LMFDB - Embedded newform 429.2.e.c.428.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(428,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("429.428");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 20x^{14} + 164x^{12} - 666x^{10} + 1300x^{8} - 924x^{6} + 273x^{4} + 404x^{2} + 64 $ x^16 - 20x^14 + 164x^12 - 666x^10 + 1300x^8 - 924x^6 + 273x^4 + 404*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			428.13
Root			$-2.14576 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	429.428
Dual form			429.2.e.c.428.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.13578i q^{2} +(0.780776 - 1.54609i) q^{3} -2.56155 q^{4} -3.09218 q^{5} +(3.30210 + 1.66757i) q^{6} -1.19935i q^{8} +(-1.78078 - 2.41430i) q^{9} +O(q^{10})$	\(q+2.13578i q^{2} +(0.780776 - 1.54609i) q^{3} -2.56155 q^{4} -3.09218 q^{5} +(3.30210 + 1.66757i) q^{6} -1.19935i q^{8} +(-1.78078 - 2.41430i) q^{9} -6.60421i q^{10} +(-3.09218 - 1.19935i) q^{11} +(-2.00000 + 3.96039i) q^{12} +(-3.30210 + 1.44780i) q^{13} +(-2.41430 + 4.78078i) q^{15} -2.56155 q^{16} -5.73384 q^{17} +(5.15641 - 3.80335i) q^{18} +2.89560 q^{19} +7.92077 q^{20} +(2.56155 - 6.60421i) q^{22} +3.09218i q^{23} +(-1.85431 - 0.936426i) q^{24} +4.56155 q^{25} +(-3.09218 - 7.05256i) q^{26} +(-5.12311 + 0.868210i) q^{27} +5.73384 q^{29} +(-10.2107 - 5.15641i) q^{30} -2.68466i q^{31} -7.86962i q^{32} +(-4.26860 + 3.84435i) q^{33} -12.2462i q^{34} +(4.56155 + 6.18435i) q^{36} -9.56155i q^{37} +6.18435i q^{38} +(-0.339781 + 6.23575i) q^{39} +3.70861i q^{40} +5.20798i q^{41} +6.60421i q^{43} +(7.92077 + 3.07221i) q^{44} +(5.50647 + 7.46543i) q^{45} -6.60421 q^{46} +(-2.00000 + 3.96039i) q^{48} -7.00000 q^{49} +9.74247i q^{50} +(-4.47685 + 8.86502i) q^{51} +(8.45851 - 3.70861i) q^{52} -6.18435i q^{53} +(-1.85431 - 10.9418i) q^{54} +(9.56155 + 3.70861i) q^{55} +(2.26081 - 4.47685i) q^{57} +12.2462i q^{58} +11.0129 q^{59} +(6.18435 - 12.2462i) q^{60} +2.89560i q^{61} +5.73384 q^{62} +11.6847 q^{64} +(10.2107 - 4.47685i) q^{65} +(-8.21068 - 9.11679i) q^{66} +2.68466i q^{67} +14.6875 q^{68} +(4.78078 + 2.41430i) q^{69} -4.82860 q^{71} +(-2.89560 + 2.13578i) q^{72} -9.49980 q^{73} +20.4214 q^{74} +(3.56155 - 7.05256i) q^{75} -7.41722 q^{76} +(-13.3182 - 0.725698i) q^{78} -0.813015i q^{79} +7.92077 q^{80} +(-2.65767 + 8.59865i) q^{81} -11.1231 q^{82} +12.4041i q^{83} +17.7300 q^{85} -14.1051 q^{86} +(4.47685 - 8.86502i) q^{87} +(-1.43845 + 3.70861i) q^{88} -6.56502 q^{89} +(-15.9445 + 11.7606i) q^{90} -7.92077i q^{92} +(-4.15072 - 2.09612i) q^{93} -8.95369 q^{95} +(-12.1671 - 6.14441i) q^{96} +14.9309i q^{97} -14.9505i q^{98} +(2.61088 + 9.60121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} - 8 q^{4} - 12 q^{9}+O(q^{10}) $ 16 * q - 4 * q^3 - 8 * q^4 - 12 * q^9	$ 16 q - 4 q^{3} - 8 q^{4} - 12 q^{9} - 32 q^{12} - 8 q^{16} + 8 q^{22} + 40 q^{25} - 16 q^{27} + 40 q^{36} - 32 q^{48} - 112 q^{49} + 120 q^{55} + 88 q^{64} + 32 q^{66} + 60 q^{69} + 24 q^{75} - 92 q^{78} - 92 q^{81} - 112 q^{82} - 56 q^{88}+O(q^{100}) $ 16 * q - 4 * q^3 - 8 * q^4 - 12 * q^9 - 32 * q^12 - 8 * q^16 + 8 * q^22 + 40 * q^25 - 16 * q^27 + 40 * q^36 - 32 * q^48 - 112 * q^49 + 120 * q^55 + 88 * q^64 + 32 * q^66 + 60 * q^69 + 24 * q^75 - 92 * q^78 - 92 * q^81 - 112 * q^82 - 56 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$			2.13578i			1.51022i	0.655596	+	0.755112i	$0.272418\pi$
$2$			2.13578i			1.51022i	−0.655596	+	0.755112i	$0.727582\pi$
$3$	0.780776	−	1.54609i	0.450781	−	0.892634i
$3$	0.780776	−	1.54609i	0.450781	−	0.892634i
$4$	−2.56155			−1.28078
$5$	−3.09218			−1.38286			−0.691432	−	0.722442i	$-0.743020\pi$
$5$	−3.09218			−1.38286			−0.691432	+	0.722442i	$0.743020\pi$
$6$	3.30210	+	1.66757i	1.34808	+	0.680781i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$		−	1.19935i		−	0.424035i
$9$	−1.78078	−	2.41430i	−0.593592	−	0.804766i
$10$		−	6.60421i		−	2.08843i
$11$	−3.09218	−	1.19935i	−0.932326	−	0.361618i
$11$	−3.09218	−	1.19935i	−0.932326	−	0.361618i
$12$	−2.00000	+	3.96039i	−0.577350	+	1.14327i
$13$	−3.30210	+	1.44780i	−0.915838	+	0.401547i
$13$	−3.30210	+	1.44780i	−0.915838	+	0.401547i
$14$		0			0
$15$	−2.41430	+	4.78078i	−0.623369	+	1.23439i
$16$	−2.56155			−0.640388
$17$	−5.73384			−1.39066			−0.695330	−	0.718691i	$-0.744742\pi$
$17$	−5.73384			−1.39066			−0.695330	+	0.718691i	$0.744742\pi$
$18$	5.15641	−	3.80335i	1.21538	−	0.896457i
$19$	2.89560			0.664295			0.332148	−	0.943227i	$-0.392227\pi$
$19$	2.89560			0.664295			0.332148	+	0.943227i	$0.392227\pi$
$20$	7.92077			1.77114
$21$		0			0
$22$	2.56155	−	6.60421i	0.546125	−	1.40802i
$23$			3.09218i			0.644763i	0.946610	+	0.322382i	$0.104483\pi$
$23$			3.09218i			0.644763i	−0.946610	+	0.322382i	$0.895517\pi$
$24$	−1.85431	−	0.936426i	−0.378508	−	0.191147i
$25$	4.56155			0.912311
$26$	−3.09218	−	7.05256i	−0.606426	−	1.38312i
$27$	−5.12311	+	0.868210i	−0.985942	+	0.167087i
$28$		0			0
$29$	5.73384			1.06475			0.532373	−	0.846510i	$-0.321300\pi$
$29$	5.73384			1.06475			0.532373	+	0.846510i	$0.321300\pi$
$30$	−10.2107	−	5.15641i	−1.86421	−	0.941427i
$31$		−	2.68466i		−	0.482179i	−0.970503	−	0.241089i	$-0.922495\pi$
$31$		−	2.68466i		−	0.482179i	0.970503	−	0.241089i	$-0.0775047\pi$
$32$		−	7.86962i		−	1.39116i
$33$	−4.26860	+	3.84435i	−0.743068	+	0.669215i
$34$		−	12.2462i		−	2.10021i
$35$		0			0
$36$	4.56155	+	6.18435i	0.760259	+	1.03073i
$37$		−	9.56155i		−	1.57191i	−0.618284	−	0.785955i	$-0.712172\pi$
$37$		−	9.56155i		−	1.57191i	0.618284	−	0.785955i	$-0.287828\pi$
$38$			6.18435i			1.00323i
$39$	−0.339781	+	6.23575i	−0.0544085	+	0.998519i
$40$			3.70861i			0.586383i
$41$			5.20798i			0.813351i	0.913573	+	0.406675i	$0.133312\pi$
$41$			5.20798i			0.813351i	−0.913573	+	0.406675i	$0.866688\pi$
$42$		0			0
$43$			6.60421i			1.00713i	0.863957	+	0.503566i	$0.167979\pi$
$43$			6.60421i			1.00713i	−0.863957	+	0.503566i	$0.832021\pi$
$44$	7.92077	+	3.07221i	1.19410	+	0.463152i
$45$	5.50647	+	7.46543i	0.820857	+	1.11288i
$46$	−6.60421			−0.973737
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−2.00000	+	3.96039i	−0.288675	+	0.571633i
$49$	−7.00000			−1.00000
$50$			9.74247i			1.37779i
$51$	−4.47685	+	8.86502i	−0.626884	+	1.24135i
$52$	8.45851	−	3.70861i	1.17298	−	0.514292i
$53$		−	6.18435i		−	0.849486i	−0.905314	−	0.424743i	$-0.860364\pi$
$53$		−	6.18435i		−	0.849486i	0.905314	−	0.424743i	$-0.139636\pi$
$54$	−1.85431	−	10.9418i	−0.252339	−	1.48899i
$55$	9.56155	+	3.70861i	1.28928	+	0.500069i
$56$		0			0
$57$	2.26081	−	4.47685i	0.299452	−	0.592973i
$58$			12.2462i			1.60801i
$59$	11.0129			1.43376			0.716882	−	0.697195i	$-0.245569\pi$
$59$	11.0129			1.43376			0.716882	+	0.697195i	$0.245569\pi$
$60$	6.18435	−	12.2462i	0.798396	−	1.58098i
$61$			2.89560i			0.370743i	0.982669	+	0.185371i	$0.0593488\pi$
$61$			2.89560i			0.370743i	−0.982669	+	0.185371i	$0.940651\pi$
$62$	5.73384			0.728198
$63$		0			0
$64$	11.6847			1.46058
$65$	10.2107	−	4.47685i	1.26648	−	0.555284i
$66$	−8.21068	−	9.11679i	−1.01067	−	1.12220i
$67$			2.68466i			0.327983i	0.986462	+	0.163992i	$0.0524370\pi$
$67$			2.68466i			0.327983i	−0.986462	+	0.163992i	$0.947563\pi$
$68$	14.6875			1.78112
$69$	4.78078	+	2.41430i	0.575538	+	0.290647i
$70$		0			0
$71$	−4.82860			−0.573049			−0.286524	−	0.958073i	$-0.592500\pi$
$71$	−4.82860			−0.573049			−0.286524	+	0.958073i	$0.592500\pi$
$72$	−2.89560	+	2.13578i	−0.341249	+	0.251704i
$73$	−9.49980			−1.11187			−0.555934	−	0.831227i	$-0.687639\pi$
$73$	−9.49980			−1.11187			−0.555934	+	0.831227i	$0.687639\pi$
$74$	20.4214			2.37394
$75$	3.56155	−	7.05256i	0.411253	−	0.814360i
$76$	−7.41722			−0.850814
$77$		0			0
$78$	−13.3182	−	0.725698i	−1.50799	−	0.0821691i
$79$		−	0.813015i		−	0.0914713i	−0.998954	−	0.0457357i	$-0.985437\pi$
$79$		−	0.813015i		−	0.0914713i	0.998954	−	0.0457357i	$-0.0145632\pi$
$80$	7.92077			0.885569
$81$	−2.65767	+	8.59865i	−0.295297	+	0.955406i
$82$	−11.1231			−1.22834
$83$			12.4041i			1.36153i	0.732503	+	0.680764i	$0.238352\pi$
$83$			12.4041i			1.36153i	−0.732503	+	0.680764i	$0.761648\pi$
$84$		0			0
$85$	17.7300			1.92309
$86$	−14.1051			−1.52099
$87$	4.47685	−	8.86502i	0.479968	−	0.950430i
$88$	−1.43845	+	3.70861i	−0.153339	+	0.395339i
$89$	−6.56502			−0.695890			−0.347945	−	0.937515i	$-0.613120\pi$
$89$	−6.56502			−0.695890			−0.347945	+	0.937515i	$0.613120\pi$
$90$	−15.9445	+	11.7606i	−1.68070	+	1.23968i
$91$		0			0
$92$		−	7.92077i		−	0.825798i
$93$	−4.15072	−	2.09612i	−0.430409	−	0.217357i
$94$		0			0
$95$	−8.95369			−0.918629
$96$	−12.1671	−	6.14441i	−1.24180	−	0.627111i
$97$			14.9309i			1.51600i	0.652254	+	0.758000i	$0.273823\pi$
$97$			14.9309i			1.51600i	−0.652254	+	0.758000i	$0.726177\pi$
$98$		−	14.9505i		−	1.51022i
$99$	2.61088	+	9.60121i	0.262403	+	0.964958i
$100$	−11.6847			−1.16847
$101$	14.6875			1.46146			0.730732	−	0.682665i	$-0.239179\pi$
$101$	14.6875			1.46146			0.730732	+	0.682665i	$0.239179\pi$
$102$	−18.9337	−	9.56155i	−1.87472	−	0.946735i
$103$	−3.12311			−0.307729			−0.153864	−	0.988092i	$-0.549172\pi$
$103$	−3.12311			−0.307729			−0.153864	+	0.988092i	$0.549172\pi$
$104$	1.73642	+	3.96039i	0.170270	+	0.388348i
$105$		0			0
$106$	13.2084			1.28291
$107$	−20.4214			−1.97421			−0.987104	−	0.160080i	$-0.948825\pi$
$107$	−20.4214			−1.97421			−0.987104	+	0.160080i	$0.948825\pi$
$108$	13.1231	−	2.22397i	1.26277	−	0.214001i
$109$	−12.3954			−1.18726			−0.593632	−	0.804737i	$-0.702306\pi$
$109$	−12.3954			−1.18726			−0.593632	+	0.804737i	$0.702306\pi$
$110$	−7.92077	+	20.4214i	−0.755216	+	1.94710i
$111$	−14.7830	−	7.46543i	−1.40314	−	0.708588i
$112$		0			0
$113$		−	17.1973i		−	1.61779i	−0.587956	−	0.808893i	$-0.700067\pi$
$113$		−	17.1973i		−	1.61779i	0.587956	−	0.808893i	$-0.299933\pi$
$114$	9.56155	+	4.82860i	0.895521	+	0.452239i
$115$		−	9.56155i		−	0.891619i
$116$	−14.6875			−1.36370
$117$	9.37572	+	5.39406i	0.866786	+	0.498681i
$118$			23.5212i			2.16530i
$119$		0			0
$120$	5.73384	+	2.89560i	0.523425	+	0.264330i
$121$	8.12311	+	7.41722i	0.738464	+	0.674293i
$122$	−6.18435			−0.559905
$123$	8.05200	+	4.06627i	0.726025	+	0.366643i
$124$			6.87689i			0.617563i
$125$	1.35576			0.121262
$126$		0			0
$127$		−	16.9170i		−	1.50114i	−0.660789	−	0.750571i	$-0.729778\pi$
$127$		−	16.9170i		−	1.50114i	0.660789	−	0.750571i	$-0.270222\pi$
$128$			9.21662i			0.814642i
$129$	10.2107	+	5.15641i	0.899000	+	0.453996i
$130$	9.56155	+	21.8078i	0.838604	+	1.91267i
$131$	−11.4677			−1.00194			−0.500968	−	0.865466i	$-0.667022\pi$
$131$	−11.4677			−1.00194			−0.500968	+	0.865466i	$0.667022\pi$
$132$	10.9343	−	9.84751i	0.951705	−	0.857115i
$133$		0			0
$134$	−5.73384			−0.495328
$135$	15.8415	−	2.68466i	1.36342	−	0.231059i
$136$			6.87689i			0.589689i
$137$	3.09218			0.264182			0.132091	−	0.991238i	$-0.457831\pi$
$137$	3.09218			0.264182			0.132091	+	0.991238i	$0.457831\pi$
$138$	−5.15641	+	10.2107i	−0.438943	+	0.869191i
$139$			11.1258i			0.943681i	0.881684	+	0.471840i	$0.156410\pi$
$139$			11.1258i			0.943681i	−0.881684	+	0.471840i	$0.843590\pi$
$140$		0			0
$141$		0			0
$142$		−	10.3128i		−	0.865432i
$143$	11.9471	−	0.516459i	0.999067	−	0.0431885i
$144$	4.56155	+	6.18435i	0.380129	+	0.515363i
$145$	−17.7300			−1.47240
$146$		−	20.2895i		−	1.67917i
$147$	−5.46543	+	10.8226i	−0.450781	+	0.892634i
$148$			24.4924i			2.01326i
$149$		−	8.54312i		−	0.699879i	−0.936772	−	0.349940i	$-0.886202\pi$
$149$		−	8.54312i		−	0.699879i	0.936772	−	0.349940i	$-0.113798\pi$
$150$	15.0627	+	7.60669i	1.22987	+	0.621084i
$151$	−4.52162			−0.367965			−0.183982	−	0.982930i	$-0.558899\pi$
$151$	−4.52162			−0.367965			−0.183982	+	0.982930i	$0.558899\pi$
$152$		−	3.47284i		−	0.281685i
$153$	10.2107	+	13.8432i	0.825485	+	1.11916i
$154$		0			0
$155$			8.30144i			0.666787i
$156$	0.870368	−	15.9732i	0.0696852	−	1.27888i
$157$	−7.56155			−0.603478			−0.301739	−	0.953391i	$-0.597567\pi$
$157$	−7.56155			−0.603478			−0.301739	+	0.953391i	$0.597567\pi$
$158$	1.73642			0.138142
$159$	−9.56155	−	4.82860i	−0.758280	−	0.382933i
$160$			24.3342i			1.92379i
$161$		0			0
$162$	−18.3648	−	5.67620i	−1.44288	−	0.445964i
$163$		−	12.2462i		−	0.959197i	−0.877488	−	0.479599i	$-0.840782\pi$
$163$		−	12.2462i		−	0.959197i	0.877488	−	0.479599i	$-0.159218\pi$
$164$		−	13.3405i		−	1.04172i
$165$	13.1993	−	11.8874i	1.02756	−	0.925433i
$166$	−26.4924			−2.05621
$167$		−	13.8664i		−	1.07301i	−0.843896	−	0.536506i	$-0.819744\pi$
$167$		−	13.8664i		−	1.07301i	0.843896	−	0.536506i	$-0.180256\pi$
$168$		0			0
$169$	8.80776	−	9.56155i	0.677520	−	0.735504i
$170$			37.8674i			2.90430i
$171$	−5.15641	−	6.99083i	−0.394320	−	0.534602i
$172$		−	16.9170i		−	1.28991i
$173$	5.73384			0.435936			0.217968	−	0.975956i	$-0.430057\pi$
$173$	5.73384			0.435936			0.217968	+	0.975956i	$0.430057\pi$
$174$	18.9337	+	9.56155i	1.43536	+	0.724859i
$175$		0			0
$176$	7.92077	+	3.07221i	0.597051	+	0.231576i
$177$	8.59865	−	17.0270i	0.646314	−	1.27983i
$178$		−	14.0214i		−	1.05095i
$179$		−	0.380664i		−	0.0284522i	−0.999899	−	0.0142261i	$-0.995472\pi$
$179$		−	0.380664i		−	0.0284522i	0.999899	−	0.0142261i	$-0.00452846\pi$
$180$	−14.1051	−	19.1231i	−1.05133	−	1.42535i
$181$	−5.80776			−0.431688			−0.215844	−	0.976428i	$-0.569250\pi$
$181$	−5.80776			−0.431688			−0.215844	+	0.976428i	$0.569250\pi$
$182$		0			0
$183$	4.47685	+	2.26081i	0.330938	+	0.167124i
$184$	3.70861			0.273402
$185$			29.5660i			2.17374i
$186$	4.47685	−	8.86502i	0.328258	−	0.650015i
$187$	17.7300	+	6.87689i	1.29655	+	0.502888i
$188$		0			0
$189$		0			0
$190$		−	19.1231i		−	1.38734i
$191$			3.09218i			0.223742i	0.993723	+	0.111871i	$0.0356843\pi$
$191$			3.09218i			0.223742i	−0.993723	+	0.111871i	$0.964316\pi$
$192$	9.12311	−	18.0655i	0.658403	−	1.30377i
$193$	−3.70861			−0.266952			−0.133476	−	0.991052i	$-0.542614\pi$
$193$	−3.70861			−0.266952			−0.133476	+	0.991052i	$0.542614\pi$
$194$	−31.8890			−2.28950
$195$	1.05066	−	19.2820i	0.0752396	−	1.38081i
$196$	17.9309			1.28078
$197$			7.72197i			0.550168i	0.961420	+	0.275084i	$0.0887056\pi$
$197$			7.72197i			0.550168i	−0.961420	+	0.275084i	$0.911294\pi$
$198$	−20.5061	+	5.57626i	−1.45730	+	0.396288i
$199$	9.36932			0.664173			0.332087	−	0.943249i	$-0.392247\pi$
$199$	9.36932			0.664173			0.332087	+	0.943249i	$0.392247\pi$
$200$		−	5.47091i		−	0.386852i
$201$	4.15072	+	2.09612i	0.292769	+	0.147849i
$202$			31.3693i			2.20714i
$203$		0			0
$204$	11.4677	−	22.7082i	0.802898	−	1.58989i
$205$		−	16.1040i		−	1.12475i
$206$		−	6.67026i		−	0.464739i
$207$	7.46543	−	5.50647i	0.518884	−	0.382726i
$208$	8.45851	−	3.70861i	0.586492	−	0.257146i
$209$	−8.95369	−	3.47284i	−0.619340	−	0.240221i
$210$		0			0
$211$		−	24.3342i		−	1.67524i	−0.546255	−	0.837619i	$-0.683947\pi$
$211$		−	24.3342i		−	1.67524i	0.546255	−	0.837619i	$-0.316053\pi$
$212$			15.8415i			1.08800i
$213$	−3.77005	+	7.46543i	−0.258320	+	0.511523i
$214$		−	43.6155i		−	2.98150i
$215$		−	20.4214i		−	1.39273i
$216$	1.04129	+	6.14441i	0.0708508	+	0.418074i
$217$		0			0
$218$		−	26.4738i		−	1.79303i
$219$	−7.41722	+	14.6875i	−0.501209	+	0.992491i
$220$	−24.4924	−	9.49980i	−1.65128	−	0.640476i
$221$	18.9337	−	8.30144i	1.27362	−	0.558415i
$222$	15.9445	−	31.5732i	1.07013	−	2.11906i
$223$		−	2.68466i		−	0.179778i	−0.995952	−	0.0898890i	$-0.971349\pi$
$223$		−	2.68466i		−	0.179778i	0.995952	−	0.0898890i	$-0.0286512\pi$
$224$		0			0
$225$	−8.12311	−	11.0129i	−0.541540	−	0.734197i
$226$	36.7296			2.44322
$227$			2.80928i			0.186458i	0.995645	+	0.0932292i	$0.0297189\pi$
$227$			2.80928i			0.186458i	−0.995645	+	0.0932292i	$0.970281\pi$
$228$	−5.79119	+	11.4677i	−0.383531	+	0.759465i
$229$		−	9.56155i		−	0.631845i	−0.948785	−	0.315923i	$-0.897686\pi$
$229$		−	9.56155i		−	0.631845i	0.948785	−	0.315923i	$-0.102314\pi$
$230$	20.4214			1.34654
$231$		0			0
$232$		−	6.87689i		−	0.451490i
$233$	−14.6875			−0.962212			−0.481106	−	0.876662i	$-0.659765\pi$
$233$	−14.6875			−0.962212			−0.481106	+	0.876662i	$0.659765\pi$
$234$	−11.5205	+	20.0245i	−0.753120	+	1.30904i
$235$		0			0
$236$	−28.2102			−1.83633
$237$	−1.25699	−	0.634783i	−0.0816504	−	0.0412336i
$238$		0			0
$239$		−	21.3578i		−	1.38152i	−0.723084	−	0.690760i	$-0.757276\pi$
$239$		−	21.3578i		−	1.38152i	0.723084	−	0.690760i	$-0.242724\pi$
$240$	6.18435	−	12.2462i	0.399198	−	0.790490i
$241$	−14.0214			−0.903199			−0.451600	−	0.892221i	$-0.649146\pi$
$241$	−14.0214			−0.903199			−0.451600	+	0.892221i	$0.649146\pi$
$242$	−15.8415	+	17.3492i	−1.01833	+	1.11525i
$243$	11.2192	+	10.8226i	0.719714	+	0.694271i
$244$		−	7.41722i		−	0.474839i
$245$	21.6452			1.38286
$246$	−8.68466	+	17.1973i	−0.553714	+	1.09646i
$247$	−9.56155	+	4.19224i	−0.608387	+	0.266746i
$248$	−3.21985			−0.204461
$249$	19.1778	+	9.68483i	1.21535	+	0.613751i
$250$			2.89560i			0.183134i
$251$			28.5909i			1.80464i	0.431064	+	0.902321i	$0.358138\pi$
$251$			28.5909i			1.80464i	−0.431064	+	0.902321i	$0.641862\pi$
$252$		0			0
$253$	3.70861	−	9.56155i	0.233158	−	0.601130i
$254$	36.1310			2.26706
$255$	13.8432	−	27.4122i	0.866894	−	1.71662i
$256$	3.68466			0.230291
$257$		−	15.0802i		−	0.940678i	−0.882486	−	0.470339i	$-0.844132\pi$
$257$		−	15.0802i		−	0.940678i	0.882486	−	0.470339i	$-0.155868\pi$
$258$	−11.0129	+	21.8078i	−0.685636	+	1.35769i
$259$		0			0
$260$	−26.1552	+	11.4677i	−1.62208	+	0.711195i
$261$	−10.2107	−	13.8432i	−0.632025	−	0.856872i
$262$		−	24.4924i		−	1.51315i
$263$	−22.9354			−1.41425			−0.707127	−	0.707086i	$-0.750009\pi$
$263$	−22.9354			−1.41425			−0.707127	+	0.707086i	$0.750009\pi$
$264$	4.61073	+	5.11956i	0.283771	+	0.315087i
$265$			19.1231i			1.17472i
$266$		0			0
$267$	−5.12581	+	10.1501i	−0.313694	+	0.621176i
$268$		−	6.87689i		−	0.420073i
$269$			25.4987i			1.55469i	0.629077	+	0.777343i	$0.283433\pi$
$269$			25.4987i			1.55469i	−0.629077	+	0.777343i	$0.716567\pi$
$270$	5.73384	+	33.8340i	0.348950	+	2.05907i
$271$	5.79119			0.351790			0.175895	−	0.984409i	$-0.443718\pi$
$271$	5.79119			0.351790			0.175895	+	0.984409i	$0.443718\pi$
$272$	14.6875			0.890562
$273$		0			0
$274$			6.60421i			0.398975i
$275$	−14.1051	−	5.47091i	−0.850571	−	0.329908i
$276$	−12.2462	−	6.18435i	−0.737135	−	0.372254i
$277$			13.2084i			0.793616i	0.917902	+	0.396808i	$0.129882\pi$
$277$			13.2084i			0.793616i	−0.917902	+	0.396808i	$0.870118\pi$
$278$	−23.7623			−1.42517
$279$	−6.48157	+	4.78078i	−0.388041	+	0.286218i
$280$		0			0
$281$			10.4160i			0.621365i	0.950514	+	0.310682i	$0.100558\pi$
$281$			10.4160i			0.621365i	−0.950514	+	0.310682i	$0.899442\pi$
$282$		0			0
$283$			6.60421i			0.392579i	0.980546	+	0.196290i	$0.0628893\pi$
$283$			6.60421i			0.392579i	−0.980546	+	0.196290i	$0.937111\pi$
$284$	12.3687			0.733948
$285$	−6.99083	+	13.8432i	−0.414101	+	0.820000i
$286$	1.10304	+	25.5164i	0.0652243	+	1.50881i
$287$		0			0
$288$	−18.9996	+	14.0140i	−1.11956	+	0.825785i
$289$	15.8769			0.933935
$290$		−	37.8674i		−	2.22365i
$291$	23.0844	+	11.6577i	1.35323	+	0.683385i
$292$	24.3342			1.42405
$293$			33.7619i			1.97239i	0.165585	+	0.986195i	$0.447049\pi$
$293$			33.7619i			1.97239i	−0.165585	+	0.986195i	$0.552951\pi$
$294$	−23.1147	−	11.6730i	−1.34808	−	0.680781i
$295$	−34.0540			−1.98270
$296$	−11.4677			−0.666545
$297$	16.8828	+	3.45975i	0.979641	+	0.200755i
$298$	18.2462			1.05697
$299$	−4.47685	−	10.2107i	−0.258903	−	0.590499i
$300$	−9.12311	+	18.0655i	−0.526723	+	1.04301i
$301$		0			0
$302$		−	9.65719i		−	0.555709i
$303$	11.4677	−	22.7082i	0.658801	−	1.30455i
$304$	−7.41722			−0.425407
$305$		−	8.95369i		−	0.512687i
$306$	−29.5660	+	21.8078i	−1.69018	+	1.24667i
$307$	18.9996			1.08436			0.542182	−	0.840261i	$-0.317598\pi$
$307$	18.9996			1.08436			0.542182	+	0.840261i	$0.317598\pi$
$308$		0			0
$309$	−2.43845	+	4.82860i	−0.138718	+	0.274689i
$310$	−17.7300			−1.00700
$311$		−	23.7623i		−	1.34744i	−0.738988	−	0.673719i	$-0.764696\pi$
$311$		−	23.7623i		−	1.34744i	0.738988	−	0.673719i	$-0.235304\pi$
$312$	7.47886	+	0.407518i	0.423407	+	0.0230711i
$313$	26.6847			1.50831			0.754153	−	0.656699i	$-0.228048\pi$
$313$	26.6847			1.50831			0.754153	+	0.656699i	$0.228048\pi$
$314$		−	16.1498i		−	0.911386i
$315$		0			0
$316$			2.08258i			0.117154i
$317$	−5.80369			−0.325968			−0.162984	−	0.986629i	$-0.552112\pi$
$317$	−5.80369			−0.325968			−0.162984	+	0.986629i	$0.552112\pi$
$318$	10.3128	−	20.4214i	0.578314	−	1.14517i
$319$	−17.7300	−	6.87689i	−0.992691	−	0.385032i
$320$	−36.1310			−2.01979
$321$	−15.9445	+	31.5732i	−0.889936	+	1.76225i
$322$		0			0
$323$	−16.6029			−0.923809
$324$	6.80776	−	22.0259i	0.378209	−	1.22366i
$325$	−15.0627	+	6.60421i	−0.835529	+	0.366335i
$326$	26.1552			1.44860
$327$	−9.67803	+	19.1644i	−0.535196	+	1.05979i
$328$	6.24621			0.344889
$329$		0			0
$330$	25.3889	+	28.1907i	1.39761	+	1.55185i
$331$		−	8.05398i		−	0.442687i	−0.975196	−	0.221343i	$-0.928956\pi$
$331$		−	8.05398i		−	0.442687i	0.975196	−	0.221343i	$-0.0710441\pi$
$332$		−	31.7738i		−	1.74381i
$333$	−23.0844	+	17.0270i	−1.26502	+	0.933073i
$334$	29.6155			1.62049
$335$		−	8.30144i		−	0.453556i
$336$		0			0
$337$			4.52162i			0.246309i	0.992388	+	0.123154i	$0.0393010\pi$
$337$			4.52162i			0.246309i	−0.992388	+	0.123154i	$0.960699\pi$
$338$	20.4214	+	18.8114i	1.11078	+	1.02321i
$339$	−26.5885	−	13.4272i	−1.44409	−	0.729268i
$340$	−45.4164			−2.46305
$341$	−3.21985	+	8.30144i	−0.174365	+	0.449548i
$342$	14.9309	−	11.0129i	0.807369	−	0.595512i
$343$		0			0
$344$	7.92077			0.427059
$345$	−14.7830	−	7.46543i	−0.795890	−	0.401926i
$346$			12.2462i			0.658360i
$347$	−20.4214			−1.09628			−0.548138	−	0.836388i	$-0.684663\pi$
$347$	−20.4214			−1.09628			−0.548138	+	0.836388i	$0.684663\pi$
$348$	−11.4677	+	22.7082i	−0.614732	+	1.21729i
$349$	14.0214			0.750550			0.375275	−	0.926914i	$-0.377548\pi$
$349$	14.0214			0.750550			0.375275	+	0.926914i	$0.377548\pi$
$350$		0			0
$351$	15.6600	−	10.2841i	0.835870	−	0.548927i
$352$	−9.43845	+	24.3342i	−0.503071	+	1.29702i
$353$	−18.9337			−1.00774			−0.503870	−	0.863779i	$-0.668091\pi$
$353$	−18.9337			−1.00774			−0.503870	+	0.863779i	$0.668091\pi$
$354$	36.3659	+	18.3648i	1.93283	+	0.976079i
$355$	14.9309			0.792448
$356$	16.8166			0.891280
$357$		0			0
$358$	0.813015			0.0429692
$359$			27.6175i			1.45759i	0.684729	+	0.728797i	$0.259920\pi$
$359$			27.6175i			1.45759i	−0.684729	+	0.728797i	$0.740080\pi$
$360$	8.95369	−	6.60421i	0.471901	−	0.348072i
$361$	−10.6155			−0.558712
$362$		−	12.4041i		−	0.651945i
$363$	17.8100	−	6.76785i	0.934783	−	0.355220i
$364$		0			0
$365$	29.3751			1.53756
$366$	−4.82860	+	9.56155i	−0.252395	+	0.499790i
$367$	−26.0540			−1.36001			−0.680003	−	0.733209i	$-0.738022\pi$
$367$	−26.0540			−1.36001			−0.680003	+	0.733209i	$0.738022\pi$
$368$		−	7.92077i		−	0.412899i
$369$	12.5736	−	9.27426i	0.654557	−	0.482799i
$370$	−63.1465			−3.28283
$371$		0			0
$372$	10.6323	+	5.36932i	0.551258	+	0.278386i
$373$			13.2084i			0.683906i	0.939717	+	0.341953i	$0.111088\pi$
$373$			13.2084i			0.683906i	−0.939717	+	0.341953i	$0.888912\pi$
$374$	−14.6875	+	37.8674i	−0.759474	+	1.95808i
$375$	1.05854	−	2.09612i	0.0546629	−	0.108243i
$376$		0			0
$377$	−18.9337	+	8.30144i	−0.975136	+	0.427546i
$378$		0			0
$379$		−	16.4384i		−	0.844386i	−0.906506	−	0.422193i	$-0.861260\pi$
$379$		−	16.4384i		−	0.844386i	0.906506	−	0.422193i	$-0.138740\pi$
$380$	22.9354			1.17656
$381$	−26.1552	−	13.2084i	−1.33997	−	0.676687i
$382$	−6.60421			−0.337901
$383$	−26.8545			−1.37220			−0.686100	−	0.727507i	$-0.740679\pi$
$383$	−26.8545			−1.37220			−0.686100	+	0.727507i	$0.740679\pi$
$384$	14.2497	+	7.19612i	0.727177	+	0.367225i
$385$		0			0
$386$		−	7.92077i		−	0.403157i
$387$	15.9445	−	11.7606i	0.810506	−	0.597826i
$388$		−	38.2462i		−	1.94166i
$389$			1.35576i			0.0687396i	0.999409	+	0.0343698i	$0.0109424\pi$
$389$			1.35576i			0.0687396i	−0.999409	+	0.0343698i	$0.989058\pi$
$390$	41.1822	+	2.24399i	2.08534	+	0.113629i
$391$		−	17.7300i		−	0.896646i
$392$			8.39547i			0.424035i
$393$	−8.95369	+	17.7300i	−0.451654	+	0.894362i
$394$	−16.4924			−0.830876
$395$			2.51398i			0.126492i
$396$	−6.68790	−	24.5940i	−0.336080	−	1.23590i
$397$			24.4924i			1.22924i	0.788824	+	0.614620i	$0.210691\pi$
$397$			24.4924i			1.22924i	−0.788824	+	0.614620i	$0.789309\pi$
$398$			20.0108i			1.00305i
$399$		0			0
$400$	−11.6847			−0.584233
$401$	17.5780			0.877802			0.438901	−	0.898536i	$-0.355368\pi$
$401$	17.5780			0.877802			0.438901	+	0.898536i	$0.355368\pi$
$402$	−4.47685	+	8.86502i	−0.223285	+	0.442147i
$403$	3.88684	+	8.86502i	0.193617	+	0.441598i
$404$	−37.6229			−1.87181
$405$	8.21799	−	26.5885i	0.408355	−	1.32120i
$406$		0			0
$407$	−11.4677	+	29.5660i	−0.568432	+	1.46553i
$408$	10.6323	+	5.36932i	0.526376	+	0.265821i
$409$	11.1258			0.550137			0.275068	−	0.961425i	$-0.411299\pi$
$409$	11.1258			0.550137			0.275068	+	0.961425i	$0.411299\pi$
$410$	34.3946			1.69863
$411$	2.41430	−	4.78078i	0.119089	−	0.235818i
$412$	8.00000			0.394132
$413$		0			0
$414$	11.7606	+	15.9445i	0.578003	+	0.783630i
$415$		−	38.3557i		−	1.88281i
$416$	11.3936	+	25.9863i	0.558618	+	1.27408i
$417$	17.2015	+	8.68679i	0.842362	+	0.425394i
$418$	7.41722	−	19.1231i	0.362788	−	0.935342i
$419$		−	32.6582i		−	1.59546i	−0.603017	−	0.797728i	$-0.706035\pi$
$419$		−	32.6582i		−	1.59546i	0.603017	−	0.797728i	$-0.293965\pi$
$420$		0			0
$421$			5.36932i			0.261684i	0.991403	+	0.130842i	$0.0417681\pi$
$421$			5.36932i			0.261684i	−0.991403	+	0.130842i	$0.958232\pi$
$422$	51.9726			2.52998
$423$		0			0
$424$	−7.41722			−0.360212
$425$	−26.1552			−1.26871
$426$	−15.9445	−	8.05200i	−0.772515	−	0.390121i
$427$		0			0
$428$	52.3104			2.52852
$429$	8.52953	−	18.8745i	0.411809	−	0.911270i
$430$	43.6155			2.10333
$431$		−	19.8955i		−	0.958333i	−0.877724	−	0.479167i	$-0.840939\pi$
$431$		−	19.8955i		−	0.958333i	0.877724	−	0.479167i	$-0.159061\pi$
$432$	13.1231	−	2.22397i	0.631386	−	0.107001i
$433$	−17.8078			−0.855787			−0.427893	−	0.903829i	$-0.640744\pi$
$433$	−17.8078			−0.855787			−0.427893	+	0.903829i	$0.640744\pi$
$434$		0			0
$435$	−13.8432	+	27.4122i	−0.663730	+	1.31431i
$436$	31.7515			1.52062
$437$			8.95369i			0.428313i
$438$	−31.3693	−	15.8415i	−1.49888	−	0.756938i
$439$		−	38.8122i		−	1.85241i	−0.377025	−	0.926203i	$-0.623053\pi$
$439$		−	38.8122i		−	1.85241i	0.377025	−	0.926203i	$-0.376947\pi$
$440$	4.44793	−	11.4677i	0.212047	−	0.546700i
$441$	12.4654	+	16.9001i	0.593592	+	0.804766i
$442$	17.7300	+	40.4382i	0.843332	+	1.92345i
$443$		−	5.80369i		−	0.275742i	−0.990450	−	0.137871i	$-0.955974\pi$
$443$		−	5.80369i		−	0.275742i	0.990450	−	0.137871i	$-0.0440259\pi$
$444$	37.8674	+	19.1231i	1.79711	+	0.907542i
$445$	20.3002			0.962321
$446$	5.73384			0.271505
$447$	−13.2084	−	6.67026i	−0.624736	−	0.315493i
$448$		0			0
$449$	−3.85350			−0.181858			−0.0909291	−	0.995857i	$-0.528984\pi$
$449$	−3.85350			−0.181858			−0.0909291	+	0.995857i	$0.528984\pi$
$450$	23.5212	−	17.3492i	1.10880	−	0.817847i
$451$	6.24621	−	16.1040i	0.294123	−	0.758308i
$452$			44.0518i			2.07202i
$453$	−3.53038	+	6.99083i	−0.165872	+	0.328458i
$454$	−6.00000			−0.281594
$455$		0			0
$456$	−5.36932	−	2.71151i	−0.251441	−	0.126978i
$457$	7.87377			0.368319			0.184160	−	0.982896i	$-0.441044\pi$
$457$	7.87377			0.368319			0.184160	+	0.982896i	$0.441044\pi$
$458$	20.4214			0.954228
$459$	29.3751	−	4.97818i	1.37111	−	0.232361i
$460$			24.4924i			1.14197i
$461$			0.410574i			0.0191223i	0.999954	+	0.00956116i	$0.00304346\pi$
$461$			0.410574i			0.0191223i	−0.999954	+	0.00956116i	$0.996957\pi$
$462$		0			0
$463$			27.1771i			1.26303i	0.775365	+	0.631513i	$0.217566\pi$
$463$			27.1771i			1.26303i	−0.775365	+	0.631513i	$0.782434\pi$
$464$	−14.6875			−0.681851
$465$	12.8348	+	6.48157i	0.595197	+	0.300575i
$466$		−	31.3693i		−	1.45316i
$467$		−	0.380664i		−	0.0176150i	−0.999961	−	0.00880752i	$-0.997196\pi$
$467$		−	0.380664i		−	0.0176150i	0.999961	−	0.00880752i	$-0.00280356\pi$
$468$	−24.0164	−	13.8172i	−1.11016	−	0.638698i
$469$		0			0
$470$		0			0
$471$	−5.90388	+	11.6908i	−0.272037	+	0.538685i
$472$		−	13.2084i		−	0.607966i
$473$	7.92077	−	20.4214i	0.364197	−	0.938975i
$474$	1.35576	−	2.68466i	0.0622719	−	0.123310i
$475$	13.2084			0.606043
$476$		0			0
$477$	−14.9309	+	11.0129i	−0.683638	+	0.504248i
$478$	45.6155			2.08641
$479$		−	13.8664i		−	0.633571i	−0.948497	−	0.316786i	$-0.897396\pi$
$479$		−	13.8664i		−	0.633571i	0.948497	−	0.316786i	$-0.102604\pi$
$480$	37.6229	+	18.9996i	1.71724	+	0.867209i
$481$	13.8432	+	31.5732i	0.631195	+	1.43962i
$482$		−	29.9467i		−	1.36403i
$483$		0			0
$484$	−20.8078	−	18.9996i	−0.945807	−	0.863618i
$485$		−	46.1689i		−	2.09642i
$486$	−23.1147	+	23.9618i	−1.04850	+	1.08693i
$487$			16.4384i			0.744897i	0.928053	+	0.372449i	$0.121482\pi$
$487$			16.4384i			0.744897i	−0.928053	+	0.372449i	$0.878518\pi$
$488$	3.47284			0.157208
$489$	−18.9337	−	9.56155i	−0.856212	−	0.432388i
$490$			46.2294i			2.08843i
$491$	11.4677			0.517529			0.258764	−	0.965940i	$-0.416685\pi$
$491$	11.4677			0.517529			0.258764	+	0.965940i	$0.416685\pi$
$492$	−20.6256	−	10.4160i	−0.929875	−	0.469588i
$493$	−32.8769			−1.48070
$494$	−8.95369	−	20.4214i	−0.402846	−	0.918801i
$495$	−8.07330	−	29.6886i	−0.362868	−	1.33441i
$496$			6.87689i			0.308782i
$497$		0			0
$498$	−20.6847	+	40.9596i	−0.926902	+	1.83544i
$499$		−	12.2462i		−	0.548216i	−0.961699	−	0.274108i	$-0.911617\pi$
$499$		−	12.2462i		−	0.548216i	0.961699	−	0.274108i	$-0.0883825\pi$
$500$	−3.47284			−0.155310
$501$	−21.4386	−	10.8265i	−0.957808	−	0.483694i
$502$	−61.0639			−2.72541
$503$	−40.8427			−1.82109			−0.910544	−	0.413413i	$-0.864337\pi$
$503$	−40.8427			−1.82109			−0.910544	+	0.413413i	$0.864337\pi$
$504$		0			0
$505$	−45.4164			−2.02100
$506$	20.4214	+	7.92077i	0.907840	+	0.352121i
$507$	−7.90611	−	21.0830i	−0.351123	−	0.936329i
$508$			43.3338i			1.92263i
$509$	−5.80369			−0.257244			−0.128622	−	0.991694i	$-0.541055\pi$
$509$	−5.80369			−0.257244			−0.128622	+	0.991694i	$0.541055\pi$
$510$	58.5464	+	29.5660i	2.59248	+	1.30920i
$511$		0			0
$512$			26.3029i			1.16243i
$513$	−14.8344	+	2.51398i	−0.654957	+	0.110995i
$514$	32.2080			1.42063
$515$	9.65719			0.425547
$516$	−26.1552	−	13.2084i	−1.15142	−	0.581468i
$517$		0			0
$518$		0			0
$519$	4.47685	−	8.86502i	0.196512	−	0.389131i
$520$	−5.36932	−	12.2462i	−0.235460	−	0.537032i
$521$		−	14.4858i		−	0.634634i	−0.948320	−	0.317317i	$-0.897218\pi$
$521$		−	14.4858i		−	0.634634i	0.948320	−	0.317317i	$-0.102782\pi$
$522$	29.5660	−	21.8078i	1.29407	−	0.954500i
$523$			38.8122i			1.69714i	0.529083	+	0.848570i	$0.322536\pi$
$523$			38.8122i			1.69714i	−0.529083	+	0.848570i	$0.677464\pi$
$524$	29.3751			1.28326
$525$		0			0
$526$		−	48.9848i		−	2.13584i
$527$			15.3934i			0.670547i
$528$	10.9343	−	9.84751i	0.475852	−	0.428558i
$529$	13.4384			0.584280
$530$	−40.8427			−1.77409
$531$	−19.6116	−	26.5885i	−0.851071	−	1.15384i
$532$		0			0
$533$	−7.54011	−	17.1973i	−0.326598	−	0.744898i
$534$	−21.6784	−	10.9476i	−0.938114	−	0.473749i
$535$	63.1465			2.73006
$536$	3.21985			0.139076
$537$	−0.588540	−	0.297214i	−0.0253974	−	0.0128257i
$538$	−54.4597			−2.34792
$539$	21.6452	+	8.39547i	0.932326	+	0.361618i
$540$	−40.5790	+	6.87689i	−1.74624	+	0.295934i
$541$	14.0214			0.602828			0.301414	−	0.953493i	$-0.402541\pi$
$541$	14.0214			0.602828			0.301414	+	0.953493i	$0.402541\pi$
$542$			12.3687i			0.531281i
$543$	−4.53457	+	8.97931i	−0.194597	+	0.385339i
$544$			45.1231i			1.93464i
$545$	38.3287			1.64182
$546$		0			0
$547$			7.87377i			0.336658i	0.985731	+	0.168329i	$0.0538371\pi$
$547$			7.87377i			0.336658i	−0.985731	+	0.168329i	$0.946163\pi$
$548$	−7.92077			−0.338359
$549$	6.99083	−	5.15641i	0.298361	−	0.220070i
$550$	11.6847	−	30.1254i	0.498236	−	1.28455i
$551$	16.6029			0.707306
$552$	2.89560	−	5.73384i	0.123245	−	0.244048i
$553$		0			0
$554$	−28.2102			−1.19854
$555$	45.7116	+	23.0844i	1.94035	+	0.979880i
$556$		−	28.4994i		−	1.20864i
$557$		−	26.2705i		−	1.11312i	−0.830809	−	0.556558i	$-0.812122\pi$
$557$		−	26.2705i		−	1.11312i	0.830809	−	0.556558i	$-0.187878\pi$
$558$	−10.2107	−	13.8432i	−0.432253	−	0.586029i
$559$	−9.56155	−	21.8078i	−0.404411	−	0.922370i
$560$		0			0
$561$	24.4755	−	22.0429i	1.03336	−	0.930651i
$562$	−22.2462			−0.938400
$563$	20.4214			0.860658			0.430329	−	0.902672i	$-0.358398\pi$
$563$	20.4214			0.860658			0.430329	+	0.902672i	$0.358398\pi$
$564$		0			0
$565$			53.1771i			2.23718i
$566$	−14.1051			−0.592883
$567$		0			0
$568$			5.79119i			0.242993i
$569$	−14.6875			−0.615733			−0.307867	−	0.951430i	$-0.599615\pi$
$569$	−14.6875			−0.615733			−0.307867	+	0.951430i	$0.599615\pi$
$570$	−29.5660	−	14.9309i	−1.23838	−	0.625385i
$571$		−	21.0822i		−	0.882262i	−0.897443	−	0.441131i	$-0.854577\pi$
$571$		−	21.0822i		−	0.882262i	0.897443	−	0.441131i	$-0.145423\pi$
$572$	−30.6031	+	1.32294i	−1.27958	+	0.0553148i
$573$	4.78078	+	2.41430i	0.199720	+	0.100859i
$574$		0			0
$575$			14.1051i			0.588224i
$576$	−20.8078	−	28.2102i	−0.866990	−	1.17543i
$577$			23.3153i			0.970630i	0.874339	+	0.485315i	$0.161295\pi$
$577$			23.3153i			0.970630i	−0.874339	+	0.485315i	$0.838705\pi$
$578$			33.9095i			1.41045i
$579$	−2.89560	+	5.73384i	−0.120337	+	0.238290i
$580$	45.4164			1.88581
$581$		0			0
$582$	−24.8982	+	49.3033i	−1.03206	+	2.04369i
$583$	−7.41722	+	19.1231i	−0.307190	+	0.791998i
$584$			11.3936i			0.471471i
$585$	−28.9914	−	16.6794i	−1.19865	−	0.689607i
$586$	−72.1080			−2.97875
$587$	−21.2646			−0.877683			−0.438841	−	0.898565i	$-0.644611\pi$
$587$	−21.2646			−0.877683			−0.438841	+	0.898565i	$0.644611\pi$
$588$	14.0000	−	27.7227i	0.577350	−	1.14327i
$589$		−	7.77368i		−	0.320309i
$590$		−	72.7318i		−	2.99432i
$591$	11.9388	+	6.02913i	0.491098	+	0.248005i
$592$			24.4924i			1.00663i
$593$		−	30.4268i		−	1.24948i	−0.780834	−	0.624739i	$-0.785206\pi$
$593$		−	30.4268i		−	1.24948i	0.780834	−	0.624739i	$-0.214794\pi$
$594$	−7.38927	+	36.0580i	−0.303185	+	1.47948i
$595$		0			0
$596$			21.8836i			0.896389i
$597$	7.31534	−	14.4858i	0.299397	−	0.592864i
$598$	21.8078	−	9.56155i	0.891786	−	0.391001i
$599$			27.2352i			1.11280i	0.830915	+	0.556399i	$0.187817\pi$
$599$			27.2352i			1.11280i	−0.830915	+	0.556399i	$0.812183\pi$
$600$	−8.45851	−	4.27156i	−0.345317	−	0.174386i
$601$			14.8344i			0.605109i	0.953132	+	0.302555i	$0.0978395\pi$
$601$			14.8344i			0.605109i	−0.953132	+	0.302555i	$0.902160\pi$
$602$		0			0
$603$	6.48157	−	4.78078i	0.263950	−	0.194688i
$604$	11.5824			0.471280
$605$	−25.1181	−	22.9354i	−1.02119	−	0.932455i
$606$	48.4997	+	24.4924i	1.97017	+	0.994937i
$607$		−	7.87377i		−	0.319587i	−0.987151	−	0.159793i	$-0.948917\pi$
$607$		−	7.87377i		−	0.319587i	0.987151	−	0.159793i	$-0.0510828\pi$
$608$		−	22.7872i		−	0.924144i
$609$		0			0
$610$	19.1231			0.774272
$611$		0			0
$612$	−26.1552	−	35.4601i	−1.05726	−	1.43339i
$613$	−6.60421			−0.266741			−0.133371	−	0.991066i	$-0.542580\pi$
$613$	−6.60421			−0.266741			−0.133371	+	0.991066i	$0.542580\pi$
$614$			40.5790i			1.63763i
$615$	−24.8982	−	12.5736i	−1.00399	−	0.507018i
$616$		0			0
$617$	5.20926			0.209717			0.104858	−	0.994487i	$-0.466561\pi$
$617$	5.20926			0.209717			0.104858	+	0.994487i	$0.466561\pi$
$618$	−10.3128	−	5.20798i	−0.414842	−	0.209496i
$619$			21.8078i			0.876528i	0.898846	+	0.438264i	$0.144407\pi$
$619$			21.8078i			0.876528i	−0.898846	+	0.438264i	$0.855593\pi$
$620$		−	21.2646i		−	0.854006i
$621$	−2.68466	−	15.8415i	−0.107732	−	0.635699i
$622$	50.7511			2.03493
$623$		0			0
$624$	0.870368	−	15.9732i	0.0348426	−	0.639440i
$625$	−27.0000			−1.08000
$626$			56.9925i			2.27788i
$627$	−12.3601	+	11.1317i	−0.493617	+	0.444557i
$628$	19.3693			0.772920
$629$			54.8244i			2.18599i
$630$		0			0
$631$		−	21.8078i		−	0.868153i	−0.900876	−	0.434077i	$-0.857075\pi$
$631$		−	21.8078i		−	0.868153i	0.900876	−	0.434077i	$-0.142925\pi$
$632$	−0.975092			−0.0387871
$633$	−37.6229	−	18.9996i	−1.49538	−	0.755166i
$634$		−	12.3954i		−	0.492284i
$635$			52.3104i			2.07588i
$636$	24.4924	+	12.3687i	0.971188	+	0.490451i
$637$	23.1147	−	10.1346i	0.915838	−	0.401547i
$638$	14.6875	−	37.8674i	0.581485	−	1.49919i
$639$	8.59865	+	11.6577i	0.340157	+	0.461170i
$640$		−	28.4994i		−	1.12654i
$641$			26.8545i			1.06069i	0.847782	+	0.530344i	$0.177937\pi$
$641$			26.8545i			1.06069i	−0.847782	+	0.530344i	$0.822063\pi$
$642$	−67.4334	−	34.0540i	−2.66139	−	1.34400i
$643$			32.5464i			1.28350i	0.766912	+	0.641752i	$0.221792\pi$
$643$			32.5464i			1.28350i	−0.766912	+	0.641752i	$0.778208\pi$
$644$		0			0
$645$	−31.5732	−	15.9445i	−1.24319	−	0.627815i
$646$		−	35.4601i		−	1.39516i
$647$			25.1181i			0.987493i	0.869606	+	0.493747i	$0.164373\pi$
$647$			25.1181i			0.987493i	−0.869606	+	0.493747i	$0.835627\pi$
$648$	10.3128	+	3.18748i	0.405126	+	0.125216i
$649$	−34.0540	−	13.2084i	−1.33674	−	0.518475i
$650$	−14.1051	−	32.1706i	−0.553248	−	1.26184i
$651$		0			0
$652$			31.3693i			1.22852i
$653$			13.7245i			0.537080i	0.963269	+	0.268540i	$0.0865411\pi$
$653$			13.7245i			0.537080i	−0.963269	+	0.268540i	$0.913459\pi$
$654$	−40.9309	−	20.6701i	−1.60052	−	0.808266i
$655$	35.4601			1.38554
$656$		−	13.3405i		−	0.520860i
$657$	16.9170	+	22.9354i	0.659996	+	0.894793i
$658$		0			0
$659$	2.51398			0.0979310			0.0489655	−	0.998800i	$-0.484408\pi$
$659$	2.51398			0.0979310			0.0489655	+	0.998800i	$0.484408\pi$
$660$	−33.8106	+	30.4502i	−1.31608	+	1.18527i
$661$		−	39.4233i		−	1.53339i	−0.642012	−	0.766694i	$-0.721900\pi$
$661$		−	39.4233i		−	1.53339i	0.642012	−	0.766694i	$-0.278100\pi$
$662$	17.2015			0.668556
$663$	1.94825	−	35.7548i	0.0756638	−	1.38860i
$664$	14.8769			0.577335
$665$		0			0
$666$	−36.3659	−	49.3033i	−1.40915	−	1.91046i
$667$			17.7300i			0.686510i
$668$			35.5195i			1.37429i
$669$	−4.15072	−	2.09612i	−0.160476	−	0.0810406i
$670$	17.7300			0.684971
$671$	3.47284	−	8.95369i	0.134068	−	0.345653i
$672$		0			0
$673$			36.7296i			1.41582i	0.706301	+	0.707912i	$0.250363\pi$
$673$			36.7296i			1.41582i	−0.706301	+	0.707912i	$0.749637\pi$
$674$	−9.65719			−0.371981
$675$	−23.3693	+	3.96039i	−0.899485	+	0.152435i
$676$	−22.5616	+	24.4924i	−0.867752	+	0.942016i
$677$	32.5949			1.25272			0.626362	−	0.779532i	$-0.284543\pi$
$677$	32.5949			1.25272			0.626362	+	0.779532i	$0.284543\pi$
$678$	28.6776	−	56.7873i	1.10136	−	2.18090i
$679$		0			0
$680$		−	21.2646i		−	0.815459i
$681$	4.34339	+	2.19342i	0.166439	+	0.0840520i
$682$	−17.7300	−	6.87689i	−0.678918	−	0.263330i
$683$	33.6333			1.28694			0.643471	−	0.765471i	$-0.277494\pi$
$683$	33.6333			1.28694			0.643471	+	0.765471i	$0.277494\pi$
$684$	13.2084	+	17.9074i	0.505036	+	0.684706i
$685$	−9.56155			−0.365328
$686$		0			0
$687$	−14.7830	−	7.46543i	−0.564007	−	0.284824i
$688$		−	16.9170i		−	0.644955i
$689$	8.95369	+	20.4214i	0.341108	+	0.777992i
$690$	15.9445	−	31.5732i	0.606998	−	1.20197i
$691$			32.5464i			1.23812i	0.785342	+	0.619062i	$0.212487\pi$
$691$			32.5464i			1.23812i	−0.785342	+	0.619062i	$0.787513\pi$
$692$	−14.6875			−0.558336
$693$		0			0
$694$		−	43.6155i		−	1.65562i
$695$		−	34.4030i		−	1.30498i
$696$	−10.6323	−	5.36932i	−0.403016	−	0.203523i
$697$		−	29.8617i		−	1.13109i
$698$			29.9467i			1.13350i
$699$	−11.4677	+	22.7082i	−0.433747	+	0.858903i
$700$		0			0
$701$	37.6229			1.42100			0.710498	−	0.703699i	$-0.248470\pi$
$701$	37.6229			1.42100			0.710498	+	0.703699i	$0.248470\pi$
$702$	21.9647	+	33.4464i	0.829002	+	1.26235i
$703$		−	27.6864i		−	1.04421i
$704$	−36.1310	−	14.0140i	−1.36174	−	0.528174i
$705$		0			0
$706$		−	40.4382i		−	1.52191i
$707$		0			0
$708$	−22.0259	+	43.6155i	−0.827784	+	1.63917i
$709$		−	9.56155i		−	0.359092i	−0.983750	−	0.179546i	$-0.942537\pi$
$709$		−	9.56155i		−	0.359092i	0.983750	−	0.179546i	$-0.0574628\pi$
$710$			31.8890i			1.19677i
$711$	−1.96286	+	1.44780i	−0.0736130	+	0.0542967i
$712$			7.87377i			0.295082i
$713$	8.30144			0.310891
$714$		0			0
$715$	−36.9425	+	1.59698i	−1.38157	+	0.0597237i
$716$			0.975092i			0.0364409i
$717$	−33.0210	−	16.6757i	−1.23319	−	0.622764i
$718$	−58.9848			−2.20129
$719$		−	21.6452i		−	0.807231i	−0.914929	−	0.403615i	$-0.867753\pi$
$719$		−	21.6452i		−	0.807231i	0.914929	−	0.403615i	$-0.132247\pi$
$720$	−14.1051	−	19.1231i	−0.525667	−	0.712676i
$721$		0			0
$722$		−	22.6724i		−	0.843780i
$723$	−10.9476	+	21.6784i	−0.407146	+	0.806227i
$724$	14.8769			0.552895
$725$	26.1552			0.971380
$726$	14.4546	+	38.0382i	0.536461	+	1.41173i
$727$	−11.8078			−0.437926			−0.218963	−	0.975733i	$-0.570267\pi$
$727$	−11.8078			−0.437926			−0.218963	+	0.975733i	$0.570267\pi$
$728$		0			0
$729$	25.4924	−	8.89586i	0.944164	−	0.329476i
$730$			62.7386i			2.32206i
$731$		−	37.8674i		−	1.40058i
$732$	−11.4677	−	5.79119i	−0.423857	−	0.214049i
$733$	31.3950			1.15960			0.579800	−	0.814759i	$-0.303131\pi$
$733$	31.3950			1.15960			0.579800	+	0.814759i	$0.303131\pi$
$734$		−	55.6455i		−	2.05391i
$735$	16.9001	−	33.4654i	0.623369	−	1.23439i
$736$	24.3342			0.896972
$737$	3.21985	−	8.30144i	0.118605	−	0.305787i
$738$	19.8078	+	26.8545i	0.729134	+	0.988528i
$739$	7.41722			0.272847			0.136423	−	0.990651i	$-0.456439\pi$
$739$	7.41722			0.272847			0.136423	+	0.990651i	$0.456439\pi$
$740$		−	75.7349i		−	2.78407i
$741$	−0.983869	+	18.0562i	−0.0361433	+	0.663311i
$742$		0			0
$743$			20.9472i			0.768479i	0.923233	+	0.384239i	$0.125536\pi$
$743$			20.9472i			0.768479i	−0.923233	+	0.384239i	$0.874464\pi$
$744$	−2.51398	+	4.97818i	−0.0921672	+	0.182509i
$745$			26.4168i			0.967837i
$746$	−28.2102			−1.03285
$747$	29.9472	−	22.0889i	1.09571	−	0.808192i
$748$	−45.4164	−	17.6155i	−1.66059	−	0.644087i
$749$		0			0
$750$	4.47685	+	2.26081i	0.163471	+	0.0825532i
$751$	32.3002			1.17865			0.589325	−	0.807896i	$-0.299394\pi$
$751$	32.3002			1.17865			0.589325	+	0.807896i	$0.299394\pi$
$752$		0			0
$753$	44.2041	+	22.3231i	1.61089	+	0.813499i
$754$	−17.7300	−	40.4382i	−0.645690	−	1.47267i
$755$	13.9817			0.508845
$756$		0			0
$757$	50.1080			1.82120			0.910602	−	0.413284i	$-0.135618\pi$
$757$	50.1080			1.82120			0.910602	+	0.413284i	$0.135618\pi$
$758$	35.1089			1.27521
$759$	−11.8874	−	13.1993i	−0.431486	−	0.479103i
$760$			10.7386i			0.389531i
$761$			36.4559i			1.32153i	0.750595	+	0.660763i	$0.229767\pi$
$761$			36.4559i			1.32153i	−0.750595	+	0.660763i	$0.770233\pi$
$762$	28.2102	−	55.8617i	1.02195	−	2.02366i
$763$		0			0
$764$		−	7.92077i		−	0.286563i
$765$	−31.5732	−	42.8056i	−1.14153	−	1.54764i
$766$		−	57.3553i		−	2.07233i
$767$	−36.3659	+	15.9445i	−1.31310	+	0.575723i
$768$	2.87689	−	5.69681i	0.103811	−	0.205566i
$769$	−41.7078			−1.50402			−0.752011	−	0.659150i	$-0.770916\pi$
$769$	−41.7078			−1.50402			−0.752011	+	0.659150i	$0.770916\pi$
$770$		0			0
$771$	−23.3153	−	11.7743i	−0.839682	−	0.424040i
$772$	9.49980			0.341905
$773$	33.4195			1.20202			0.601008	−	0.799243i	$-0.294766\pi$
$773$	33.4195			1.20202			0.601008	+	0.799243i	$0.294766\pi$
$774$	25.1181	+	34.0540i	0.902850	+	1.22404i
$775$		−	12.2462i		−	0.439897i
$776$	17.9074			0.642838
$777$		0			0
$778$	−2.89560			−0.103812
$779$			15.0802i			0.540305i
$780$	−2.69133	+	49.3919i	−0.0963651	+	1.76852i
$781$	14.9309	+	5.79119i	0.534269	+	0.207225i
$782$	37.8674			1.35414
$783$	−29.3751	+	4.97818i	−1.04978	+	0.177905i
$784$	17.9309			0.640388
$785$	23.3817			0.834527
$786$	−37.8674	−	19.1231i	−1.35069	−	0.682099i
$787$	−42.8773			−1.52841			−0.764205	−	0.644973i	$-0.776869\pi$
$787$	−42.8773			−1.52841			−0.764205	+	0.644973i	$0.776869\pi$
$788$		−	19.7802i		−	0.704642i
$789$	−17.9074	+	35.4601i	−0.637520	+	1.26241i
$790$	−5.36932			−0.191032
$791$		0			0
$792$	11.5152	−	3.13137i	0.409176	−	0.111268i
$793$	−4.19224	−	9.56155i	−0.148871	−	0.339541i
$794$	−52.3104			−1.85643
$795$	29.5660	+	14.9309i	1.04860	+	0.529543i
$796$	−24.0000			−0.850657
$797$		−	45.4075i		−	1.60842i	−0.594347	−	0.804209i	$-0.702589\pi$
$797$		−	45.4075i		−	1.60842i	0.594347	−	0.804209i	$-0.297411\pi$
$798$		0			0
$799$		0			0
$800$		−	35.8977i		−	1.26917i
$801$	11.6908	+	15.8499i	0.413075	+	0.560029i
$802$			37.5427i			1.32568i
$803$	29.3751	+	11.3936i	1.03662	+	0.402072i
$804$	−10.6323	−	5.36932i	−0.374972	−	0.189361i
$805$		0			0
$806$	−18.9337	+	8.30144i	−0.666912	+	0.292406i
$807$	39.4233	+	19.9088i	1.38777	+	0.700823i
$808$		−	17.6155i		−	0.619712i
$809$	3.21985			0.113204			0.0566020	−	0.998397i	$-0.481973\pi$
$809$	3.21985			0.113204			0.0566020	+	0.998397i	$0.481973\pi$
$810$	56.7873	+	17.5518i	1.99530	+	0.616708i
$811$	−35.1036			−1.23265			−0.616327	−	0.787490i	$-0.711380\pi$
$811$	−35.1036			−1.23265			−0.616327	+	0.787490i	$0.711380\pi$
$812$		0			0
$813$	4.52162	−	8.95369i	0.158580	−	0.314020i
$814$	−63.1465	−	24.4924i	−2.21328	−	0.858459i
$815$			37.8674i			1.32644i
$816$	11.4677	−	22.7082i	0.401449	−	0.794946i
$817$			19.1231i			0.669033i
$818$			23.7623i			0.830830i
$819$		0			0
$820$			41.2513i			1.44056i
$821$			11.6477i			0.406507i	0.979126	+	0.203254i	$0.0651516\pi$
$821$			11.6477i			0.406507i	−0.979126	+	0.203254i	$0.934848\pi$
$822$	10.2107	+	5.15641i	0.356138	+	0.179850i
$823$	13.9460			0.486128			0.243064	−	0.970010i	$-0.421848\pi$
$823$	13.9460			0.486128			0.243064	+	0.970010i	$0.421848\pi$
$824$			3.74571i			0.130488i
$825$	−19.4715	+	17.5362i	−0.677909	+	0.610532i
$826$		0			0
$827$		−	45.5249i		−	1.58305i	−0.611134	−	0.791527i	$-0.709286\pi$
$827$		−	45.5249i		−	1.58305i	0.611134	−	0.791527i	$-0.290714\pi$
$828$	−19.1231	+	14.1051i	−0.664574	+	0.490187i
$829$	3.94602			0.137051			0.0685256	−	0.997649i	$-0.478171\pi$
$829$	3.94602			0.137051			0.0685256	+	0.997649i	$0.478171\pi$
$830$	81.9192			2.84346
$831$	20.4214	+	10.3128i	0.708409	+	0.357748i
$832$	−38.5839	+	16.9170i	−1.33766	+	0.586492i
$833$	40.1369			1.39066
$834$	−18.5531	+	36.7386i	−0.642440	+	1.27215i
$835$			42.8773i			1.48383i
$836$	22.9354	+	8.89586i	0.793236	+	0.307670i
$837$	2.33085	+	13.7538i	0.0805659	+	0.475400i
$838$	69.7507			2.40950
$839$	−33.8002			−1.16691			−0.583456	−	0.812145i	$-0.698300\pi$
$839$	−33.8002			−1.16691			−0.583456	+	0.812145i	$0.698300\pi$
$840$		0			0
$841$	3.87689			0.133686
$842$	−11.4677			−0.395202
$843$	16.1040	+	8.13254i	0.554651	+	0.280100i
$844$			62.3334i			2.14561i
$845$	−27.2352	+	29.5660i	−0.936918	+	1.01710i
$846$		0			0
$847$		0			0
$848$			15.8415i			0.544001i
$849$	10.2107	+	5.15641i	0.350430	+	0.176967i
$850$		−	55.8617i		−	1.91604i
$851$	29.5660			1.01351
$852$	9.65719	−	19.1231i	0.330850	−	0.655147i
$853$	12.7519			0.436615			0.218308	−	0.975880i	$-0.429946\pi$
$853$	12.7519			0.436615			0.218308	+	0.975880i	$0.429946\pi$
$854$		0			0
$855$	15.9445	+	21.6169i	0.545291	+	0.739282i
$856$			24.4924i			0.837134i
$857$	−32.5949			−1.11342			−0.556710	−	0.830707i	$-0.687937\pi$
$857$	−32.5949			−1.11342			−0.556710	+	0.830707i	$0.687937\pi$
$858$	40.3118	+	18.2172i	1.37622	+	0.621924i
$859$	14.4384			0.492633			0.246317	−	0.969189i	$-0.420780\pi$
$859$	14.4384			0.492633			0.246317	+	0.969189i	$0.420780\pi$
$860$			52.3104i			1.78377i
$861$		0			0
$862$	42.4924			1.44730
$863$	19.3144			0.657469			0.328735	−	0.944422i	$-0.393378\pi$
$863$	19.3144			0.657469			0.328735	+	0.944422i	$0.393378\pi$
$864$	6.83248	+	40.3169i	0.232446	+	1.37161i
$865$	−17.7300			−0.602839
$866$		−	38.0335i		−	1.29243i
$867$	12.3963	−	24.5471i	0.421001	−	0.833662i
$868$		0			0
$869$	−0.975092	+	2.51398i	−0.0330777	+	0.0852811i
$870$	−58.5464	−	29.5660i	−1.98491	−	1.00238i
$871$	−3.88684	−	8.86502i	−0.131701	−	0.300380i
$872$			14.8665i			0.503442i
$873$	36.0476	−	26.5885i	1.22003	−	0.899886i
$874$	−19.1231			−0.646849
$875$		0			0
$876$	18.9996	−	37.6229i	0.641937	−	1.27116i
$877$	25.6038			0.864579			0.432290	−	0.901735i	$-0.357706\pi$
$877$	25.6038			0.864579			0.432290	+	0.901735i	$0.357706\pi$
$878$	82.8943			2.79755
$879$	52.1989	+	26.3605i	1.76062	+	0.889117i
$880$	−24.4924	−	9.49980i	−0.825639	−	0.320238i
$881$		−	22.6203i		−	0.762098i	−0.924555	−	0.381049i	$-0.875563\pi$
$881$		−	22.6203i		−	0.762098i	0.924555	−	0.381049i	$-0.124437\pi$
$882$	−36.0949	+	26.6234i	−1.21538	+	0.896457i
$883$	21.3693			0.719135			0.359567	−	0.933119i	$-0.382924\pi$
$883$	21.3693			0.719135			0.359567	+	0.933119i	$0.382924\pi$
$884$	−48.4997	+	21.2646i	−1.63122	+	0.715205i
$885$	−26.5885	+	52.6504i	−0.893764	+	1.76983i
$886$	12.3954			0.416431
$887$	−8.95369			−0.300635			−0.150318	−	0.988638i	$-0.548030\pi$
$887$	−8.95369			−0.300635			−0.150318	+	0.988638i	$0.548030\pi$
$888$	−8.95369	+	17.7300i	−0.300466	+	0.594981i
$889$		0			0
$890$			43.3567i			1.45332i
$891$	18.5308	−	23.4011i	0.620805	−	0.783965i
$892$			6.87689i			0.230255i
$893$		0			0
$894$	14.2462	−	28.2102i	0.476465	−	0.943492i
$895$			1.17708i			0.0393455i
$896$		0			0
$897$	−19.2820	−	1.05066i	−0.643808	−	0.0350806i
$898$		−	8.23023i		−	0.274646i
$899$		−	15.3934i		−	0.513398i
$900$	20.8078	+	28.2102i	0.693592	+	0.940342i
$901$			35.4601i			1.18135i
$902$	34.3946	+	13.3405i	1.14521	+	0.444191i
$903$		0			0
$904$	−20.6256			−0.685998
$905$	17.9586			0.596965
$906$	−14.9309	−	7.54011i	−0.496045	−	0.250503i
$907$	−26.2462			−0.871491			−0.435746	−	0.900070i	$-0.643515\pi$
$907$	−26.2462			−0.871491			−0.435746	+	0.900070i	$0.643515\pi$
$908$		−	7.19612i		−	0.238812i
$909$	−26.1552	−	35.4601i	−0.867513	−	1.17614i
$910$		0			0
$911$			0.975092i			0.0323062i	0.999870	+	0.0161531i	$0.00514192\pi$
$911$			0.975092i			0.0323062i	−0.999870	+	0.0161531i	$0.994858\pi$
$912$	−5.79119	+	11.4677i	−0.191765	+	0.379733i
$913$	14.8769	−	38.3557i	0.492353	−	1.26939i
$914$			16.8166i			0.556245i
$915$	−13.8432	−	6.99083i	−0.457642	−	0.231110i
$916$			24.4924i			0.809252i
$917$		0			0
$918$	10.6323	+	62.7386i	0.350918	+	2.07068i
$919$			46.2294i			1.52497i	0.647007	+	0.762484i	$0.276021\pi$
$919$			46.2294i			1.52497i	−0.647007	+	0.762484i	$0.723979\pi$
$920$	−11.4677			−0.378078
$921$	14.8344	−	29.3751i	0.488811	−	0.967941i
$922$	−0.876894			−0.0288790
$923$	15.9445	−	6.99083i	0.524820	−	0.230106i
$924$		0			0
$925$		−	43.6155i		−	1.43407i
$926$	−58.0442			−1.90745
$927$	5.56155	+	7.54011i	0.182665	+	0.247650i
$928$		−	45.1231i		−	1.48124i
$929$	13.3438			0.437796			0.218898	−	0.975748i	$-0.429754\pi$
$929$	13.3438			0.437796			0.218898	+	0.975748i	$0.429754\pi$
$930$	−13.8432	+	27.4122i	−0.453936	+	0.898881i
$931$	−20.2692			−0.664295
$932$	37.6229			1.23238
$933$	−36.7386	−	18.5531i	−1.20277	−	0.607400i
$934$	0.813015			0.0266027
$935$	−54.8244	−	21.2646i	−1.79295	−	0.695426i
$936$	6.46938	−	11.2448i	0.211458	−	0.367548i
$937$		−	17.3736i		−	0.567570i	−0.958888	−	0.283785i	$-0.908410\pi$
$937$		−	17.3736i		−	0.567570i	0.958888	−	0.283785i	$-0.0915902\pi$
$938$		0			0
$939$	20.8348	−	41.2568i	0.679916	−	1.34637i
$940$		0			0
$941$		−	36.6865i		−	1.19594i	−0.801517	−	0.597972i	$-0.795973\pi$
$941$		−	36.6865i		−	1.19594i	0.801517	−	0.597972i	$-0.204027\pi$
$942$	−24.9690	−	12.6094i	−0.813535	−	0.410836i
$943$	−16.1040			−0.524419
$944$	−28.2102			−0.918165
$945$		0			0
$946$	43.6155	+	16.9170i	1.41806	+	0.550020i
$947$	4.06727			0.132168			0.0660842	−	0.997814i	$-0.478949\pi$
$947$	4.06727			0.132168			0.0660842	+	0.997814i	$0.478949\pi$
$948$	3.21985	+	1.62603i	0.104576	+	0.0528110i
$949$	31.3693	−	13.7538i	1.01829	−	0.446467i
$950$			28.2102i			0.915261i
$951$	−4.53138	+	8.97301i	−0.146940	+	0.290970i
$952$		0			0
$953$	3.21985			0.104301			0.0521506	−	0.998639i	$-0.483392\pi$
$953$	3.21985			0.104301			0.0521506	+	0.998639i	$0.483392\pi$
$954$	−23.5212	−	31.8890i	−0.761528	−	1.03245i
$955$		−	9.56155i		−	0.309405i
$956$			54.7091i			1.76942i
$957$	−24.4755	+	22.0429i	−0.791180	+	0.712545i
$958$	29.6155			0.956834
$959$		0			0
$960$	−28.2102	+	55.8617i	−0.910482	+	1.80293i
$961$	23.7926			0.767504
$962$	−67.4334	+	29.5660i	−2.17414	+	0.953246i
$963$	36.3659	+	49.3033i	1.17187	+	1.58878i
$964$	35.9166			1.15680
$965$	11.4677			0.369158
$966$		0			0
$967$	−32.2080			−1.03574			−0.517870	−	0.855459i	$-0.673275\pi$
$967$	−32.2080			−1.03574			−0.517870	+	0.855459i	$0.673275\pi$
$968$	8.89586	−	9.74247i	0.285924	−	0.313135i
$969$	−12.9631	+	25.6695i	−0.416436	+	0.824623i
$970$	98.6065			3.16606
$971$			46.3826i			1.48849i	0.667907	+	0.744245i	$0.267190\pi$
$971$			46.3826i			1.48849i	−0.667907	+	0.744245i	$0.732810\pi$
$972$	−28.7386	−	27.7227i	−0.921792	−	0.889206i
$973$		0			0
$974$	−35.1089			−1.12496
$975$	−1.54993	+	28.4447i	−0.0496375	+	0.910959i
$976$		−	7.41722i		−	0.237419i
$977$	−53.3283			−1.70612			−0.853062	−	0.521809i	$-0.825257\pi$
$977$	−53.3283			−1.70612			−0.853062	+	0.521809i	$0.825257\pi$
$978$	20.4214	−	40.4382i	0.653003	−	1.29307i
$979$	20.3002	+	7.87377i	0.648797	+	0.251647i
$980$	−55.4454			−1.77114
$981$	22.0734	+	29.9262i	0.704750	+	0.955469i
$982$			24.4924i			0.781585i
$983$	14.4858			0.462025			0.231012	−	0.972951i	$-0.425796\pi$
$983$	14.4858			0.462025			0.231012	+	0.972951i	$0.425796\pi$
$984$	4.87689	−	9.65719i	0.155470	−	0.307860i
$985$		−	23.8777i		−	0.760806i
$986$		−	70.2178i		−	2.23619i
$987$		0			0
$988$	24.4924	−	10.7386i	0.779208	−	0.341641i
$989$	−20.4214			−0.649362
$990$	63.4084	−	17.2428i	2.01525	−	0.548012i
$991$	−18.7386			−0.595252			−0.297626	−	0.954682i	$-0.596195\pi$
$991$	−18.7386			−0.595252			−0.297626	+	0.954682i	$0.596195\pi$
$992$	−21.1272			−0.670790
$993$	−12.4522	−	6.28835i	−0.395157	−	0.199555i
$994$		0			0
$995$	−28.9716			−0.918461
$996$	−49.1250	−	24.8082i	−1.55659	−	0.786078i
$997$		−	48.6685i		−	1.54135i	−0.637231	−	0.770673i	$-0.719920\pi$
$997$		−	48.6685i		−	1.54135i	0.637231	−	0.770673i	$-0.280080\pi$
$998$	26.1552			0.827928
$999$	8.30144	+	48.9848i	0.262646	+	1.54981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.e.c.428.13	yes	16
3.2	odd	2	inner	429.2.e.c.428.4	yes	16
11.10	odd	2	inner	429.2.e.c.428.1	✓	16
13.12	even	2	inner	429.2.e.c.428.2	yes	16
33.32	even	2	inner	429.2.e.c.428.16	yes	16
39.38	odd	2	inner	429.2.e.c.428.15	yes	16
143.142	odd	2	inner	429.2.e.c.428.14	yes	16
429.428	even	2	inner	429.2.e.c.428.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.e.c.428.1	✓	16	11.10	odd	2	inner
429.2.e.c.428.2	yes	16	13.12	even	2	inner
429.2.e.c.428.3	yes	16	429.428	even	2	inner
429.2.e.c.428.4	yes	16	3.2	odd	2	inner
429.2.e.c.428.13	yes	16	1.1	even	1	trivial
429.2.e.c.428.14	yes	16	143.142	odd	2	inner
429.2.e.c.428.15	yes	16	39.38	odd	2	inner
429.2.e.c.428.16	yes	16	33.32	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.13578i q^{2} +(0.780776 - 1.54609i) q^{3} -2.56155 q^{4} -3.09218 q^{5} +(3.30210 + 1.66757i) q^{6} -1.19935i q^{8} +(-1.78078 - 2.41430i) q^{9} +O(q^{10})\)	\(q+2.13578i q^{2} +(0.780776 - 1.54609i) q^{3} -2.56155 q^{4} -3.09218 q^{5} +(3.30210 + 1.66757i) q^{6} -1.19935i q^{8} +(-1.78078 - 2.41430i) q^{9} -6.60421i q^{10} +(-3.09218 - 1.19935i) q^{11} +(-2.00000 + 3.96039i) q^{12} +(-3.30210 + 1.44780i) q^{13} +(-2.41430 + 4.78078i) q^{15} -2.56155 q^{16} -5.73384 q^{17} +(5.15641 - 3.80335i) q^{18} +2.89560 q^{19} +7.92077 q^{20} +(2.56155 - 6.60421i) q^{22} +3.09218i q^{23} +(-1.85431 - 0.936426i) q^{24} +4.56155 q^{25} +(-3.09218 - 7.05256i) q^{26} +(-5.12311 + 0.868210i) q^{27} +5.73384 q^{29} +(-10.2107 - 5.15641i) q^{30} -2.68466i q^{31} -7.86962i q^{32} +(-4.26860 + 3.84435i) q^{33} -12.2462i q^{34} +(4.56155 + 6.18435i) q^{36} -9.56155i q^{37} +6.18435i q^{38} +(-0.339781 + 6.23575i) q^{39} +3.70861i q^{40} +5.20798i q^{41} +6.60421i q^{43} +(7.92077 + 3.07221i) q^{44} +(5.50647 + 7.46543i) q^{45} -6.60421 q^{46} +(-2.00000 + 3.96039i) q^{48} -7.00000 q^{49} +9.74247i q^{50} +(-4.47685 + 8.86502i) q^{51} +(8.45851 - 3.70861i) q^{52} -6.18435i q^{53} +(-1.85431 - 10.9418i) q^{54} +(9.56155 + 3.70861i) q^{55} +(2.26081 - 4.47685i) q^{57} +12.2462i q^{58} +11.0129 q^{59} +(6.18435 - 12.2462i) q^{60} +2.89560i q^{61} +5.73384 q^{62} +11.6847 q^{64} +(10.2107 - 4.47685i) q^{65} +(-8.21068 - 9.11679i) q^{66} +2.68466i q^{67} +14.6875 q^{68} +(4.78078 + 2.41430i) q^{69} -4.82860 q^{71} +(-2.89560 + 2.13578i) q^{72} -9.49980 q^{73} +20.4214 q^{74} +(3.56155 - 7.05256i) q^{75} -7.41722 q^{76} +(-13.3182 - 0.725698i) q^{78} -0.813015i q^{79} +7.92077 q^{80} +(-2.65767 + 8.59865i) q^{81} -11.1231 q^{82} +12.4041i q^{83} +17.7300 q^{85} -14.1051 q^{86} +(4.47685 - 8.86502i) q^{87} +(-1.43845 + 3.70861i) q^{88} -6.56502 q^{89} +(-15.9445 + 11.7606i) q^{90} -7.92077i q^{92} +(-4.15072 - 2.09612i) q^{93} -8.95369 q^{95} +(-12.1671 - 6.14441i) q^{96} +14.9309i q^{97} -14.9505i q^{98} +(2.61088 + 9.60121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} - 8 q^{4} - 12 q^{9}+O(q^{10}) \) 16 * q - 4 * q^3 - 8 * q^4 - 12 * q^9	\( 16 q - 4 q^{3} - 8 q^{4} - 12 q^{9} - 32 q^{12} - 8 q^{16} + 8 q^{22} + 40 q^{25} - 16 q^{27} + 40 q^{36} - 32 q^{48} - 112 q^{49} + 120 q^{55} + 88 q^{64} + 32 q^{66} + 60 q^{69} + 24 q^{75} - 92 q^{78} - 92 q^{81} - 112 q^{82} - 56 q^{88}+O(q^{100}) \) 16 * q - 4 * q^3 - 8 * q^4 - 12 * q^9 - 32 * q^12 - 8 * q^16 + 8 * q^22 + 40 * q^25 - 16 * q^27 + 40 * q^36 - 32 * q^48 - 112 * q^49 + 120 * q^55 + 88 * q^64 + 32 * q^66 + 60 * q^69 + 24 * q^75 - 92 * q^78 - 92 * q^81 - 112 * q^82 - 56 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more