$		0			0
$329$	386.946	−	670.211i	1.17613	−	2.03711i
$330$		0			0
$331$			445.932i			1.34723i	0.739084	+	0.673614i	$0.235259\pi$
$331$			445.932i			1.34723i	−0.739084	+	0.673614i	$0.764741\pi$
$332$		0			0
$333$	46.0683	+	26.5975i	0.138343	+	0.0798725i
$334$		0			0
$335$		−	642.165i		−	1.91691i
$336$		0			0
$337$	−144.500	+	83.4273i	−0.428785	+	0.247559i	−0.698829	−	0.715289i	$-0.746295\pi$
$337$	−144.500	+	83.4273i	−0.428785	+	0.247559i	0.270044	+	0.962848i	$0.412962\pi$
$338$		0			0
$339$	9.86310	+	17.0834i	0.0290947	+	0.0503935i
$340$		0			0
$341$		−	268.183i		−	0.786462i
$342$		0			0
$343$	257.173			0.749776
$344$		0			0
$345$	−247.973	+	143.168i	−0.718764	+	0.414978i
$346$		0			0
$347$	−89.1691	−	154.445i	−0.256971	−	0.445088i	0.708458	−	0.705753i	$-0.249391\pi$
$347$	−89.1691	−	154.445i	−0.256971	−	0.445088i	−0.965429	+	0.260666i	$0.916058\pi$
$348$		0			0
$349$	195.242			0.559432			0.279716	−	0.960083i	$-0.409760\pi$
$349$	195.242			0.559432			0.279716	+	0.960083i	$0.409760\pi$
$350$		0			0
$351$	−39.8269	+	68.9823i	−0.113467	+	0.196531i
$352$		0			0
$353$	−459.142			−1.30068			−0.650342	−	0.759641i	$-0.725375\pi$
$353$	−459.142			−1.30068			−0.650342	+	0.759641i	$0.725375\pi$
$354$		0			0
$355$	244.717	+	141.287i	0.689343	+	0.397993i
$356$		0			0
$357$	399.845	+	230.851i	1.12001	+	0.646641i
$358$		0			0
$359$	6.90699	+	11.9633i	0.0192395	+	0.0333238i	0.875485	−	0.483246i	$-0.160542\pi$
$359$	6.90699	+	11.9633i	0.0192395	+	0.0333238i	−0.856245	+	0.516569i	$0.827209\pi$
$360$		0			0
$361$	196.225	−	303.013i	0.543561	−	0.839370i
$362$		0			0
$363$	−262.293	+	151.435i	−0.722571	+	0.417176i
$364$		0			0
$365$	−314.539	+	544.797i	−0.861751	+	1.49260i
$366$		0			0
$367$	−271.094	+	469.549i	−0.738676	+	1.27942i	0.214416	+	0.976743i	$0.431215\pi$
$367$	−271.094	+	469.549i	−0.738676	+	1.27942i	−0.953092	+	0.302682i	$0.902118\pi$
$368$		0			0
$369$		−	151.195i		−	0.409742i
$370$		0			0
$371$	−141.321	−	81.5917i	−0.380919	−	0.219924i
$372$		0			0
$373$			152.952i			0.410059i	0.978756	+	0.205029i	$0.0657290\pi$
$373$			152.952i			0.410059i	−0.978756	+	0.205029i	$0.934271\pi$
$374$		0			0
$375$	73.5180	−	42.4457i	0.196048	−	0.113188i
$376$		0			0
$377$	94.6879	+	164.004i	0.251162	+	0.435025i
$378$		0			0
$379$			268.912i			0.709531i	0.934955	+	0.354766i	$0.115439\pi$
$379$			268.912i			0.709531i	−0.934955	+	0.354766i	$0.884561\pi$
$380$		0			0
$381$	−21.5944			−0.0566781
$382$		0			0
$383$	−416.214	+	240.301i	−1.08672	+	0.627419i	−0.932702	−	0.360649i	$-0.882555\pi$
$383$	−416.214	+	240.301i	−1.08672	+	0.627419i	−0.154020	+	0.988068i	$0.549222\pi$
$384$		0			0
$385$	−617.477	−	1069.50i	−1.60384	−	2.77792i
$386$		0			0
$387$	190.152			0.491348
$388$		0			0
$389$	−204.382	+	354.001i	−0.525405	+	0.910027i	0.474158	+	0.880440i	$0.342753\pi$
$389$	−204.382	+	354.001i	−0.525405	+	0.910027i	−0.999562	+	0.0295874i	$0.990581\pi$
$390$		0			0
$391$	613.774			1.56976
$392$		0			0
$393$	−60.0691	−	34.6809i	−0.152847	−	0.0882465i
$394$		0			0
$395$	261.666	+	151.073i	0.662447	+	0.382464i
$396$		0			0
$397$	−177.881	−	308.098i	−0.448062	−	0.776067i	0.550198	−	0.835034i	$-0.314552\pi$
$397$	−177.881	−	308.098i	−0.448062	−	0.776067i	−0.998260	+	0.0589678i	$0.981219\pi$
$398$		0			0
$399$	189.215	−	309.217i	0.474224	−	0.774981i
$400$		0			0
$401$	278.116	−	160.570i	0.693556	−	0.400425i	−0.111387	−	0.993777i	$-0.535529\pi$
$401$	278.116	−	160.570i	0.693556	−	0.400425i	0.804943	+	0.593352i	$0.202196\pi$
$402$		0			0
$403$	119.504	−	206.987i	0.296536	−	0.513615i
$404$		0			0
$405$	−29.3296	+	50.8003i	−0.0724187	+	0.125433i
$406$		0			0
$407$			304.997i			0.749377i
$408$		0			0
$409$	−578.692	−	334.108i	−1.41490	−	0.816890i	−0.419051	−	0.907963i	$-0.637637\pi$
$409$	−578.692	−	334.108i	−1.41490	−	0.816890i	−0.995844	+	0.0910728i	$0.970970\pi$
$410$		0			0
$411$			188.295i			0.458139i
$412$		0			0
$413$	659.193	−	380.585i	1.59611	−	0.921514i
$414$		0			0
$415$	216.785	+	375.482i	0.522373	+	0.904776i
$416$		0			0
$417$		−	323.300i		−	0.775301i
$418$		0			0
$419$	584.124			1.39409			0.697046	−	0.717027i	$-0.254497\pi$
$419$	584.124			1.39409			0.697046	+	0.717027i	$0.254497\pi$
$420$		0			0
$421$	−541.860	+	312.843i	−1.28708	+	0.743095i	−0.978132	−	0.207985i	$-0.933310\pi$
$421$	−541.860	+	312.843i	−1.28708	+	0.743095i	−0.308946	+	0.951080i	$0.599976\pi$
$422$		0			0
$423$	−105.380	−	182.524i	−0.249126	−	0.431499i
$424$		0			0
$425$	422.993			0.995277
$426$		0			0
$427$	204.985	−	355.044i	0.480058	−	0.831485i
$428$		0			0
$429$	−456.699			−1.06457
$430$		0			0
$431$	−599.653	−	346.210i	−1.39131	−	0.803271i	−0.397847	−	0.917452i	$-0.630242\pi$
$431$	−599.653	−	346.210i	−1.39131	−	0.803271i	−0.993460	+	0.114181i	$0.963576\pi$
$432$		0			0
$433$	573.776	+	331.270i	1.32512	+	0.765057i	0.984540	−	0.175160i	$-0.0560443\pi$
$433$	573.776	+	331.270i	1.32512	+	0.765057i	0.340577	+	0.940217i	$0.389378\pi$
$434$		0			0
$435$	69.7306	+	120.777i	0.160300	+	0.277648i
$436$		0			0
$437$	12.3056	−	481.762i	0.0281592	−	1.10243i
$438$		0			0
$439$	445.746	−	257.351i	1.01537	−	0.586222i	0.102608	−	0.994722i	$-0.467281\pi$
$439$	445.746	−	257.351i	1.01537	−	0.586222i	0.912758	+	0.408500i	$0.133948\pi$
$440$		0			0
$441$	108.519	−	187.960i	0.246075	−	0.426214i
$442$		0			0
$443$	−356.813	+	618.018i	−0.805446	+	1.39507i	0.110543	+	0.993871i	$0.464741\pi$
$443$	−356.813	+	618.018i	−0.805446	+	1.39507i	−0.915989	+	0.401203i	$0.868592\pi$
$444$		0			0
$445$		−	245.068i		−	0.550714i
$446$		0			0
$447$	60.0746	+	34.6841i	0.134395	+	0.0775931i
$448$		0			0
$449$		−	44.5816i		−	0.0992909i	−0.998767	−	0.0496454i	$-0.984191\pi$
$449$		−	44.5816i		−	0.0992909i	0.998767	−	0.0496454i	$-0.0158091\pi$
$450$		0			0
$451$	750.742	−	433.441i	1.66462	−	0.961067i
$452$		0			0
$453$	126.863	+	219.733i	0.280051	+	0.485062i
$454$		0			0
$455$		−	1100.60i		−	2.41891i
$456$		0			0
$457$	−79.2570			−0.173429			−0.0867144	−	0.996233i	$-0.527637\pi$
$457$	−79.2570			−0.173429			−0.0867144	+	0.996233i	$0.527637\pi$
$458$		0			0
$459$	108.893	−	62.8695i	0.237240	−	0.136970i
$460$		0			0
$461$	−239.553	−	414.918i	−0.519638	−	0.900040i	−0.999739	−	0.0228267i	$-0.992733\pi$
$461$	−239.553	−	414.918i	−0.519638	−	0.900040i	0.480101	−	0.877213i	$-0.340600\pi$
$462$		0			0
$463$	−423.831			−0.915402			−0.457701	−	0.889106i	$-0.651327\pi$
$463$	−423.831			−0.915402			−0.457701	+	0.889106i	$0.651327\pi$
$464$		0			0
$465$	88.0057	−	152.430i	0.189260	−	0.327807i
$466$		0			0
$467$	−300.556			−0.643589			−0.321795	−	0.946810i	$-0.604286\pi$
$467$	−300.556			−0.643589			−0.321795	+	0.946810i	$0.604286\pi$
$468$		0			0
$469$	939.934	+	542.671i	2.00412	+	1.15708i
$470$		0			0
$471$	282.514	+	163.110i	0.599817	+	0.346305i
$472$		0			0
$473$	545.121	+	944.178i	1.15248	+	1.99615i
$474$		0			0
$475$	8.48057	−	332.014i	0.0178538	−	0.698978i
$476$		0			0
$477$	−38.4871	+	22.2205i	−0.0806858	+	0.0465839i
$478$		0			0
$479$	74.9449	−	129.808i	0.156461	−	0.270999i	−0.777129	−	0.629341i	$-0.783325\pi$
$479$	74.9449	−	129.808i	0.156461	−	0.270999i	0.933590	+	0.358343i	$0.116658\pi$
$480$		0			0
$481$	−135.908	+	235.400i	−0.282553	+	0.489397i
$482$		0			0
$483$		−	483.943i		−	1.00195i
$484$		0			0
$485$	33.3433	+	19.2508i	0.0687492	+	0.0396923i
$486$		0			0
$487$		−	632.623i		−	1.29902i	−0.760352	−	0.649511i	$-0.774974\pi$
$487$		−	632.623i		−	1.29902i	0.760352	−	0.649511i	$-0.225026\pi$
$488$		0			0
$489$	56.3063	−	32.5085i	0.115146	−	0.0664795i
$490$		0			0
$491$	15.4038	+	26.6802i	0.0313723	+	0.0543384i	0.881285	−	0.472585i	$-0.156679\pi$
$491$	15.4038	+	26.6802i	0.0313723	+	0.0543384i	−0.849913	+	0.526923i	$0.823346\pi$
$492$		0			0
$493$		−	298.942i		−	0.606374i
$494$		0			0
$495$	−336.325			−0.679444
$496$		0			0
$497$	−413.603	+	238.794i	−0.832199	+	0.480471i
$498$		0			0
$499$	−73.1554	−	126.709i	−0.146604	−	0.253926i	0.783366	−	0.621560i	$-0.213501\pi$
$499$	−73.1554	−	126.709i	−0.146604	−	0.253926i	−0.929970	+	0.367635i	$0.880168\pi$
$500$		0			0
$501$	−225.226			−0.449553
$502$		0			0
$503$	−276.946	+	479.685i	−0.550589	+	0.953648i	0.447643	+	0.894212i	$0.352263\pi$
$503$	−276.946	+	479.685i	−0.550589	+	0.953648i	−0.998232	+	0.0594355i	$0.981070\pi$
$504$		0			0
$505$	−21.4069			−0.0423899
$506$		0			0
$507$	−98.9856	−	57.1494i	−0.195238	−	0.112721i
$508$		0			0
$509$	−72.0827	−	41.6170i	−0.141616	−	0.0817622i	0.427518	−	0.904007i	$-0.359388\pi$
$509$	−72.0827	−	41.6170i	−0.141616	−	0.0817622i	−0.569134	+	0.822245i	$0.692721\pi$
$510$		0			0
$511$	−531.611	−	920.778i	−1.04034	−	1.80191i
$512$		0			0
$513$	−47.1642	−	86.7326i	−0.0919379	−	0.169069i
$514$		0			0
$515$	−709.819	+	409.814i	−1.37829	+	0.795756i
$516$		0			0
$517$	604.203	−	1046.51i	1.16867	−	2.02420i
$518$		0			0
$519$	−85.4823	+	148.060i	−0.164706	+	0.285279i
$520$		0			0
$521$			540.003i			1.03647i	0.855237	+	0.518237i	$0.173412\pi$
$521$			540.003i			1.03647i	−0.855237	+	0.518237i	$0.826588\pi$
$522$		0			0
$523$	516.923	+	298.446i	0.988381	+	0.570642i	0.904790	−	0.425858i	$-0.140028\pi$
$523$	516.923	+	298.446i	0.988381	+	0.570642i	0.0835910	+	0.996500i	$0.473361\pi$
$524$		0			0
$525$		−	333.517i		−	0.635271i
$526$		0			0
$527$	−326.743	+	188.645i	−0.620005	+	0.357960i
$528$		0			0
$529$	−57.1710	−	99.0230i	−0.108074	−	0.187189i
$530$		0			0
$531$		−	207.296i		−	0.390388i
$532$		0			0
$533$	772.575			1.44948
$534$		0			0
$535$	−211.013	+	121.828i	−0.394417	+	0.227717i
$536$		0			0
$537$	116.179	+	201.229i	0.216349	+	0.374728i
$538$		0			0
$539$	1244.40			2.30872
$540$		0			0
$541$	271.853	−	470.864i	0.502502	−	0.870359i	−0.497494	−	0.867467i	$-0.665746\pi$
$541$	271.853	−	470.864i	0.502502	−	0.870359i	0.999996	−	0.00289127i	$-0.000920321\pi$
$542$		0			0
$543$	144.438			0.266001
$544$		0			0
$545$	−553.820	−	319.748i	−1.01618	−	0.586694i
$546$		0			0
$547$	−832.824	−	480.831i	−1.52253	−	0.879033i	−0.999645	−	0.0266294i	$-0.991523\pi$
$547$	−832.824	−	480.831i	−1.52253	−	0.879033i	−0.522884	−	0.852404i	$-0.675144\pi$
$548$		0			0
$549$	−55.8252	−	96.6921i	−0.101685	−	0.176124i
$550$		0			0
$551$	−234.645	−	5.99349i	−0.425853	−	0.0108775i
$552$		0			0
$553$	−442.250	+	255.333i	−0.799729	+	0.461723i
$554$		0			0
$555$	−100.086	+	173.354i	−0.180335	+	0.312350i
$556$		0			0
$557$	−189.516	+	328.251i	−0.340244	+	0.589320i	−0.984478	−	0.175509i	$-0.943843\pi$
$557$	−189.516	+	328.251i	−0.340244	+	0.589320i	0.644234	+	0.764829i	$0.277176\pi$
$558$		0			0
$559$			971.636i			1.73817i
$560$		0			0
$561$	624.344	+	360.465i	1.11291	+	0.642540i
$562$		0			0
$563$			289.079i			0.513462i	0.966483	+	0.256731i	$0.0826455\pi$
$563$			289.079i			0.513462i	−0.966483	+	0.256731i	$0.917355\pi$
$564$		0			0
$565$	−64.2845	+	37.1147i	−0.113778	+	0.0656897i
$566$		0			0
$567$	−49.5707	−	85.8590i	−0.0874263	−	0.151427i
$568$		0			0
$569$			928.893i			1.63250i	0.577698	+	0.816251i	$0.303951\pi$
$569$			928.893i			1.63250i	−0.577698	+	0.816251i	$0.696049\pi$
$570$		0			0
$571$	229.390			0.401734			0.200867	−	0.979618i	$-0.435624\pi$
$571$	229.390			0.401734			0.200867	+	0.979618i	$0.435624\pi$
$572$		0			0
$573$	−30.9490	+	17.8684i	−0.0540122	+	0.0311840i
$574$		0			0
$575$	−221.685	−	383.969i	−0.385539	−	0.667773i
$576$		0			0
$577$	−60.9005			−0.105547			−0.0527734	−	0.998607i	$-0.516806\pi$
$577$	−60.9005			−0.105547			−0.0527734	+	0.998607i	$0.516806\pi$
$578$		0			0
$579$	29.1581	−	50.5033i	0.0503594	−	0.0872250i
$580$		0			0
$581$	−732.788			−1.26125
$582$		0			0
$583$	−220.668	−	127.403i	−0.378504	−	0.218529i
$584$		0			0
$585$	−259.579	−	149.868i	−0.443725	−	0.256185i
$586$		0			0
$587$	512.493	+	887.664i	0.873072	+	1.51220i	0.858803	+	0.512307i	$0.171209\pi$
$587$	512.493	+	887.664i	0.873072	+	1.51220i	0.0142694	+	0.999898i	$0.495458\pi$
$588$		0			0
$589$	141.520	+	260.248i	0.240271	+	0.441847i
$590$		0			0
$591$	95.1545	−	54.9375i	0.161006	−	0.0929568i
$592$		0			0
$593$	−0.435817	+	0.754857i	−0.000734935	+	0.00127295i	−0.866393	−	0.499363i	$-0.833567\pi$
$593$	−0.435817	+	0.754857i	−0.000734935	+	0.00127295i	0.865658	+	0.500636i	$0.166901\pi$
$594$		0			0
$595$	−868.687	+	1504.61i	−1.45998	+	2.52876i
$596$		0			0
$597$		−	228.390i		−	0.382563i
$598$		0			0
$599$	107.760	+	62.2154i	0.179900	+	0.103865i	0.587246	−	0.809409i	$-0.300212\pi$
$599$	107.760	+	62.2154i	0.179900	+	0.103865i	−0.407346	+	0.913274i	$0.633546\pi$
$600$		0			0
$601$			1089.57i			1.81292i	0.422287	+	0.906462i	$0.361227\pi$
$601$			1089.57i			1.81292i	−0.422287	+	0.906462i	$0.638773\pi$
$602$		0			0
$603$	255.980	−	147.790i	0.424510	−	0.245091i
$604$		0			0
$605$	−569.848	−	987.005i	−0.941897	−	1.63141i
$606$		0			0
$607$		−	642.114i		−	1.05785i	−0.848669	−	0.528925i	$-0.822595\pi$
$607$		−	642.114i		−	1.05785i	0.848669	−	0.528925i	$-0.177405\pi$
$608$		0			0
$609$	−235.707			−0.387040
$610$		0			0
$611$	932.660	−	538.472i	1.52645	−	0.881296i
$612$		0			0
$613$	−32.5919	−	56.4508i	−0.0531678	−	0.0920894i	0.838217	−	0.545337i	$-0.183598\pi$
$613$	−32.5919	−	56.4508i	−0.0531678	−	0.0920894i	−0.891384	+	0.453248i	$0.850265\pi$
$614$		0			0
$615$	568.943			0.925111
$616$		0			0
$617$	583.672	−	1010.95i	0.945984	−	1.63849i	0.192215	−	0.981353i	$-0.438433\pi$
$617$	583.672	−	1010.95i	0.945984	−	1.63849i	0.753769	−	0.657139i	$-0.228234\pi$
$618$		0			0
$619$	−201.087			−0.324857			−0.162429	−	0.986720i	$-0.551933\pi$
$619$	−201.087			−0.324857			−0.162429	+	0.986720i	$0.551933\pi$
$620$		0			0
$621$	−114.139	−	65.8981i	−0.183798	−	0.106116i
$622$		0			0
$623$	358.704	+	207.098i	0.575769	+	0.332421i
$624$		0			0
$625$	378.224	+	655.103i	0.605159	+	1.04817i
$626$		0			0
$627$	295.453	−	482.832i	0.471217	−	0.770066i
$628$		0			0
$629$	371.594	−	214.540i	0.590769	−	0.341081i
$630$		0			0
$631$	137.934	−	238.909i	0.218596	−	0.378619i	−0.735783	−	0.677217i	$-0.763186\pi$
$631$	137.934	−	238.909i	0.218596	−	0.378619i	0.954379	+	0.298598i	$0.0965191\pi$
$632$		0			0
$633$	160.542	−	278.068i	0.253621	−	0.439285i
$634$		0			0
$635$		−	81.2592i		−	0.127967i
$636$		0			0
$637$	960.440	+	554.510i	1.50776	+	0.870503i
$638$		0			0
$639$			130.065i			0.203545i
$640$		0			0
$641$	154.385	−	89.1343i	0.240850	−	0.139055i	−0.374717	−	0.927139i	$-0.622260\pi$
$641$	154.385	−	89.1343i	0.240850	−	0.139055i	0.615567	+	0.788084i	$0.288927\pi$
$642$		0			0
$643$	23.9786	+	41.5322i	0.0372918	+	0.0645913i	0.884069	−	0.467357i	$-0.154794\pi$
$643$	23.9786	+	41.5322i	0.0372918	+	0.0645913i	−0.846777	+	0.531948i	$0.821460\pi$
$644$		0			0
$645$			715.537i			1.10936i
$646$		0			0
$647$	−256.588			−0.396581			−0.198290	−	0.980143i	$-0.563539\pi$
$647$	−256.588			−0.396581			−0.198290	+	0.980143i	$0.563539\pi$
$648$		0			0
$649$	1029.31	−	594.270i	1.58599	−	0.915671i
$650$		0			0
$651$	148.741	+	257.627i	0.228481	+	0.395740i
$652$		0			0
$653$	289.100			0.442726			0.221363	−	0.975191i	$-0.428949\pi$
$653$	289.100			0.442726			0.221363	+	0.975191i	$0.428949\pi$
$654$		0			0
$655$	130.504	−	226.039i	0.199242	−	0.345098i
$656$		0			0
$657$	−289.556			−0.440725
$658$		0			0
$659$	−599.342	−	346.030i	−0.909471	−	0.525084i	−0.0292103	−	0.999573i	$-0.509299\pi$
$659$	−599.342	−	346.030i	−0.909471	−	0.525084i	−0.880261	+	0.474490i	$0.842633\pi$
$660$		0			0
$661$	−782.360	−	451.696i	−1.18360	−	0.683352i	−0.226756	−	0.973952i	$-0.572812\pi$
$661$	−782.360	−	451.696i	−1.18360	−	0.683352i	−0.956845	+	0.290600i	$0.906145\pi$
$662$		0			0
$663$	321.250	+	556.422i	0.484540	+	0.839249i
$664$		0			0
$665$	1163.58	+	712.014i	1.74974	+	1.07070i
$666$		0			0
$667$	−271.363	+	156.672i	−0.406842	+	0.234890i
$668$		0			0
$669$	−321.092	+	556.147i	−0.479957	+	0.831311i
$670$		0			0
$671$	320.076	−	554.389i	0.477014	−	0.826213i
$672$		0			0
$673$		−	414.658i		−	0.616133i	−0.951365	−	0.308067i	$-0.900318\pi$
$673$		−	414.658i		−	0.616133i	0.951365	−	0.308067i	$-0.0996820\pi$
$674$		0			0
$675$	−78.6606	−	45.4147i	−0.116534	−	0.0672811i
$676$		0			0
$677$		−	145.300i		−	0.214623i	−0.994225	−	0.107312i	$-0.965776\pi$
$677$		−	145.300i		−	0.214623i	0.994225	−	0.107312i	$-0.0342243\pi$
$678$		0			0
$679$	−56.3545	+	32.5363i	−0.0829964	+	0.0479180i
$680$		0			0
$681$	−46.7348	−	80.9470i	−0.0686267	−	0.118865i
$682$		0			0
$683$			612.684i			0.897049i	0.893771	+	0.448524i	$0.148050\pi$
$683$			612.684i			0.897049i	−0.893771	+	0.448524i	$0.851950\pi$
$684$		0			0
$685$	−708.551			−1.03438
$686$		0			0
$687$	−228.309	+	131.814i	−0.332328	+	0.191870i
$688$		0			0
$689$	−113.543	−	196.661i	−0.164793	−	0.285430i
$690$		0			0
$691$	1100.41			1.59248			0.796242	−	0.604979i	$-0.206818\pi$
$691$	1100.41			1.59248			0.796242	+	0.604979i	$0.206818\pi$
$692$		0			0
$693$	284.216	−	492.277i	0.410124	−	0.710356i
$694$		0			0
$695$	1216.57			1.75047
$696$		0			0
$697$	−1056.17	−	609.780i	−1.51531	−	0.874864i
$698$		0			0
$699$	149.339	+	86.2207i	0.213646	+	0.123349i
$700$		0			0
$701$	−542.919	−	940.363i	−0.774492	−	1.34146i	−0.935080	−	0.354438i	$-0.884672\pi$
$701$	−542.919	−	940.363i	−0.774492	−	1.34146i	0.160588	−	0.987022i	$-0.448661\pi$
$702$		0			0
$703$	−160.946	−	295.972i	−0.228942	−	0.421013i
$704$		0			0
$705$	686.834	−	396.544i	0.974233	−	0.562474i
$706$		0			0
$707$	18.0902	−	31.3332i	0.0255873	−	0.0443185i
$708$		0			0
$709$	275.398	−	477.003i	0.388431	−	0.672783i	−0.603807	−	0.797130i	$-0.706350\pi$
$709$	275.398	−	477.003i	0.388431	−	0.672783i	0.992239	+	0.124347i	$0.0396837\pi$
$710$		0			0
$711$			139.074i			0.195603i
$712$		0			0
$713$	342.483	+	197.733i	0.480341	+	0.277325i
$714$		0			0
$715$		−	1718.55i		−	2.40357i
$716$		0			0
$717$	476.898	−	275.337i	0.665130	−	0.384013i
$718$		0			0
$719$	57.4848	+	99.5667i	0.0799511	+	0.138479i	0.903229	−	0.429160i	$-0.141190\pi$
$719$	57.4848	+	99.5667i	0.0799511	+	0.138479i	−0.823278	+	0.567639i	$0.807857\pi$
$720$		0			0
$721$		−	1385.28i		−	1.92133i
$722$		0			0
$723$	−785.670			−1.08668
$724$		0			0
$725$	−187.014	+	107.973i	−0.257951	+	0.148928i
$726$		0			0
$727$	17.6897	+	30.6394i	0.0243325	+	0.0421450i	0.877935	−	0.478779i	$-0.158921\pi$
$727$	17.6897	+	30.6394i	0.0243325	+	0.0421450i	−0.853603	+	0.520924i	$0.825587\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	766.896	−	1328.30i	1.04911	−	1.81710i
$732$		0			0
$733$	−22.3884			−0.0305435			−0.0152718	−	0.999883i	$-0.504861\pi$
$733$	−22.3884			−0.0305435			−0.0152718	+	0.999883i	$0.504861\pi$
$734$		0			0
$735$	707.292	+	408.355i	0.962302	+	0.555586i
$736$		0			0
$737$	1467.67	+	847.361i	1.99141	+	1.14974i
$738$		0			0
$739$	−465.329	−	805.973i	−0.629674	−	1.09063i	−0.987617	−	0.156884i	$-0.949855\pi$
$739$	−465.329	−	805.973i	−0.629674	−	1.09063i	0.357943	−	0.933743i	$-0.383478\pi$
$740$		0			0
$741$	443.186	−	240.999i	0.598092	−	0.325235i
$742$		0			0
$743$	331.912	−	191.630i	0.446719	−	0.257913i	−0.259724	−	0.965683i	$-0.583632\pi$
$743$	331.912	−	191.630i	0.446719	−	0.257913i	0.706444	+	0.707769i	$0.250298\pi$
$744$		0			0
$745$	−130.516	+	226.060i	−0.175189	+	0.303436i
$746$		0			0
$747$	−99.7831	+	172.829i	−0.133578	+	0.231365i
$748$		0			0
$749$		−	411.812i		−	0.549815i
$750$		0			0
$751$	228.112	+	131.700i	0.303744	+	0.175367i	0.644123	−	0.764922i	$-0.277222\pi$
$751$	228.112	+	131.700i	0.303744	+	0.175367i	−0.340380	+	0.940288i	$0.610556\pi$
$752$		0			0
$753$			635.714i			0.844241i
$754$		0			0
$755$	−826.853	+	477.384i	−1.09517	+	0.632296i
$756$		0			0
$757$	725.222	+	1256.12i	0.958021	+	1.65934i	0.727298	+	0.686321i	$0.240776\pi$
$757$	725.222	+	1256.12i	0.958021	+	1.65934i	0.230723	+	0.973020i	$0.425891\pi$
$758$		0			0
$759$		−	755.660i		−	0.995599i
$760$		0			0
$761$	−586.814			−0.771109			−0.385554	−	0.922685i	$-0.625990\pi$
$761$	−586.814			−0.771109			−0.385554	+	0.922685i	$0.625990\pi$
$762$		0			0
$763$	936.027	−	540.415i	1.22677	−	0.708277i
$764$		0			0
$765$	236.577	+	409.763i	0.309251	+	0.535638i
$766$		0			0
$767$	1059.24			1.38102
$768$		0			0
$769$	337.633	−	584.798i	0.439055	−	0.760465i	−0.558562	−	0.829463i	$-0.688647\pi$
$769$	337.633	−	584.798i	0.439055	−	0.760465i	0.997617	+	0.0689977i	$0.0219801\pi$
$770$		0			0
$771$	−447.378			−0.580257
$772$		0			0
$773$	−631.467	−	364.577i	−0.816904	−	0.471640i	0.0324438	−	0.999474i	$-0.489671\pi$
$773$	−631.467	−	364.577i	−0.816904	−	0.471640i	−0.849348	+	0.527834i	$0.823004\pi$
$774$		0			0
$775$	236.028	+	136.271i	0.304552	+	0.175833i
$776$		0			0
$777$	−169.158	−	292.991i	−0.217707	−	0.377080i
$778$		0			0
$779$	−499.802	+	816.781i	−0.641595	+	1.04850i
$780$		0			0
$781$	−645.826	+	372.868i	−0.826922	+	0.477424i
$782$		0			0
$783$	−32.0960	+	55.5920i	−0.0409911	+	0.0709987i
$784$		0			0
$785$	−613.779	+	1063.10i	−0.781884	+	1.35426i
$786$		0			0
$787$			1362.43i			1.73117i	0.500761	+	0.865585i	$0.333053\pi$
$787$			1362.43i			1.73117i	−0.500761	+	0.865585i	$0.666947\pi$
$788$		0			0
$789$	43.9503	+	25.3747i	0.0557038	+	0.0321606i
$790$		0			0
$791$		−	125.457i		−	0.158606i
$792$		0			0
$793$	494.077	−	285.256i	0.623048	−	0.359717i
$794$		0			0
$795$	−83.6155	−	144.826i	−0.105177	−	0.182172i
$796$		0			0
$797$			1519.32i			1.90630i	0.302493	+	0.953151i	$0.402181\pi$
$797$			1519.32i			1.90630i	−0.302493	+	0.953151i	$0.597819\pi$
$798$		0			0
$799$	−1700.03			−2.12769
$800$		0			0
$801$	97.6889	−	56.4007i	0.121959	−	0.0704129i
$802$		0			0
$803$	−830.092	−	1437.76i	−1.03374	−	1.79049i
$804$		0			0
$805$	1821.07			2.26220
$806$		0			0
$807$	−201.089	+	348.297i	−0.249181	+	0.431594i
$808$		0			0
$809$	−455.077			−0.562518			−0.281259	−	0.959632i	$-0.590752\pi$
$809$	−455.077			−0.562518			−0.281259	+	0.959632i	$0.590752\pi$
$810$		0			0
$811$	555.111	+	320.494i	0.684477	+	0.395183i	0.801540	−	0.597941i	$-0.204014\pi$
$811$	555.111	+	320.494i	0.684477	+	0.395183i	−0.117062	+	0.993125i	$0.537348\pi$
$812$		0			0
$813$	−53.1834	−	30.7054i	−0.0654162	−	0.0377681i
$814$		0			0
$815$	122.329	+	211.880i	0.150097	+	0.259975i
$816$		0			0
$817$	−1027.23	−	628.581i	−1.25732	−	0.769377i
$818$		0			0
$819$	438.722	−	253.296i	0.535680	−	0.309275i
$820$		0			0
$821$	−695.378	+	1204.43i	−0.846989	+	1.46703i	0.0368941	+	0.999319i	$0.488254\pi$
$821$	−695.378	+	1204.43i	−0.846989	+	1.46703i	−0.883883	+	0.467708i	$0.845080\pi$
$822$		0			0
$823$	506.572	−	877.409i	0.615519	−	1.06611i	−0.374774	−	0.927116i	$-0.622280\pi$
$823$	506.572	−	877.409i	0.615519	−	1.06611i	0.990293	−	0.138994i	$-0.0443870\pi$
$824$		0			0
$825$		−	520.775i		−	0.631243i
$826$		0			0
$827$	356.091	+	205.589i	0.430582	+	0.248597i	0.699595	−	0.714540i	$-0.253364\pi$
$827$	356.091	+	205.589i	0.430582	+	0.248597i	−0.269013	+	0.963137i	$0.586697\pi$
$828$		0			0
$829$		−	834.178i		−	1.00625i	−0.864215	−	0.503123i	$-0.832184\pi$
$829$		−	834.178i		−	1.00625i	0.864215	−	0.503123i	$-0.167816\pi$
$830$		0			0
$831$	−294.435	+	169.992i	−0.354314	+	0.204563i
$832$		0			0
$833$	−875.331	−	1516.12i	−1.05082	−	1.82007i
$834$		0			0
$835$		−	847.522i		−	1.01500i
$836$		0			0
$837$	81.0157			0.0967929
$838$		0			0
$839$	−1224.91	+	707.201i	−1.45996	+	0.842910i	−0.999009	−	0.0445141i	$-0.985826\pi$
$839$	−1224.91	+	707.201i	−1.45996	+	0.842910i	−0.460954	+	0.887424i	$0.652493\pi$
$840$		0			0
$841$	−344.192	−	596.158i	−0.409265	−	0.708868i
$842$		0			0
$843$	−498.581			−0.591436
$844$		0			0
$845$	215.052	−	372.481i	0.254500	−	0.440806i
$846$		0			0
$847$	1926.23			2.27418
$848$		0			0
$849$	−660.944	−	381.596i	−0.778497	−	0.449465i
$850$		0			0
$851$	−389.495	−	224.875i	−0.457691	−	0.264248i
$852$		0			0
$853$	517.102	+	895.647i	0.606215	+	1.05000i	0.991858	+	0.127348i	$0.0406464\pi$
$853$	517.102	+	895.647i	0.606215	+	1.05000i	−0.385643	+	0.922648i	$0.626020\pi$
$854$		0			0
$855$	326.373	−	177.478i	0.381723	−	0.207577i
$856$		0			0
$857$	483.510	−	279.155i	0.564189	−	0.325735i	−0.190636	−	0.981661i	$-0.561055\pi$
$857$	483.510	−	279.155i	0.564189	−	0.325735i	0.754825	+	0.655926i	$0.227722\pi$
$858$		0			0
$859$	206.987	−	358.513i	0.240963	−	0.417361i	−0.720026	−	0.693947i	$-0.755870\pi$
$859$	206.987	−	358.513i	0.240963	−	0.417361i	0.960989	+	0.276587i	$0.0892033\pi$
$860$		0			0
$861$	−480.794	+	832.759i	−0.558413	+	0.967200i
$862$		0			0
$863$			1340.96i			1.55384i	0.629602	+	0.776918i	$0.283218\pi$
$863$			1340.96i			1.55384i	−0.629602	+	0.776918i	$0.716782\pi$
$864$		0			0
$865$	−557.146	−	321.669i	−0.644100	−	0.371871i
$866$		0			0
$867$		−	513.667i		−	0.592464i
$868$		0			0
$869$	−690.557	+	398.693i	−0.794657	+	0.458796i
$870$		0			0
$871$	755.177	+	1308.01i	0.867023	+	1.50173i
$872$		0			0
$873$			17.7218i			0.0202998i
$874$		0			0
$875$	−539.903			−0.617032
$876$		0			0
$877$	180.704	−	104.329i	0.206047	−	0.118962i	−0.393426	−	0.919356i	$-0.628710\pi$
$877$	180.704	−	104.329i	0.206047	−	0.118962i	0.599473	+	0.800395i	$0.295377\pi$
$878$		0			0
$879$	−385.932	−	668.453i	−0.439058	−	0.760470i
$880$		0			0
$881$	−235.342			−0.267131			−0.133565	−	0.991040i	$-0.542643\pi$
$881$	−235.342			−0.267131			−0.133565	+	0.991040i	$0.542643\pi$
$882$		0			0
$883$	−695.203	+	1204.13i	−0.787320	+	1.36368i	0.140283	+	0.990111i	$0.455199\pi$
$883$	−695.203	+	1204.13i	−0.787320	+	1.36368i	−0.927603	+	0.373567i	$0.878135\pi$
$884$		0			0
$885$	780.051			0.881413
$886$		0			0
$887$	562.674	+	324.860i	0.634357	+	0.366246i	0.782437	−	0.622729i	$-0.213976\pi$
$887$	562.674	+	324.860i	0.634357	+	0.366246i	−0.148081	+	0.988975i	$0.547310\pi$
$888$		0			0
$889$	118.939	+	68.6692i	0.133789	+	0.0772432i
$890$		0			0
$891$	−77.4029	−	134.066i	−0.0868719	−	0.150467i
$892$		0			0
$893$	−34.0838	+	1334.38i	−0.0381678	+	1.49427i
$894$		0			0
$895$	−757.221	+	437.182i	−0.846057	+	0.488471i
$896$		0			0
$897$	336.726	−	583.227i	0.375391	−	0.650197i
$898$		0			0
$899$	96.3068	−	166.808i	0.107127	−	0.185549i
$900$		0			0
$901$			358.469i			0.397856i
$902$		0			0
$903$	−1047.33	−	604.675i	−1.15983	−	0.669629i
$904$		0			0
$905$			543.519i			0.600574i
$906$		0			0
$907$	1262.76	−	729.057i	1.39224	−	0.803811i	0.398679	−	0.917091i	$-0.369469\pi$
$907$	1262.76	−	729.057i	1.39224	−	0.803811i	0.993563	+	0.113280i	$0.0361356\pi$
$908$		0			0
$909$	−4.92666	−	8.53322i	−0.00541986	−	0.00938748i
$910$		0			0
$911$			1584.04i			1.73880i	0.494113	+	0.869398i	$0.335493\pi$
$911$			1584.04i			1.73880i	−0.494113	+	0.869398i	$0.664507\pi$
$912$		0			0
$913$	−1144.22			−1.25326
$914$		0			0
$915$	363.851	−	210.069i	0.397651	−	0.229584i
$916$		0			0
$917$	220.568	+	382.035i	0.240532	+	0.416614i
$918$		0			0
$919$	845.467			0.919986			0.459993	−	0.887923i	$-0.347852\pi$
$919$	845.467			0.919986			0.459993	+	0.887923i	$0.347852\pi$
$920$		0			0
$921$	364.933	−	632.082i	0.396235	−	0.686299i
$922$		0			0
$923$	−664.608			−0.720052
$924$		0			0
$925$	−268.427	−	154.976i	−0.290191	−	0.167542i
$926$		0			0
$927$	−326.720	−	188.632i	−0.352449	−	0.203486i
$928$		0			0
$929$	−351.209	−	608.312i	−0.378051	−	0.654803i	0.612728	−	0.790294i	$-0.290072\pi$
$929$	−351.209	−	608.312i	−0.378051	−	0.654803i	−0.990779	+	0.135491i	$0.956739\pi$
$930$		0			0
$931$	−1207.58	+	656.666i	−1.29708	+	0.705335i
$932$		0			0
$933$	446.900	−	258.018i	0.478992	−	0.276546i
$934$		0			0
$935$	−1356.42	+	2349.40i	−1.45072	+	2.51272i
$936$		0			0
$937$	−232.938	+	403.461i	−0.248600	+	0.430588i	−0.963138	−	0.269009i	$-0.913304\pi$
$937$	−232.938	+	403.461i	−0.248600	+	0.430588i	0.714538	+	0.699597i	$0.246637\pi$
$938$		0			0
$939$		−	858.312i		−	0.914070i
$940$		0			0
$941$	−1281.39	−	739.810i	−1.36173	−	0.786196i	−0.371877	−	0.928282i	$-0.621286\pi$
$941$	−1281.39	−	739.810i	−1.36173	−	0.786196i	−0.989854	+	0.142086i	$0.954619\pi$
$942$		0			0
$943$			1278.31i			1.35558i
$944$		0			0
$945$	323.086	−	186.534i	0.341890	−	0.197390i
$946$		0			0
$947$	−389.648	−	674.890i	−0.411455	−	0.712661i	0.583594	−	0.812046i	$-0.301646\pi$
$947$	−389.648	−	674.890i	−0.411455	−	0.712661i	−0.995049	+	0.0993842i	$0.968313\pi$
$948$		0			0
$949$		−	1479.57i		−	1.55909i
$950$		0			0
$951$	590.197			0.620607
$952$		0			0
$953$	406.395	−	234.632i	0.426438	−	0.246204i	−0.271390	−	0.962469i	$-0.587483\pi$
$953$	406.395	−	234.632i	0.426438	−	0.246204i	0.697828	+	0.716265i	$0.254150\pi$
$954$		0			0
$955$	−67.2386	−	116.461i	−0.0704069	−	0.121948i
$956$		0			0
$957$	−368.048			−0.384586
$958$		0			0
$959$	598.771	−	1037.10i	0.624370	−	1.08144i
$960$		0			0
$961$	717.906			0.747040
$962$		0			0
$963$	−97.1265	−	56.0760i	−0.100858	−	0.0582305i
$964$		0			0
$965$	190.043	+	109.721i	0.196936	+	0.113701i
$966$		0			0
$967$	−459.292	−	795.516i	−0.474965	−	0.822664i	0.524623	−	0.851334i	$-0.324206\pi$
$967$	−459.292	−	795.516i	−0.474965	−	0.822664i	−0.999589	+	0.0286701i	$0.990873\pi$
$968$		0			0
$969$	−796.087	−	20.3343i	−0.821555	−	0.0209848i
$970$		0			0
$971$	−958.564	+	553.427i	−0.987192	+	0.569956i	−0.904434	−	0.426614i	$-0.859706\pi$
$971$	−958.564	+	553.427i	−0.987192	+	0.569956i	−0.0827583	+	0.996570i	$0.526373\pi$
$972$		0			0
$973$	−1028.08	+	1780.69i	−1.05661	+	1.83011i
$974$		0			0
$975$	232.060	−	401.940i	0.238010	−	0.412246i
$976$		0			0
$977$			1650.69i			1.68955i	0.535122	+	0.844775i	$0.320266\pi$
$977$			1650.69i			1.68955i	−0.535122	+	0.844775i	$0.679734\pi$
$978$		0			0
$979$	560.104	+	323.376i	0.572118	+	0.330313i
$980$		0			0
$981$		−	294.351i		−	0.300052i
$982$		0			0
$983$	−503.841	+	290.893i	−0.512554	+	0.295923i	−0.733883	−	0.679276i	$-0.762294\pi$
$983$	−503.841	+	290.893i	−0.512554	+	0.295923i	0.221329	+	0.975199i	$0.428961\pi$
$984$		0			0
$985$	206.729	+	358.065i	0.209877	+	0.363518i
$986$		0			0
$987$			1340.42i			1.35808i
$988$		0			0
$989$	−1607.68			−1.62556
$990$		0			0
$991$	295.801	−	170.781i	0.298487	−	0.172332i	−0.343276	−	0.939235i	$-0.611537\pi$
$991$	295.801	−	170.781i	0.298487	−	0.172332i	0.641763	+	0.766903i	$0.278203\pi$
$992$		0			0
$993$	−386.189	−	668.898i	−0.388911	−	0.673614i
$994$		0			0
$995$	859.428			0.863746
$996$		0			0
$997$	−12.0149	+	20.8104i	−0.0120511	+	0.0208730i	−0.871988	−	0.489527i	$-0.837169\pi$
$997$	−12.0149	+	20.8104i	−0.0120511	+	0.0208730i	0.859937	+	0.510400i	$0.170503\pi$
$998$		0			0
$999$	−92.1366			−0.0922288

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.g.145.1		8
4.3	odd	2		114.3.f.b.31.1	✓	8
12.11	even	2		342.3.m.b.145.4		8
19.8	odd	6	inner	912.3.be.g.673.1		8
76.27	even	6		114.3.f.b.103.1	yes	8
228.179	odd	6		342.3.m.b.217.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.3.f.b.31.1	✓	8	4.3	odd	2
114.3.f.b.103.1	yes	8	76.27	even	6
342.3.m.b.145.4		8	12.11	even	2
342.3.m.b.217.4		8	228.179	odd	6
912.3.be.g.145.1		8	1.1	even	1	trivial
912.3.be.g.673.1		8	19.8	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-3.25884 - 5.64448i) q^{5} +11.0157 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(-3.25884 - 5.64448i) q^{5} +11.0157 q^{7} +(1.50000 - 2.59808i) q^{9} +17.2006 q^{11} +(13.2756 + 7.66470i) q^{13} +(9.77652 + 5.64448i) q^{15} +(-12.0992 - 20.9565i) q^{17} +(-16.6917 + 9.07675i) q^{19} +(-16.5236 + 9.53989i) q^{21} +(-12.6821 + 21.9660i) q^{23} +(-8.74007 + 15.1382i) q^{25} +5.19615i q^{27} +(10.6987 + 6.17689i) q^{29} -15.5915i q^{31} +(-25.8010 + 14.8962i) q^{33} +(-35.8985 - 62.1779i) q^{35} +17.7317i q^{37} -26.5513 q^{39} +(43.6462 - 25.1991i) q^{41} +(31.6919 + 54.8920i) q^{43} -19.5530 q^{45} +(35.1267 - 60.8413i) q^{47} +72.3460 q^{49} +(36.2977 + 20.9565i) q^{51} +(-12.8290 - 7.40685i) q^{53} +(-56.0541 - 97.0886i) q^{55} +(17.1768 - 28.0706i) q^{57} +(59.8411 - 34.5493i) q^{59} +(18.6084 - 32.2307i) q^{61} +(16.5236 - 28.6197i) q^{63} -99.9121i q^{65} +(85.3266 + 49.2633i) q^{67} -43.9321i q^{69} +(-37.5466 + 21.6776i) q^{71} +(-48.2593 - 83.5876i) q^{73} -30.2765i q^{75} +189.477 q^{77} +(-40.1472 + 23.1790i) q^{79} +(-4.50000 - 7.79423i) q^{81} -66.5221 q^{83} +(-78.8589 + 136.588i) q^{85} -21.3974 q^{87} +(32.5630 + 18.8002i) q^{89} +(146.241 + 84.4321i) q^{91} +(13.5026 + 23.3872i) q^{93} +(105.629 + 64.6362i) q^{95} +(-5.11583 + 2.95363i) q^{97} +(25.8010 - 44.6886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9}+O(q^{10}) \) 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9	\( 8 q - 12 q^{3} + 4 q^{5} + 24 q^{7} + 12 q^{9} + 8 q^{11} + 24 q^{13} - 12 q^{15} - 20 q^{17} - 24 q^{19} - 36 q^{21} - 40 q^{23} - 88 q^{25} - 48 q^{29} - 12 q^{33} - 32 q^{35} - 48 q^{39} + 60 q^{41} + 116 q^{43} + 24 q^{45} + 68 q^{47} - 120 q^{49} + 60 q^{51} - 168 q^{53} - 232 q^{55} + 84 q^{57} + 156 q^{59} + 72 q^{61} + 36 q^{63} + 108 q^{67} - 444 q^{71} - 68 q^{73} + 296 q^{77} - 420 q^{79} - 36 q^{81} - 424 q^{83} + 40 q^{85} + 96 q^{87} - 420 q^{89} + 228 q^{91} + 84 q^{93} + 272 q^{95} + 156 q^{97} + 12 q^{99}+O(q^{100}) \) 8 * q - 12 * q^3 + 4 * q^5 + 24 * q^7 + 12 * q^9 + 8 * q^11 + 24 * q^13 - 12 * q^15 - 20 * q^17 - 24 * q^19 - 36 * q^21 - 40 * q^23 - 88 * q^25 - 48 * q^29 - 12 * q^33 - 32 * q^35 - 48 * q^39 + 60 * q^41 + 116 * q^43 + 24 * q^45 + 68 * q^47 - 120 * q^49 + 60 * q^51 - 168 * q^53 - 232 * q^55 + 84 * q^57 + 156 * q^59 + 72 * q^61 + 36 * q^63 + 108 * q^67 - 444 * q^71 - 68 * q^73 + 296 * q^77 - 420 * q^79 - 36 * q^81 - 424 * q^83 + 40 * q^85 + 96 * q^87 - 420 * q^89 + 228 * q^91 + 84 * q^93 + 272 * q^95 + 156 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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