LMFDB - Embedded newform 440.2.y.c.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [440,2,Mod(81,440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(440, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("440.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, 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:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 5 x^{10} + 4 x^{9} + 28 x^{8} - 81 x^{7} + 335 x^{6} - 235 x^{5} + 782 x^{4} + \cdots + 1 $ x^12 - x^11 + 5x^10 + 4x^9 + 28x^8 - 81x^7 + 335x^6 - 235x^5 + 782x^4 - 302x^3 + 711x^2 - 43x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$1.85498 - 1.34772i$ of defining polynomial
Character	$\chi$	$=$	440.81
Dual form			440.2.y.c.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01756 + 3.13172i) q^{3} +(0.809017 - 0.587785i) q^{5} +(1.08622 + 3.34304i) q^{7} +(-6.34518 - 4.61004i) q^{9} +O(q^{10})$	\(q+(-1.01756 + 3.13172i) q^{3} +(0.809017 - 0.587785i) q^{5} +(1.08622 + 3.34304i) q^{7} +(-6.34518 - 4.61004i) q^{9} +(-1.91497 + 2.70793i) q^{11} +(3.45546 + 2.51054i) q^{13} +(1.01756 + 3.13172i) q^{15} +(-1.28632 + 0.934565i) q^{17} +(1.71533 - 5.27925i) q^{19} -11.5747 q^{21} -6.39042 q^{23} +(0.309017 - 0.951057i) q^{25} +(12.9019 - 9.37380i) q^{27} +(-0.117804 - 0.362562i) q^{29} +(0.615229 + 0.446990i) q^{31} +(-6.53187 - 8.75262i) q^{33} +(2.84376 + 2.06611i) q^{35} +(-0.448664 - 1.38085i) q^{37} +(-11.3784 + 8.26690i) q^{39} +(-1.89183 + 5.82245i) q^{41} -7.19067 q^{43} -7.84307 q^{45} +(1.33546 - 4.11012i) q^{47} +(-4.33291 + 3.14804i) q^{49} +(-1.61789 - 4.97936i) q^{51} +(5.62189 + 4.08454i) q^{53} +(0.0424355 + 3.31635i) q^{55} +(14.7877 + 10.7439i) q^{57} +(3.92793 + 12.0889i) q^{59} +(7.19700 - 5.22893i) q^{61} +(8.51929 - 26.2197i) q^{63} +4.27118 q^{65} +12.5135 q^{67} +(6.50261 - 20.0130i) q^{69} +(-5.95347 + 4.32545i) q^{71} +(2.17304 + 6.68793i) q^{73} +(2.66400 + 1.93551i) q^{75} +(-11.1328 - 3.46042i) q^{77} +(5.65811 + 4.11086i) q^{79} +(8.95672 + 27.5660i) q^{81} +(8.69768 - 6.31923i) q^{83} +(-0.491330 + 1.51216i) q^{85} +1.25531 q^{87} +0.451594 q^{89} +(-4.63944 + 14.2787i) q^{91} +(-2.02588 + 1.47189i) q^{93} +(-1.71533 - 5.27925i) q^{95} +(2.24871 + 1.63379i) q^{97} +(24.6345 - 8.35419i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} + 3 q^{5} - q^{7} - 10 q^{9}+O(q^{10}) $ 12 * q - q^3 + 3 * q^5 - q^7 - 10 * q^9	$ 12 q - q^{3} + 3 q^{5} - q^{7} - 10 q^{9} + 4 q^{11} + 18 q^{13} + q^{15} + 3 q^{17} + 4 q^{19} - 28 q^{21} - 18 q^{23} - 3 q^{25} + 23 q^{27} + 15 q^{29} - 8 q^{31} + 4 q^{33} + 6 q^{35} + 6 q^{37} - 33 q^{39} + 2 q^{41} - 36 q^{43} - 10 q^{45} - 16 q^{47} - 16 q^{49} - 10 q^{51} + 19 q^{53} + 6 q^{55} + 62 q^{57} + 46 q^{59} + 18 q^{61} - 7 q^{63} + 2 q^{65} - 44 q^{67} - q^{69} - 6 q^{71} + 25 q^{73} + 4 q^{75} + 10 q^{77} + 19 q^{79} + 30 q^{81} - 3 q^{85} + 6 q^{87} - 50 q^{89} - 46 q^{91} - 37 q^{93} - 4 q^{95} - 31 q^{97} + 79 q^{99}+O(q^{100}) $ 12 * q - q^3 + 3 * q^5 - q^7 - 10 * q^9 + 4 * q^11 + 18 * q^13 + q^15 + 3 * q^17 + 4 * q^19 - 28 * q^21 - 18 * q^23 - 3 * q^25 + 23 * q^27 + 15 * q^29 - 8 * q^31 + 4 * q^33 + 6 * q^35 + 6 * q^37 - 33 * q^39 + 2 * q^41 - 36 * q^43 - 10 * q^45 - 16 * q^47 - 16 * q^49 - 10 * q^51 + 19 * q^53 + 6 * q^55 + 62 * q^57 + 46 * q^59 + 18 * q^61 - 7 * q^63 + 2 * q^65 - 44 * q^67 - q^69 - 6 * q^71 + 25 * q^73 + 4 * q^75 + 10 * q^77 + 19 * q^79 + 30 * q^81 - 3 * q^85 + 6 * q^87 - 50 * q^89 - 46 * q^91 - 37 * q^93 - 4 * q^95 - 31 * q^97 + 79 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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
$3$	−1.01756	+	3.13172i	−0.587487	+	1.80810i	0.00156040	+	0.999999i	$0.499503\pi$
$3$	−1.01756	+	3.13172i	−0.587487	+	1.80810i	−0.589047	+	0.808099i	$0.700497\pi$
$4$		0			0
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$		0			0
$7$	1.08622	+	3.34304i	0.410552	+	1.26355i	0.916169	+	0.400791i	$0.131265\pi$
$7$	1.08622	+	3.34304i	0.410552	+	1.26355i	−0.505617	+	0.862758i	$0.668735\pi$
$8$		0			0
$9$	−6.34518	−	4.61004i	−2.11506	−	1.53668i
$10$		0			0
$11$	−1.91497	+	2.70793i	−0.577386	+	0.816471i
$11$	−1.91497	+	2.70793i	−0.577386	+	0.816471i
$12$		0			0
$13$	3.45546	+	2.51054i	0.958372	+	0.696298i	0.952772	−	0.303687i	$-0.0982176\pi$
$13$	3.45546	+	2.51054i	0.958372	+	0.696298i	0.00559963	+	0.999984i	$0.498218\pi$
$14$		0			0
$15$	1.01756	+	3.13172i	0.262732	+	0.808606i
$16$		0			0
$17$	−1.28632	+	0.934565i	−0.311978	+	0.226665i	−0.732745	−	0.680504i	$-0.761761\pi$
$17$	−1.28632	+	0.934565i	−0.311978	+	0.226665i	0.420767	+	0.907169i	$0.361761\pi$
$18$		0			0
$19$	1.71533	−	5.27925i	0.393525	−	1.21114i	−0.536580	−	0.843849i	$-0.680284\pi$
$19$	1.71533	−	5.27925i	0.393525	−	1.21114i	0.930105	−	0.367295i	$-0.119716\pi$
$20$		0			0
$21$	−11.5747			−2.52581
$22$		0			0
$23$	−6.39042			−1.33249			−0.666247	−	0.745731i	$-0.732100\pi$
$23$	−6.39042			−1.33249			−0.666247	+	0.745731i	$0.732100\pi$
$24$		0			0
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$		0			0
$27$	12.9019	−	9.37380i	2.48298	−	1.80399i
$28$		0			0
$29$	−0.117804	−	0.362562i	−0.0218756	−	0.0673261i	0.939523	−	0.342486i	$-0.111269\pi$
$29$	−0.117804	−	0.362562i	−0.0218756	−	0.0673261i	−0.961398	+	0.275160i	$0.911269\pi$
$30$		0			0
$31$	0.615229	+	0.446990i	0.110498	+	0.0802818i	0.641662	−	0.766987i	$-0.278245\pi$
$31$	0.615229	+	0.446990i	0.110498	+	0.0802818i	−0.531164	+	0.847269i	$0.678245\pi$
$32$		0			0
$33$	−6.53187	−	8.75262i	−1.13705	−	1.52364i
$34$		0			0
$35$	2.84376	+	2.06611i	0.480683	+	0.349236i
$36$		0			0
$37$	−0.448664	−	1.38085i	−0.0737599	−	0.227010i	0.907379	−	0.420313i	$-0.138080\pi$
$37$	−0.448664	−	1.38085i	−0.0737599	−	0.227010i	−0.981139	+	0.193304i	$0.938080\pi$
$38$		0			0
$39$	−11.3784	+	8.26690i	−1.82200	+	1.32376i
$40$		0			0
$41$	−1.89183	+	5.82245i	−0.295454	+	0.909313i	0.687615	+	0.726076i	$0.258658\pi$
$41$	−1.89183	+	5.82245i	−0.295454	+	0.909313i	−0.983069	+	0.183238i	$0.941342\pi$
$42$		0			0
$43$	−7.19067			−1.09657			−0.548284	−	0.836293i	$-0.684719\pi$
$43$	−7.19067			−1.09657			−0.548284	+	0.836293i	$0.684719\pi$
$44$		0			0
$45$	−7.84307			−1.16918
$46$		0			0
$47$	1.33546	−	4.11012i	0.194797	−	0.599523i	−0.805182	−	0.593028i	$-0.797932\pi$
$47$	1.33546	−	4.11012i	0.194797	−	0.599523i	0.999979	−	0.00649536i	$-0.00206755\pi$
$48$		0			0
$49$	−4.33291	+	3.14804i	−0.618987	+	0.449720i
$50$		0			0
$51$	−1.61789	−	4.97936i	−0.226550	−	0.697250i
$52$		0			0
$53$	5.62189	+	4.08454i	0.772226	+	0.561055i	0.902636	−	0.430405i	$-0.141629\pi$
$53$	5.62189	+	4.08454i	0.772226	+	0.561055i	−0.130410	+	0.991460i	$0.541629\pi$
$54$		0			0
$55$	0.0424355	+	3.31635i	0.00572200	+	0.447177i
$56$		0			0
$57$	14.7877	+	10.7439i	1.95868	+	1.42306i
$58$		0			0
$59$	3.92793	+	12.0889i	0.511373	+	1.57384i	0.789786	+	0.613382i	$0.210192\pi$
$59$	3.92793	+	12.0889i	0.511373	+	1.57384i	−0.278413	+	0.960461i	$0.589808\pi$
$60$		0			0
$61$	7.19700	−	5.22893i	0.921482	−	0.669496i	−0.0224105	−	0.999749i	$-0.507134\pi$
$61$	7.19700	−	5.22893i	0.921482	−	0.669496i	0.943892	+	0.330253i	$0.107134\pi$
$62$		0			0
$63$	8.51929	−	26.2197i	1.07333	−	3.30337i
$64$		0			0
$65$	4.27118			0.529775
$66$		0			0
$67$	12.5135			1.52877			0.764383	−	0.644763i	$-0.223044\pi$
$67$	12.5135			1.52877			0.764383	+	0.644763i	$0.223044\pi$
$68$		0			0
$69$	6.50261	−	20.0130i	0.782823	−	2.40928i
$70$		0			0
$71$	−5.95347	+	4.32545i	−0.706547	+	0.513336i	−0.882058	−	0.471141i	$-0.843842\pi$
$71$	−5.95347	+	4.32545i	−0.706547	+	0.513336i	0.175511	+	0.984477i	$0.443842\pi$
$72$		0			0
$73$	2.17304	+	6.68793i	0.254335	+	0.782763i	0.993960	+	0.109743i	$0.0350029\pi$
$73$	2.17304	+	6.68793i	0.254335	+	0.782763i	−0.739625	+	0.673019i	$0.764997\pi$
$74$		0			0
$75$	2.66400	+	1.93551i	0.307612	+	0.223493i
$76$		0			0
$77$	−11.1328	−	3.46042i	−1.26870	−	0.394352i
$78$		0			0
$79$	5.65811	+	4.11086i	0.636587	+	0.462508i	0.858676	−	0.512519i	$-0.171288\pi$
$79$	5.65811	+	4.11086i	0.636587	+	0.462508i	−0.222089	+	0.975026i	$0.571288\pi$
$80$		0			0
$81$	8.95672	+	27.5660i	0.995191	+	3.06288i
$82$		0			0
$83$	8.69768	−	6.31923i	0.954694	−	0.693626i	0.00278190	−	0.999996i	$-0.499114\pi$
$83$	8.69768	−	6.31923i	0.954694	−	0.693626i	0.951912	+	0.306370i	$0.0991145\pi$
$84$		0			0
$85$	−0.491330	+	1.51216i	−0.0532922	+	0.164017i
$86$		0			0
$87$	1.25531			0.134584
$88$		0			0
$89$	0.451594			0.0478689			0.0239344	−	0.999714i	$-0.492381\pi$
$89$	0.451594			0.0478689			0.0239344	+	0.999714i	$0.492381\pi$
$90$		0			0
$91$	−4.63944	+	14.2787i	−0.486345	+	1.49682i
$92$		0			0
$93$	−2.02588	+	1.47189i	−0.210074	+	0.152627i
$94$		0			0
$95$	−1.71533	−	5.27925i	−0.175990	−	0.541640i
$96$		0			0
$97$	2.24871	+	1.63379i	0.228322	+	0.165886i	0.696065	−	0.717979i	$-0.254933\pi$
$97$	2.24871	+	1.63379i	0.228322	+	0.165886i	−0.467743	+	0.883865i	$0.654933\pi$
$98$		0			0
$99$	24.6345	−	8.35419i	2.47586	−	0.839628i
$100$		0			0
$101$	−4.31798	−	3.13719i	−0.429655	−	0.312162i	0.351856	−	0.936054i	$-0.385551\pi$
$101$	−4.31798	−	3.13719i	−0.429655	−	0.312162i	−0.781511	+	0.623892i	$0.785551\pi$
$102$		0			0
$103$	5.37124	+	16.5310i	0.529244	+	1.62884i	0.755769	+	0.654839i	$0.227263\pi$
$103$	5.37124	+	16.5310i	0.529244	+	1.62884i	−0.226525	+	0.974005i	$0.572737\pi$
$104$		0			0
$105$	−9.36416	+	6.80346i	−0.913848	+	0.663950i
$106$		0			0
$107$	1.08089	−	3.32663i	0.104493	−	0.321598i	−0.885118	−	0.465367i	$-0.845922\pi$
$107$	1.08089	−	3.32663i	0.104493	−	0.321598i	0.989611	+	0.143769i	$0.0459223\pi$
$108$		0			0
$109$	4.91209			0.470493			0.235247	−	0.971936i	$-0.424410\pi$
$109$	4.91209			0.470493			0.235247	+	0.971936i	$0.424410\pi$
$110$		0			0
$111$	4.78096			0.453789
$112$		0			0
$113$	−5.30638	+	16.3314i	−0.499182	+	1.53633i	0.311153	+	0.950360i	$0.399285\pi$
$113$	−5.30638	+	16.3314i	−0.499182	+	1.53633i	−0.810336	+	0.585966i	$0.800715\pi$
$114$		0			0
$115$	−5.16996	+	3.75619i	−0.482101	+	0.350267i
$116$		0			0
$117$	−10.3518	−	31.8596i	−0.957026	−	2.94542i
$118$		0			0
$119$	−4.52151	−	3.28507i	−0.414486	−	0.301142i
$120$		0			0
$121$	−3.66576	−	10.3712i	−0.333251	−	0.942838i
$122$		0			0
$123$	−16.3092	−	11.8493i	−1.47055	−	1.06842i
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$		0			0
$127$	−12.5303	+	9.10381i	−1.11189	+	0.807833i	−0.982960	−	0.183822i	$-0.941153\pi$
$127$	−12.5303	+	9.10381i	−1.11189	+	0.807833i	−0.128927	+	0.991654i	$0.541153\pi$
$128$		0			0
$129$	7.31691	−	22.5191i	0.644218	−	1.98270i
$130$		0			0
$131$	−3.64734			−0.318670			−0.159335	−	0.987225i	$-0.550935\pi$
$131$	−3.64734			−0.318670			−0.159335	+	0.987225i	$0.550935\pi$
$132$		0			0
$133$	19.5120			1.69190
$134$		0			0
$135$	4.92810	−	15.1671i	0.424143	−	1.30538i
$136$		0			0
$137$	13.1529	−	9.55615i	1.12373	−	0.816437i	0.138959	−	0.990298i	$-0.455624\pi$
$137$	13.1529	−	9.55615i	1.12373	−	0.816437i	0.984770	+	0.173861i	$0.0556244\pi$
$138$		0			0
$139$	−2.31525	−	7.12562i	−0.196377	−	0.604387i	−0.999958	−	0.00919101i	$-0.997074\pi$
$139$	−2.31525	−	7.12562i	−0.196377	−	0.604387i	0.803580	−	0.595196i	$-0.202926\pi$
$140$		0			0
$141$	11.5128	+	8.36457i	0.969556	+	0.704423i
$142$		0			0
$143$	−13.4155	+	4.54953i	−1.12186	+	0.380450i
$144$		0			0
$145$	−0.308414	−	0.224076i	−0.0256124	−	0.0186085i
$146$		0			0
$147$	−5.44980	−	16.7727i	−0.449492	−	1.38339i
$148$		0			0
$149$	9.46754	−	6.87857i	0.775611	−	0.563514i	−0.128048	−	0.991768i	$-0.540871\pi$
$149$	9.46754	−	6.87857i	0.775611	−	0.563514i	0.903659	+	0.428254i	$0.140871\pi$
$150$		0			0
$151$	3.89383	−	11.9840i	0.316875	−	0.975242i	−0.658100	−	0.752930i	$-0.728640\pi$
$151$	3.89383	−	11.9840i	0.316875	−	0.975242i	0.974976	−	0.222312i	$-0.0713602\pi$
$152$		0			0
$153$	12.4703			1.00816
$154$		0			0
$155$	0.760465			0.0610820
$156$		0			0
$157$	−2.00136	+	6.15954i	−0.159726	+	0.491585i	−0.998609	−	0.0527263i	$-0.983209\pi$
$157$	−2.00136	+	6.15954i	−0.159726	+	0.491585i	0.838883	+	0.544311i	$0.183209\pi$
$158$		0			0
$159$	−18.5122	+	13.4499i	−1.46811	+	1.06665i
$160$		0			0
$161$	−6.94139	−	21.3634i	−0.547058	−	1.68367i
$162$		0			0
$163$	17.6153	+	12.7983i	1.37974	+	1.00244i	0.996905	+	0.0786197i	$0.0250513\pi$
$163$	17.6153	+	12.7983i	1.37974	+	1.00244i	0.382832	+	0.923818i	$0.374949\pi$
$164$		0			0
$165$	−10.4291	−	3.24168i	−0.811901	−	0.252365i
$166$		0			0
$167$	−15.4426	−	11.2197i	−1.19499	−	0.868208i	−0.201203	−	0.979550i	$-0.564485\pi$
$167$	−15.4426	−	11.2197i	−1.19499	−	0.868208i	−0.993782	+	0.111342i	$0.964485\pi$
$168$		0			0
$169$	1.62017	+	4.98638i	0.124629	+	0.383567i
$170$		0			0
$171$	−35.2217	+	25.5900i	−2.69347	+	1.95692i
$172$		0			0
$173$	−0.446930	+	1.37551i	−0.0339795	+	0.104578i	−0.966608	−	0.256261i	$-0.917509\pi$
$173$	−0.446930	+	1.37551i	−0.0339795	+	0.104578i	0.932628	+	0.360839i	$0.117509\pi$
$174$		0			0
$175$	3.51508			0.265715
$176$		0			0
$177$	−41.8560			−3.14609
$178$		0			0
$179$	−2.79036	+	8.58784i	−0.208561	+	0.641885i	0.790987	+	0.611833i	$0.209567\pi$
$179$	−2.79036	+	8.58784i	−0.208561	+	0.641885i	−0.999548	+	0.0300525i	$0.990433\pi$
$180$		0			0
$181$	0.928144	−	0.674336i	0.0689884	−	0.0501230i	−0.552757	−	0.833343i	$-0.686424\pi$
$181$	0.928144	−	0.674336i	0.0689884	−	0.0501230i	0.621745	+	0.783220i	$0.286424\pi$
$182$		0			0
$183$	9.05217	+	27.8597i	0.669156	+	2.05945i
$184$		0			0
$185$	−1.17462	−	0.853410i	−0.0863596	−	0.0627439i
$186$		0			0
$187$	−0.0674714	−	5.27293i	−0.00493400	−	0.385595i
$188$		0			0
$189$	45.3513	+	32.9496i	3.29882	+	2.39673i
$190$		0			0
$191$	−4.63116	−	14.2532i	−0.335099	−	1.03133i	−0.966673	−	0.256013i	$-0.917591\pi$
$191$	−4.63116	−	14.2532i	−0.335099	−	1.03133i	0.631574	−	0.775316i	$-0.282409\pi$
$192$		0			0
$193$	12.2825	−	8.92379i	0.884116	−	0.642348i	−0.0502209	−	0.998738i	$-0.515993\pi$
$193$	12.2825	−	8.92379i	0.884116	−	0.642348i	0.934337	+	0.356390i	$0.115993\pi$
$194$		0			0
$195$	−4.34617	+	13.3761i	−0.311236	+	0.957885i
$196$		0			0
$197$	−2.95776			−0.210731			−0.105366	−	0.994434i	$-0.533601\pi$
$197$	−2.95776			−0.210731			−0.105366	+	0.994434i	$0.533601\pi$
$198$		0			0
$199$	−5.07974			−0.360093			−0.180046	−	0.983658i	$-0.557625\pi$
$199$	−5.07974			−0.360093			−0.180046	+	0.983658i	$0.557625\pi$
$200$		0			0
$201$	−12.7332	+	39.1887i	−0.898129	+	2.76416i
$202$		0			0
$203$	1.08410	−	0.787643i	0.0760887	−	0.0552817i
$204$		0			0
$205$	1.89183	+	5.82245i	0.132131	+	0.406657i
$206$		0			0
$207$	40.5484	+	29.4601i	2.81831	+	2.04762i
$208$		0			0
$209$	11.0110	+	14.7546i	0.761649	+	1.02060i
$210$		0			0
$211$	6.88323	+	5.00096i	0.473861	+	0.344280i	0.798944	−	0.601405i	$-0.205392\pi$
$211$	6.88323	+	5.00096i	0.473861	+	0.344280i	−0.325083	+	0.945685i	$0.605392\pi$
$212$		0			0
$213$	−7.48809	−	23.0460i	−0.513076	−	1.57908i
$214$		0			0
$215$	−5.81738	+	4.22657i	−0.396742	+	0.288250i
$216$		0			0
$217$	−0.826031	+	2.54226i	−0.0560746	+	0.172580i
$218$		0			0
$219$	−23.1559			−1.56473
$220$		0			0
$221$	−6.79108			−0.456817
$222$		0			0
$223$	4.64893	−	14.3079i	0.311316	−	0.958131i	−0.665929	−	0.746015i	$-0.731965\pi$
$223$	4.64893	−	14.3079i	0.311316	−	0.958131i	0.977245	−	0.212116i	$-0.0680354\pi$
$224$		0			0
$225$	−6.34518	+	4.61004i	−0.423012	+	0.307336i
$226$		0			0
$227$	−4.85263	−	14.9349i	−0.322081	−	0.991262i	−0.972741	−	0.231894i	$-0.925508\pi$
$227$	−4.85263	−	14.9349i	−0.322081	−	0.991262i	0.650660	−	0.759369i	$-0.274492\pi$
$228$		0			0
$229$	−17.3745	−	12.6233i	−1.14814	−	0.834170i	−0.159905	−	0.987132i	$-0.551119\pi$
$229$	−17.3745	−	12.6233i	−1.14814	−	0.834170i	−0.988232	+	0.152962i	$0.951119\pi$
$230$		0			0
$231$	22.1653	−	31.3436i	1.45837	−	2.06225i
$232$		0			0
$233$	5.72472	+	4.15926i	0.375039	+	0.272482i	0.759297	−	0.650744i	$-0.225543\pi$
$233$	5.72472	+	4.15926i	0.375039	+	0.272482i	−0.384258	+	0.923226i	$0.625543\pi$
$234$		0			0
$235$	−1.33546	−	4.11012i	−0.0871158	−	0.268115i
$236$		0			0
$237$	−18.6315	+	13.5366i	−1.21025	+	0.879295i
$238$		0			0
$239$	4.01246	−	12.3491i	0.259545	−	0.798797i	−0.733355	−	0.679846i	$-0.762047\pi$
$239$	4.01246	−	12.3491i	0.259545	−	0.798797i	0.992900	−	0.118951i	$-0.0379532\pi$
$240$		0			0
$241$	4.91442			0.316565			0.158283	−	0.987394i	$-0.449404\pi$
$241$	4.91442			0.316565			0.158283	+	0.987394i	$0.449404\pi$
$242$		0			0
$243$	−47.5998			−3.05353
$244$		0			0
$245$	−1.65502	+	5.09364i	−0.105736	+	0.325421i
$246$		0			0
$247$	19.1810	−	13.9358i	1.22046	−	0.886716i
$248$		0			0
$249$	10.9397	+	33.6688i	0.693274	+	2.13368i
$250$		0			0
$251$	−3.79074	−	2.75413i	−0.239269	−	0.173839i	0.461688	−	0.887042i	$-0.347244\pi$
$251$	−3.79074	−	2.75413i	−0.239269	−	0.173839i	−0.700958	+	0.713203i	$0.747244\pi$
$252$		0			0
$253$	12.2375	−	17.3048i	0.769364	−	1.08794i
$254$		0			0
$255$	−4.23570	−	3.07741i	−0.265250	−	0.192715i
$256$		0			0
$257$	0.594723	+	1.83037i	0.0370978	+	0.114175i	0.967891	−	0.251372i	$-0.0808818\pi$
$257$	0.594723	+	1.83037i	0.0370978	+	0.114175i	−0.930793	+	0.365547i	$0.880882\pi$
$258$		0			0
$259$	4.12887	−	2.99980i	0.256556	−	0.186399i
$260$		0			0
$261$	−0.923942	+	2.84360i	−0.0571905	+	0.176014i
$262$		0			0
$263$	−16.6865			−1.02894			−0.514468	−	0.857510i	$-0.672010\pi$
$263$	−16.6865			−1.02894			−0.514468	+	0.857510i	$0.672010\pi$
$264$		0			0
$265$	6.94904			0.426876
$266$		0			0
$267$	−0.459523	+	1.41427i	−0.0281223	+	0.0865516i
$268$		0			0
$269$	3.71156	−	2.69661i	0.226298	−	0.164415i	−0.468859	−	0.883273i	$-0.655335\pi$
$269$	3.71156	−	2.69661i	0.226298	−	0.164415i	0.695157	+	0.718858i	$0.255335\pi$
$270$		0			0
$271$	6.25535	+	19.2520i	0.379985	+	1.16948i	0.940053	+	0.341028i	$0.110775\pi$
$271$	6.25535	+	19.2520i	0.379985	+	1.16948i	−0.560068	+	0.828447i	$0.689225\pi$
$272$		0			0
$273$	−39.9960	−	29.0588i	−2.42067	−	1.75872i
$274$		0			0
$275$	1.98363	+	2.65804i	0.119618	+	0.160286i
$276$		0			0
$277$	−3.88252	−	2.82082i	−0.233278	−	0.169487i	0.465005	−	0.885308i	$-0.346052\pi$
$277$	−3.88252	−	2.82082i	−0.233278	−	0.169487i	−0.698283	+	0.715821i	$0.746052\pi$
$278$		0			0
$279$	−1.84309	−	5.67246i	−0.110343	−	0.339601i
$280$		0			0
$281$	17.4731	−	12.6950i	1.04236	−	0.757319i	0.0716156	−	0.997432i	$-0.477185\pi$
$281$	17.4731	−	12.6950i	1.04236	−	0.757319i	0.970745	+	0.240113i	$0.0771845\pi$
$282$		0			0
$283$	−3.78668	+	11.6542i	−0.225095	+	0.692771i	0.773187	+	0.634178i	$0.218661\pi$
$283$	−3.78668	+	11.6542i	−0.225095	+	0.692771i	−0.998282	+	0.0585928i	$0.981339\pi$
$284$		0			0
$285$	18.2786			1.08273
$286$		0			0
$287$	−21.5196			−1.27026
$288$		0			0
$289$	−4.47209	+	13.7637i	−0.263064	+	0.809627i
$290$		0			0
$291$	−7.40475	+	5.37986i	−0.434074	+	0.315373i
$292$		0			0
$293$	4.42491	+	13.6185i	0.258506	+	0.795600i	0.993119	+	0.117113i	$0.0373640\pi$
$293$	4.42491	+	13.6185i	0.258506	+	0.795600i	−0.734612	+	0.678487i	$0.762636\pi$
$294$		0			0
$295$	10.2835	+	7.47137i	0.598726	+	0.435000i
$296$		0			0
$297$	0.676747	+	52.8881i	0.0392688	+	3.06888i
$298$		0			0
$299$	−22.0818	−	16.0434i	−1.27702	−	0.927813i
$300$		0			0
$301$	−7.81064	−	24.0387i	−0.450198	−	1.38557i
$302$		0			0
$303$	14.2186	−	10.3304i	0.816836	−	0.593466i
$304$		0			0
$305$	2.74901	−	8.46059i	0.157408	−	0.484452i
$306$		0			0
$307$	0.568487			0.0324453			0.0162226	−	0.999868i	$-0.494836\pi$
$307$	0.568487			0.0324453			0.0162226	+	0.999868i	$0.494836\pi$
$308$		0			0
$309$	−57.2358			−3.25603
$310$		0			0
$311$	3.15342	−	9.70522i	0.178814	−	0.550333i	−0.820973	−	0.570967i	$-0.806568\pi$
$311$	3.15342	−	9.70522i	0.178814	−	0.550333i	0.999787	+	0.0206341i	$0.00656849\pi$
$312$		0			0
$313$	7.55319	−	5.48771i	0.426931	−	0.310184i	−0.353489	−	0.935439i	$-0.615005\pi$
$313$	7.55319	−	5.48771i	0.426931	−	0.310184i	0.780421	+	0.625255i	$0.215005\pi$
$314$		0			0
$315$	−8.51929	−	26.2197i	−0.480008	−	1.47731i
$316$		0			0
$317$	22.8858	+	16.6275i	1.28539	+	0.933894i	0.999702	−	0.0244273i	$-0.00777624\pi$
$317$	22.8858	+	16.6275i	1.28539	+	0.933894i	0.285693	+	0.958321i	$0.407776\pi$
$318$		0			0
$319$	1.20738	+	0.375293i	0.0676004	+	0.0210124i
$320$		0			0
$321$	9.31821	+	6.77007i	0.520092	+	0.377869i
$322$		0			0
$323$	2.72734	+	8.39389i	0.151753	+	0.467049i
$324$		0			0
$325$	3.45546	−	2.51054i	0.191674	−	0.139260i
$326$		0			0
$327$	−4.99833	+	15.3833i	−0.276408	+	0.850697i
$328$		0			0
$329$	15.1909			0.837501
$330$		0			0
$331$	−5.31846			−0.292329			−0.146164	−	0.989260i	$-0.546693\pi$
$331$	−5.31846			−0.292329			−0.146164	+	0.989260i	$0.546693\pi$
$332$		0			0
$333$	−3.51890	+	10.8301i	−0.192835	+	0.593484i
$334$		0			0
$335$	10.1236	−	7.35524i	0.553113	−	0.401860i
$336$		0			0
$337$	−5.44920	−	16.7709i	−0.296837	−	0.913570i	−0.982598	−	0.185743i	$-0.940531\pi$
$337$	−5.44920	−	16.7709i	−0.296837	−	0.913570i	0.685762	−	0.727826i	$-0.259469\pi$
$338$		0			0
$339$	−45.7457	−	33.2362i	−2.48456	−	1.80514i
$340$		0			0
$341$	−2.38856	+	0.810023i	−0.129348	+	0.0438652i
$342$		0			0
$343$	4.67580	+	3.39717i	0.252469	+	0.183430i
$344$		0			0
$345$	−6.50261	−	20.0130i	−0.350089	−	1.07746i
$346$		0			0
$347$	9.56975	−	6.95283i	0.513731	−	0.373247i	−0.300506	−	0.953780i	$-0.597156\pi$
$347$	9.56975	−	6.95283i	0.513731	−	0.373247i	0.814237	+	0.580533i	$0.197156\pi$
$348$		0			0
$349$	−2.88972	+	8.89363i	−0.154683	+	0.476065i	−0.998129	−	0.0611492i	$-0.980523\pi$
$349$	−2.88972	+	8.89363i	−0.154683	+	0.476065i	0.843446	+	0.537215i	$0.180523\pi$
$350$		0			0
$351$	68.1154			3.63573
$352$		0			0
$353$	−17.7336			−0.943863			−0.471932	−	0.881635i	$-0.656443\pi$
$353$	−17.7336			−0.943863			−0.471932	+	0.881635i	$0.656443\pi$
$354$		0			0
$355$	−2.27402	+	6.99873i	−0.120693	+	0.371454i
$356$		0			0
$357$	14.8888	−	10.8173i	0.787999	−	0.572514i
$358$		0			0
$359$	−5.83547	−	17.9597i	−0.307984	−	0.947878i	−0.978547	−	0.206025i	$-0.933947\pi$
$359$	−5.83547	−	17.9597i	−0.307984	−	0.947878i	0.670562	−	0.741853i	$-0.266053\pi$
$360$		0			0
$361$	−9.55683	−	6.94344i	−0.502991	−	0.365444i
$362$		0			0
$363$	36.2098	−	0.926821i	1.90052	−	0.0486455i
$364$		0			0
$365$	5.68909	+	4.13337i	0.297781	+	0.216350i
$366$		0			0
$367$	−8.15607	−	25.1018i	−0.425744	−	1.31030i	−0.902281	−	0.431149i	$-0.858108\pi$
$367$	−8.15607	−	25.1018i	−0.425744	−	1.31030i	0.476537	−	0.879154i	$-0.341892\pi$
$368$		0			0
$369$	38.8457	−	28.2231i	2.02223	−	1.46923i
$370$		0			0
$371$	−7.54817	+	23.2309i	−0.391882	+	1.20609i
$372$		0			0
$373$	−19.2368			−0.996043			−0.498022	−	0.867165i	$-0.665940\pi$
$373$	−19.2368			−0.996043			−0.498022	+	0.867165i	$0.665940\pi$
$374$		0			0
$375$	3.29288			0.170044
$376$		0			0
$377$	0.503160	−	1.54857i	0.0259141	−	0.0797553i
$378$		0			0
$379$	27.8840	−	20.2589i	1.43230	−	1.04063i	0.442720	−	0.896660i	$-0.354014\pi$
$379$	27.8840	−	20.2589i	1.43230	−	1.04063i	0.989582	−	0.143969i	$-0.0459865\pi$
$380$		0			0
$381$	−15.7602	−	48.5051i	−0.807422	−	2.48499i
$382$		0			0
$383$	18.0549	+	13.1177i	0.922564	+	0.670282i	0.944161	−	0.329485i	$-0.106875\pi$
$383$	18.0549	+	13.1177i	0.922564	+	0.670282i	−0.0215967	+	0.999767i	$0.506875\pi$
$384$		0			0
$385$	−11.0406	+	3.74415i	−0.562681	+	0.190819i
$386$		0			0
$387$	45.6261	+	33.1493i	2.31930	+	1.68507i
$388$		0			0
$389$	−4.97726	−	15.3184i	−0.252357	−	0.776675i	−0.994339	−	0.106255i	$-0.966114\pi$
$389$	−4.97726	−	15.3184i	−0.252357	−	0.776675i	0.741982	−	0.670420i	$-0.233886\pi$
$390$		0			0
$391$	8.22011	−	5.97226i	0.415709	−	0.302030i
$392$		0			0
$393$	3.71138	−	11.4224i	0.187214	−	0.576186i
$394$		0			0
$395$	6.99381			0.351897
$396$		0			0
$397$	16.8311			0.844731			0.422365	−	0.906426i	$-0.361200\pi$
$397$	16.8311			0.844731			0.422365	+	0.906426i	$0.361200\pi$
$398$		0			0
$399$	−19.8545	+	61.1060i	−0.993970	+	3.05912i
$400$		0			0
$401$	−4.26126	+	3.09599i	−0.212797	+	0.154606i	−0.689078	−	0.724687i	$-0.741984\pi$
$401$	−4.26126	+	3.09599i	−0.212797	+	0.154606i	0.476281	+	0.879293i	$0.341984\pi$
$402$		0			0
$403$	1.00371	+	3.08911i	0.0499985	+	0.153880i
$404$		0			0
$405$	23.4490	+	17.0367i	1.16519	+	0.846560i
$406$		0			0
$407$	4.59841	+	1.42933i	0.227935	+	0.0708493i
$408$		0			0
$409$	−18.8805	−	13.7175i	−0.933581	−	0.678286i	0.0132860	−	0.999912i	$-0.495771\pi$
$409$	−18.8805	−	13.7175i	−0.933581	−	0.678286i	−0.946867	+	0.321625i	$0.895771\pi$
$410$		0			0
$411$	16.5433	+	50.9151i	0.816022	+	2.51146i
$412$		0			0
$413$	−36.1471	+	26.2624i	−1.77868	+	1.29229i
$414$		0			0
$415$	3.32222	−	10.2247i	0.163081	−	0.501913i
$416$		0			0
$417$	24.6713			1.20816
$418$		0			0
$419$	9.21755			0.450307			0.225153	−	0.974323i	$-0.427712\pi$
$419$	9.21755			0.450307			0.225153	+	0.974323i	$0.427712\pi$
$420$		0			0
$421$	6.48628	−	19.9627i	0.316122	−	0.972924i	−0.659168	−	0.751996i	$-0.729091\pi$
$421$	6.48628	−	19.9627i	0.316122	−	0.972924i	0.975290	−	0.220928i	$-0.0709086\pi$
$422$		0			0
$423$	−27.4216	+	19.9229i	−1.33328	+	0.968686i
$424$		0			0
$425$	0.491330	+	1.51216i	0.0238330	+	0.0733504i
$426$		0			0
$427$	25.2980	+	18.3801i	1.22426	+	0.889475i
$428$		0			0
$429$	−0.596834	−	46.6428i	−0.0288154	−	2.25194i
$430$		0			0
$431$	−29.7863	−	21.6410i	−1.43476	−	1.04241i	−0.989106	−	0.147205i	$-0.952972\pi$
$431$	−29.7863	−	21.6410i	−1.43476	−	1.04241i	−0.445651	−	0.895207i	$-0.647028\pi$
$432$		0			0
$433$	3.59506	+	11.0645i	0.172768	+	0.531724i	0.999524	−	0.0308355i	$-0.00981681\pi$
$433$	3.59506	+	11.0645i	0.172768	+	0.531724i	−0.826757	+	0.562559i	$0.809817\pi$
$434$		0			0
$435$	1.01557	−	0.737855i	0.0486928	−	0.0353774i
$436$		0			0
$437$	−10.9617	+	33.7366i	−0.524369	+	1.61384i
$438$		0			0
$439$	−12.4765			−0.595471			−0.297735	−	0.954648i	$-0.596231\pi$
$439$	−12.4765			−0.595471			−0.297735	+	0.954648i	$0.596231\pi$
$440$		0			0
$441$	42.0057			2.00027
$442$		0			0
$443$	2.54233	−	7.82449i	0.120790	−	0.371753i	−0.872321	−	0.488934i	$-0.837386\pi$
$443$	2.54233	−	7.82449i	0.120790	−	0.371753i	0.993111	+	0.117181i	$0.0373859\pi$
$444$		0			0
$445$	0.365347	−	0.265440i	0.0173191	−	0.0125831i
$446$		0			0
$447$	11.9080	+	36.6490i	0.563228	+	1.73344i
$448$		0			0
$449$	27.7003	+	20.1255i	1.30726	+	0.949779i	0.999998	−	0.00184649i	$-0.000587755\pi$
$449$	27.7003	+	20.1255i	1.30726	+	0.949779i	0.307260	+	0.951625i	$0.400588\pi$
$450$		0			0
$451$	−12.1440	−	16.2728i	−0.571837	−	0.766254i
$452$		0			0
$453$	33.5682	+	24.3887i	1.57717	+	1.14588i
$454$		0			0
$455$	4.63944	+	14.2787i	0.217500	+	0.669397i
$456$		0			0
$457$	−19.7657	+	14.3606i	−0.924600	+	0.671761i	−0.944665	−	0.328038i	$-0.893613\pi$
$457$	−19.7657	+	14.3606i	−0.924600	+	0.671761i	0.0200648	+	0.999799i	$0.493613\pi$
$458$		0			0
$459$	−7.83557	+	24.1154i	−0.365733	+	1.12561i
$460$		0			0
$461$	−15.4406			−0.719141			−0.359571	−	0.933118i	$-0.617077\pi$
$461$	−15.4406			−0.719141			−0.359571	+	0.933118i	$0.617077\pi$
$462$		0			0
$463$	−25.6507			−1.19209			−0.596046	−	0.802951i	$-0.703262\pi$
$463$	−25.6507			−1.19209			−0.596046	+	0.802951i	$0.703262\pi$
$464$		0			0
$465$	−0.773816	+	2.38156i	−0.0358849	+	0.110442i
$466$		0			0
$467$	6.31075	−	4.58503i	0.292027	−	0.212170i	−0.432119	−	0.901816i	$-0.642234\pi$
$467$	6.31075	−	4.58503i	0.292027	−	0.212170i	0.724146	+	0.689647i	$0.242234\pi$
$468$		0			0
$469$	13.5924	+	41.8330i	0.627638	+	1.93167i
$470$		0			0
$471$	−17.2534	−	12.5354i	−0.794997	−	0.577599i
$472$		0			0
$473$	13.7699	−	19.4718i	0.633142	−	0.895316i
$474$		0			0
$475$	−4.49080	−	3.26276i	−0.206052	−	0.149706i
$476$		0			0
$477$	−16.8420	−	51.8343i	−0.771141	−	2.37333i
$478$		0			0
$479$	31.4994	−	22.8856i	1.43924	−	1.04567i	0.451042	−	0.892503i	$-0.351052\pi$
$479$	31.4994	−	22.8856i	1.43924	−	1.04567i	0.988200	−	0.153168i	$-0.0489475\pi$
$480$		0			0
$481$	1.91633	−	5.89784i	0.0873769	−	0.268918i
$482$		0			0
$483$	73.9674			3.36563
$484$		0			0
$485$	2.77956			0.126213
$486$		0			0
$487$	−5.50829	+	16.9528i	−0.249605	+	0.768204i	0.745240	+	0.666796i	$0.232335\pi$
$487$	−5.50829	+	16.9528i	−0.249605	+	0.768204i	−0.994845	+	0.101408i	$0.967665\pi$
$488$		0			0
$489$	−58.0051	+	42.1432i	−2.62308	+	1.90578i
$490$		0			0
$491$	1.35228	+	4.16188i	0.0610274	+	0.187823i	0.976922	−	0.213595i	$-0.0685174\pi$
$491$	1.35228	+	4.16188i	0.0610274	+	0.187823i	−0.915895	+	0.401418i	$0.868517\pi$
$492$		0			0
$493$	0.490371	+	0.356275i	0.0220852	+	0.0160458i
$494$		0			0
$495$	15.0193	−	21.2385i	0.675066	−	0.954599i
$496$		0			0
$497$	−20.9269	−	15.2043i	−0.938700	−	0.682006i
$498$		0			0
$499$	12.5515	+	38.6296i	0.561883	+	1.72930i	0.677037	+	0.735949i	$0.263264\pi$
$499$	12.5515	+	38.6296i	0.561883	+	1.72930i	−0.115154	+	0.993348i	$0.536736\pi$
$500$		0			0
$501$	50.8507	−	36.9452i	2.27184	−	1.65059i
$502$		0			0
$503$	1.95322	−	6.01140i	0.0870899	−	0.268035i	−0.898022	−	0.439951i	$-0.854996\pi$
$503$	1.95322	−	6.01140i	0.0870899	−	0.268035i	0.985112	+	0.171916i	$0.0549958\pi$
$504$		0			0
$505$	−5.33731			−0.237507
$506$		0			0
$507$	−17.2645			−0.766745
$508$		0			0
$509$	−3.99655	+	12.3001i	−0.177144	+	0.545193i	−0.999725	−	0.0234549i	$-0.992533\pi$
$509$	−3.99655	+	12.3001i	−0.177144	+	0.545193i	0.822581	+	0.568648i	$0.192533\pi$
$510$		0			0
$511$	−19.9976	+	14.5291i	−0.884642	+	0.642730i
$512$		0			0
$513$	−27.3556	−	84.1918i	−1.20778	−	3.71716i
$514$		0			0
$515$	14.0621	+	10.2167i	0.619649	+	0.450201i
$516$		0			0
$517$	8.57255	+	11.4871i	0.377020	+	0.505202i
$518$		0			0
$519$	−3.85293	−	2.79932i	−0.169125	−	0.122876i
$520$		0			0
$521$	−5.07670	−	15.6245i	−0.222414	−	0.684521i	−0.998544	−	0.0539474i	$-0.982820\pi$
$521$	−5.07670	−	15.6245i	−0.222414	−	0.684521i	0.776129	−	0.630574i	$-0.217180\pi$
$522$		0			0
$523$	17.2807	−	12.5552i	0.755632	−	0.548999i	−0.141936	−	0.989876i	$-0.545333\pi$
$523$	17.2807	−	12.5552i	0.755632	−	0.548999i	0.897567	+	0.440877i	$0.145333\pi$
$524$		0			0
$525$	−3.57679	+	11.0082i	−0.156104	+	0.480438i
$526$		0			0
$527$	−1.20912			−0.0526702
$528$		0			0
$529$	17.8375			0.775542
$530$		0			0
$531$	30.8070	−	94.8143i	1.33691	−	4.11459i
$532$		0			0
$533$	−21.1546	+	15.3697i	−0.916307	+	0.665736i
$534$		0			0
$535$	−1.08089	−	3.32663i	−0.0467309	−	0.143823i
$536$		0			0
$537$	−24.0553	−	17.4772i	−1.03806	−	0.754198i
$538$		0			0
$539$	−0.227275	−	17.7616i	−0.00978941	−	0.765047i
$540$		0			0
$541$	−19.4975	−	14.1658i	−0.838265	−	0.609035i	0.0836204	−	0.996498i	$-0.473352\pi$
$541$	−19.4975	−	14.1658i	−0.838265	−	0.609035i	−0.921885	+	0.387462i	$0.873352\pi$
$542$		0			0
$543$	1.16739	+	3.59286i	0.0500976	+	0.154184i
$544$		0			0
$545$	3.97397	−	2.88725i	0.170226	−	0.123676i
$546$		0			0
$547$	6.85674	−	21.1029i	0.293173	−	0.902293i	−0.690656	−	0.723183i	$-0.742678\pi$
$547$	6.85674	−	21.1029i	0.293173	−	0.902293i	0.983829	−	0.179110i	$-0.0573218\pi$
$548$		0			0
$549$	−69.7719			−2.97779
$550$		0			0
$551$	−2.11613			−0.0901501
$552$		0			0
$553$	−7.59680	+	23.3806i	−0.323049	+	0.994243i
$554$		0			0
$555$	3.86788	−	2.81018i	0.164182	−	0.119285i
$556$		0			0
$557$	10.9315	+	33.6437i	0.463182	+	1.42553i	0.861254	+	0.508174i	$0.169679\pi$
$557$	10.9315	+	33.6437i	0.463182	+	1.42553i	−0.398072	+	0.917354i	$0.630321\pi$
$558$		0			0
$559$	−24.8471	−	18.0524i	−1.05092	−	0.763537i
$560$		0			0
$561$	16.5820	+	5.15420i	0.700091	+	0.217610i
$562$		0			0
$563$	5.49638	+	3.99335i	0.231645	+	0.168300i	0.697553	−	0.716533i	$-0.254272\pi$
$563$	5.49638	+	3.99335i	0.231645	+	0.168300i	−0.465908	+	0.884833i	$0.654272\pi$
$564$		0			0
$565$	5.30638	+	16.3314i	0.223241	+	0.687066i
$566$		0			0
$567$	−82.4251	+	59.8853i	−3.46153	+	2.51495i
$568$		0			0
$569$	11.2890	−	34.7440i	0.473259	−	1.45654i	−0.375032	−	0.927012i	$-0.622368\pi$
$569$	11.2890	−	34.7440i	0.473259	−	1.45654i	0.848291	−	0.529530i	$-0.177632\pi$
$570$		0			0
$571$	30.4606			1.27474			0.637369	−	0.770559i	$-0.280023\pi$
$571$	30.4606			1.27474			0.637369	+	0.770559i	$0.280023\pi$
$572$		0			0
$573$	49.3496			2.06161
$574$		0			0
$575$	−1.97475	+	6.07765i	−0.0823527	+	0.253456i
$576$		0			0
$577$	−8.50077	+	6.17617i	−0.353892	+	0.257117i	−0.750500	−	0.660871i	$-0.770187\pi$
$577$	−8.50077	+	6.17617i	−0.353892	+	0.257117i	0.396608	+	0.917988i	$0.370187\pi$
$578$		0			0
$579$	15.4486	+	47.5459i	0.642022	+	1.97594i
$580$		0			0
$581$	30.5730	+	22.2126i	1.26838	+	0.921534i
$582$		0			0
$583$	−21.8264	+	7.40189i	−0.903957	+	0.306555i
$584$		0			0
$585$	−27.1014	−	19.6903i	−1.12051	−	0.814095i
$586$		0			0
$587$	−6.77626	−	20.8552i	−0.279686	−	0.860785i	−0.987941	−	0.154829i	$-0.950517\pi$
$587$	−6.77626	−	20.8552i	−0.279686	−	0.860785i	0.708255	−	0.705956i	$-0.249483\pi$
$588$		0			0
$589$	3.41510	−	2.48121i	0.140717	−	0.102237i
$590$		0			0
$591$	3.00969	−	9.26286i	0.123802	−	0.381023i
$592$		0			0
$593$	−21.6482			−0.888987			−0.444493	−	0.895782i	$-0.646616\pi$
$593$	−21.6482			−0.888987			−0.444493	+	0.895782i	$0.646616\pi$
$594$		0			0
$595$	−5.58889			−0.229122
$596$		0			0
$597$	5.16892	−	15.9083i	0.211550	−	0.651083i
$598$		0			0
$599$	35.3626	−	25.6924i	1.44488	−	1.04976i	0.457880	−	0.889014i	$-0.348609\pi$
$599$	35.3626	−	25.6924i	1.44488	−	1.04976i	0.986995	−	0.160750i	$-0.0513912\pi$
$600$		0			0
$601$	1.26659	+	3.89816i	0.0516653	+	0.159009i	0.973560	−	0.228431i	$-0.0733594\pi$
$601$	1.26659	+	3.89816i	0.0516653	+	0.159009i	−0.921895	+	0.387440i	$0.873359\pi$
$602$		0			0
$603$	−79.4003	−	57.6877i	−3.23343	−	2.34922i
$604$		0			0
$605$	−9.06171	−	6.23581i	−0.368411	−	0.253522i
$606$		0			0
$607$	−34.1107	−	24.7829i	−1.38451	−	1.00591i	−0.996443	−	0.0842744i	$-0.973143\pi$
$607$	−34.1107	−	24.7829i	−1.38451	−	1.00591i	−0.388067	−	0.921631i	$-0.626857\pi$
$608$		0			0
$609$	1.36354	+	4.19656i	0.0552536	+	0.170053i
$610$		0			0
$611$	14.9332	−	10.8496i	0.604134	−	0.438929i
$612$		0			0
$613$	−3.29326	+	10.1356i	−0.133014	+	0.409374i	−0.995276	−	0.0970885i	$-0.969047\pi$
$613$	−3.29326	+	10.1356i	−0.133014	+	0.409374i	0.862262	+	0.506462i	$0.169047\pi$
$614$		0			0
$615$	−20.1593			−0.812901
$616$		0			0
$617$	6.71898			0.270496			0.135248	−	0.990812i	$-0.456817\pi$
$617$	6.71898			0.270496			0.135248	+	0.990812i	$0.456817\pi$
$618$		0			0
$619$	−10.6056	+	32.6407i	−0.426275	+	1.31194i	0.475493	+	0.879719i	$0.342270\pi$
$619$	−10.6056	+	32.6407i	−0.426275	+	1.31194i	−0.901768	+	0.432220i	$0.857730\pi$
$620$		0			0
$621$	−82.4488	+	59.9025i	−3.30855	+	2.40381i
$622$		0			0
$623$	0.490530	+	1.50970i	0.0196527	+	0.0604847i
$624$		0			0
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$		0			0
$627$	−57.4117	+	19.4698i	−2.29280	+	0.777547i
$628$		0			0
$629$	1.86762	+	1.35690i	0.0744667	+	0.0541032i
$630$		0			0
$631$	3.40926	+	10.4926i	0.135721	+	0.417705i	0.995701	−	0.0926212i	$-0.0295245\pi$
$631$	3.40926	+	10.4926i	0.135721	+	0.417705i	−0.859981	+	0.510327i	$0.829525\pi$
$632$		0			0
$633$	−22.6657	+	16.4676i	−0.900879	+	0.654527i
$634$		0			0
$635$	−4.78616	+	14.7303i	−0.189933	+	0.584553i
$636$		0			0
$637$	−22.8755			−0.906358
$638$		0			0
$639$	57.7163			2.28322
$640$		0			0
$641$	−7.81307	+	24.0462i	−0.308598	+	0.949767i	0.669712	+	0.742621i	$0.266417\pi$
$641$	−7.81307	+	24.0462i	−0.308598	+	0.949767i	−0.978310	+	0.207146i	$0.933583\pi$
$642$		0			0
$643$	4.31960	−	3.13838i	0.170349	−	0.123765i	−0.499344	−	0.866404i	$-0.666426\pi$
$643$	4.31960	−	3.13838i	0.170349	−	0.123765i	0.669693	+	0.742638i	$0.266426\pi$
$644$		0			0
$645$	−7.31691	−	22.5191i	−0.288103	−	0.886691i
$646$		0			0
$647$	−2.79236	−	2.02877i	−0.109779	−	0.0797591i	0.531541	−	0.847032i	$-0.321613\pi$
$647$	−2.79236	−	2.02877i	−0.109779	−	0.0797591i	−0.641320	+	0.767273i	$0.721613\pi$
$648$		0			0
$649$	−40.2578	−	12.5134i	−1.58026	−	0.491194i
$650$		0			0
$651$	−7.12111	−	5.17379i	−0.279098	−	0.202777i
$652$		0			0
$653$	3.49945	+	10.7702i	0.136944	+	0.421471i	0.995887	−	0.0906000i	$-0.0288785\pi$
$653$	3.49945	+	10.7702i	0.136944	+	0.421471i	−0.858943	+	0.512071i	$0.828878\pi$
$654$		0			0
$655$	−2.95076	+	2.14385i	−0.115296	+	0.0837673i
$656$		0			0
$657$	17.0433	−	52.4539i	0.664923	−	2.04642i
$658$		0			0
$659$	12.0511			0.469444			0.234722	−	0.972063i	$-0.424582\pi$
$659$	12.0511			0.469444			0.234722	+	0.972063i	$0.424582\pi$
$660$		0			0
$661$	−11.9301			−0.464027			−0.232013	−	0.972713i	$-0.574531\pi$
$661$	−11.9301			−0.464027			−0.232013	+	0.972713i	$0.574531\pi$
$662$		0			0
$663$	6.91031	−	21.2677i	0.268374	−	0.825971i
$664$		0			0
$665$	15.7855	−	11.4688i	0.612136	−	0.444743i
$666$		0			0
$667$	0.752814	+	2.31692i	0.0291491	+	0.0897116i
$668$		0			0
$669$	40.0779	+	29.1183i	1.54950	+	1.12578i
$670$		0			0
$671$	0.377505	+	29.5022i	0.0145734	+	1.13892i
$672$		0			0
$673$	26.9841	+	19.6051i	1.04016	+	0.755720i	0.970317	−	0.241838i	$-0.0777502\pi$
$673$	26.9841	+	19.6051i	1.04016	+	0.755720i	0.0698428	+	0.997558i	$0.477750\pi$
$674$		0			0
$675$	−4.92810	−	15.1671i	−0.189683	−	0.583783i
$676$		0			0
$677$	−24.2644	+	17.6291i	−0.932555	+	0.677541i	−0.946617	−	0.322360i	$-0.895524\pi$
$677$	−24.2644	+	17.6291i	−0.932555	+	0.677541i	0.0140621	+	0.999901i	$0.495524\pi$
$678$		0			0
$679$	−3.01921	+	9.29218i	−0.115867	+	0.356601i
$680$		0			0
$681$	51.7096			1.98152
$682$		0			0
$683$	13.1505			0.503190			0.251595	−	0.967833i	$-0.419045\pi$
$683$	13.1505			0.503190			0.251595	+	0.967833i	$0.419045\pi$
$684$		0			0
$685$	5.02396	−	15.4622i	0.191956	−	0.590779i
$686$		0			0
$687$	57.2121	−	41.5670i	2.18278	−	1.58588i
$688$		0			0
$689$	9.17181	+	28.2279i	0.349418	+	1.07540i
$690$		0			0
$691$	21.1770	+	15.3860i	0.805613	+	0.585312i	0.912555	−	0.408953i	$-0.134106\pi$
$691$	21.1770	+	15.3860i	0.805613	+	0.585312i	−0.106942	+	0.994265i	$0.534106\pi$
$692$		0			0
$693$	54.6868	+	73.2796i	2.07738	+	2.78366i
$694$		0			0
$695$	−6.06141	−	4.40387i	−0.229923	−	0.167048i
$696$		0			0
$697$	−3.00796	−	9.25755i	−0.113935	−	0.350655i
$698$		0			0
$699$	−18.8508	+	13.6959i	−0.713004	+	0.518028i
$700$		0			0
$701$	0.437201	−	1.34557i	0.0165129	−	0.0508214i	−0.942461	−	0.334317i	$-0.891494\pi$
$701$	0.437201	−	1.34557i	0.0165129	−	0.0508214i	0.958973	+	0.283496i	$0.0914943\pi$
$702$		0			0
$703$	−8.05944			−0.303968
$704$		0			0
$705$	14.2306			0.535957
$706$		0			0
$707$	5.79749	−	17.8428i	0.218037	−	0.671049i
$708$		0			0
$709$	−2.97859	+	2.16407i	−0.111863	+	0.0812734i	−0.642310	−	0.766445i	$-0.722024\pi$
$709$	−2.97859	+	2.16407i	−0.111863	+	0.0812734i	0.530447	+	0.847718i	$0.322024\pi$
$710$		0			0
$711$	−16.9505	−	52.1682i	−0.635693	−	1.95646i
$712$		0			0
$713$	−3.93157	−	2.85645i	−0.147238	−	0.106975i
$714$		0			0
$715$	−8.17919	+	11.5661i	−0.305885	+	0.432546i
$716$		0			0
$717$	34.5910	+	25.1318i	1.29182	+	0.938565i
$718$		0			0
$719$	−2.45788	−	7.56458i	−0.0916635	−	0.282111i	0.894706	−	0.446655i	$-0.147385\pi$
$719$	−2.45788	−	7.56458i	−0.0916635	−	0.282111i	−0.986370	+	0.164544i	$0.947385\pi$
$720$		0			0
$721$	−49.4293	+	35.9125i	−1.84084	+	1.33745i
$722$		0			0
$723$	−5.00070	+	15.3906i	−0.185978	+	0.572381i
$724$		0			0
$725$	−0.381220			−0.0141582
$726$		0			0
$727$	−35.6495			−1.32217			−0.661083	−	0.750313i	$-0.729903\pi$
$727$	−35.6495			−1.32217			−0.661083	+	0.750313i	$0.729903\pi$
$728$		0			0
$729$	21.5653	−	66.3711i	0.798714	−	2.45819i
$730$		0			0
$731$	9.24949	−	6.72015i	0.342105	−	0.248554i
$732$		0			0
$733$	2.94883	+	9.07558i	0.108918	+	0.335214i	0.990630	−	0.136573i	$-0.0436089\pi$
$733$	2.94883	+	9.07558i	0.108918	+	0.335214i	−0.881712	+	0.471788i	$0.843609\pi$
$734$		0			0
$735$	−14.2678	−	10.3661i	−0.526274	−	0.382360i
$736$		0			0
$737$	−23.9630	+	33.8856i	−0.882688	+	1.24819i
$738$		0			0
$739$	−28.2796	−	20.5463i	−1.04028	−	0.755808i	−0.0699400	−	0.997551i	$-0.522281\pi$
$739$	−28.2796	−	20.5463i	−1.04028	−	0.755808i	−0.970340	+	0.241743i	$0.922281\pi$
$740$		0			0
$741$	24.1253	+	74.2500i	0.886265	+	2.72764i
$742$		0			0
$743$	−27.3175	+	19.8473i	−1.00218	+	0.728128i	−0.962555	−	0.271087i	$-0.912617\pi$
$743$	−27.3175	+	19.8473i	−1.00218	+	0.728128i	−0.0396268	+	0.999215i	$0.512617\pi$
$744$		0			0
$745$	3.61628	−	11.1298i	0.132490	−	0.407763i
$746$		0			0
$747$	−84.3203			−3.08512
$748$		0			0
$749$	12.2951			0.449255
$750$		0			0
$751$	−4.10288	+	12.6274i	−0.149716	+	0.460779i	−0.997587	−	0.0694236i	$-0.977884\pi$
$751$	−4.10288	+	12.6274i	−0.149716	+	0.460779i	0.847871	+	0.530202i	$0.177884\pi$
$752$		0			0
$753$	12.4825	−	9.06903i	0.454886	−	0.330494i
$754$		0			0
$755$	−3.89383	−	11.9840i	−0.141711	−	0.436141i
$756$		0			0
$757$	−13.1915	−	9.58418i	−0.479453	−	0.348343i	0.321661	−	0.946855i	$-0.395759\pi$
$757$	−13.1915	−	9.58418i	−0.479453	−	0.348343i	−0.801114	+	0.598512i	$0.795759\pi$
$758$		0			0
$759$	41.7414	+	55.9329i	1.51512	+	2.03024i
$760$		0			0
$761$	17.2081	+	12.5025i	0.623795	+	0.453214i	0.854245	−	0.519871i	$-0.174020\pi$
$761$	17.2081	+	12.5025i	0.623795	+	0.453214i	−0.230450	+	0.973084i	$0.574020\pi$
$762$		0			0
$763$	5.33560	+	16.4213i	0.193162	+	0.594491i
$764$		0			0
$765$	10.0887	−	7.32986i	0.364757	−	0.265012i
$766$		0			0
$767$	−16.7769	+	51.6340i	−0.605779	+	1.86440i
$768$		0			0
$769$	−5.81494			−0.209692			−0.104846	−	0.994488i	$-0.533435\pi$
$769$	−5.81494			−0.209692			−0.104846	+	0.994488i	$0.533435\pi$
$770$		0			0
$771$	−6.33737			−0.228235
$772$		0			0
$773$	5.76962	−	17.7571i	0.207519	−	0.638677i	−0.792082	−	0.610415i	$-0.791003\pi$
$773$	5.76962	−	17.7571i	0.207519	−	0.638677i	0.999601	−	0.0282619i	$-0.00899724\pi$
$774$		0			0
$775$	0.615229	−	0.446990i	0.0220997	−	0.0160564i
$776$		0			0
$777$	5.19317	+	15.9829i	0.186304	+	0.573384i
$778$		0			0
$779$	27.4931	+	19.9749i	0.985041	+	0.715674i
$780$		0			0
$781$	−0.312278	−	24.4047i	−0.0111742	−	0.873269i
$782$		0			0
$783$	−4.91848	−	3.57348i	−0.175772	−	0.127706i
$784$		0			0
$785$	2.00136	+	6.15954i	0.0714315	+	0.219843i
$786$		0			0
$787$	37.4747	−	27.2270i	1.33583	−	0.970536i	0.336242	−	0.941775i	$-0.390844\pi$
$787$	37.4747	−	27.2270i	1.33583	−	0.970536i	0.999586	−	0.0287609i	$-0.00915614\pi$
$788$		0			0
$789$	16.9795	−	52.2575i	0.604486	−	1.86042i
$790$		0			0
$791$	−60.3602			−2.14616
$792$		0			0
$793$	37.9964			1.34929
$794$		0			0
$795$	−7.07104	+	21.7624i	−0.250784	+	0.771833i
$796$		0			0
$797$	4.94938	−	3.59593i	0.175316	−	0.127375i	−0.496667	−	0.867941i	$-0.665443\pi$
$797$	4.94938	−	3.59593i	0.175316	−	0.127375i	0.671983	+	0.740567i	$0.265443\pi$
$798$		0			0
$799$	2.12335	+	6.53500i	0.0751187	+	0.231192i
$800$		0			0
$801$	−2.86545	−	2.08187i	−0.101246	−	0.0735592i
$802$		0			0
$803$	−22.2717	−	6.92276i	−0.785953	−	0.244299i
$804$		0			0
$805$	−18.1728	−	13.2033i	−0.640507	−	0.465356i
$806$		0			0
$807$	4.66828	+	14.3675i	0.164331	+	0.505760i
$808$		0			0
$809$	−11.4981	+	8.35384i	−0.404251	+	0.293706i	−0.771270	−	0.636508i	$-0.780378\pi$
$809$	−11.4981	+	8.35384i	−0.404251	+	0.293706i	0.367019	+	0.930213i	$0.380378\pi$
$810$		0			0
$811$	9.46843	−	29.1408i	0.332482	−	1.02327i	−0.635468	−	0.772128i	$-0.719193\pi$
$811$	9.46843	−	29.1408i	0.332482	−	1.02327i	0.967949	−	0.251146i	$-0.0808074\pi$
$812$		0			0
$813$	−66.6570			−2.33776
$814$		0			0
$815$	21.7737			0.762700
$816$		0			0
$817$	−12.3344	+	37.9614i	−0.431526	+	1.32810i
$818$		0			0
$819$	95.2635	−	69.2130i	3.32878	−	2.41850i
$820$		0			0
$821$	−1.09135	−	3.35884i	−0.0380885	−	0.117224i	0.930204	−	0.367042i	$-0.119629\pi$
$821$	−1.09135	−	3.35884i	−0.0380885	−	0.117224i	−0.968293	+	0.249817i	$0.919629\pi$
$822$		0			0
$823$	−24.1029	−	17.5118i	−0.840174	−	0.610422i	0.0822455	−	0.996612i	$-0.473791\pi$
$823$	−24.1029	−	17.5118i	−0.840174	−	0.610422i	−0.922419	+	0.386190i	$0.873791\pi$
$824$		0			0
$825$	−10.3427	+	3.50747i	−0.360087	+	0.122115i
$826$		0			0
$827$	40.8255	+	29.6614i	1.41964	+	1.03143i	0.991831	+	0.127561i	$0.0407147\pi$
$827$	40.8255	+	29.6614i	1.41964	+	1.03143i	0.427810	+	0.903869i	$0.359285\pi$
$828$		0			0
$829$	−5.96340	−	18.3535i	−0.207117	−	0.637442i	−0.999620	−	0.0275731i	$-0.991222\pi$
$829$	−5.96340	−	18.3535i	−0.207117	−	0.637442i	0.792502	−	0.609869i	$-0.208778\pi$
$830$		0			0
$831$	12.7847	−	9.28862i	0.443496	−	0.322219i
$832$		0			0
$833$	2.63145	−	8.09877i	0.0911743	−	0.280606i
$834$		0			0
$835$	−19.0881			−0.660572
$836$		0			0
$837$	12.1276			0.419193
$838$		0			0
$839$	−5.22204	+	16.0718i	−0.180285	+	0.554859i	−0.999835	−	0.0181475i	$-0.994223\pi$
$839$	−5.22204	+	16.0718i	−0.180285	+	0.554859i	0.819551	+	0.573007i	$0.194223\pi$
$840$		0			0
$841$	23.3439	−	16.9604i	0.804963	−	0.584840i
$842$		0			0
$843$	21.9772	+	67.6388i	0.756934	+	2.32960i
$844$		0			0
$845$	4.24167	+	3.08175i	0.145918	+	0.106015i
$846$		0			0
$847$	30.6896	−	23.5202i	1.05451	−	0.808163i
$848$		0			0
$849$	−32.6445	−	23.7176i	−1.12036	−	0.813987i
$850$		0			0
$851$	2.86715	+	8.82418i	0.0982847	+	0.302489i
$852$		0			0
$853$	38.4944	−	27.9678i	1.31802	−	0.957599i	0.318067	−	0.948068i	$-0.396966\pi$
$853$	38.4944	−	27.9678i	1.31802	−	0.957599i	0.999955	−	0.00953082i	$-0.00303380\pi$
$854$		0			0
$855$	−13.4535	+	41.4056i	−0.460099	+	1.41604i
$856$		0			0
$857$	21.8041			0.744813			0.372406	−	0.928070i	$-0.378533\pi$
$857$	21.8041			0.744813			0.372406	+	0.928070i	$0.378533\pi$
$858$		0			0
$859$	−23.3331			−0.796116			−0.398058	−	0.917360i	$-0.630316\pi$
$859$	−23.3331			−0.796116			−0.398058	+	0.917360i	$0.630316\pi$
$860$		0			0
$861$	21.8974	−	67.3933i	0.746261	−	2.29676i
$862$		0			0
$863$	17.7244	−	12.8775i	0.603346	−	0.438357i	−0.243719	−	0.969846i	$-0.578367\pi$
$863$	17.7244	−	12.8775i	0.603346	−	0.438357i	0.847065	+	0.531489i	$0.178367\pi$
$864$		0			0
$865$	0.446930	+	1.37551i	0.0151961	+	0.0467688i
$866$		0			0
$867$	−38.5533	−	28.0106i	−1.30934	−	0.951290i
$868$		0			0
$869$	−21.9670	+	7.44958i	−0.745181	+	0.252710i
$870$		0			0
$871$	43.2398	+	31.4156i	1.46513	+	1.06448i
$872$		0			0
$873$	−6.73667	−	20.7333i	−0.228002	−	0.701717i
$874$		0			0
$875$	2.84376	−	2.06611i	0.0961365	−	0.0698473i
$876$		0			0
$877$	16.2963	−	50.1547i	0.550286	−	1.69361i	−0.157794	−	0.987472i	$-0.550438\pi$
$877$	16.2963	−	50.1547i	0.550286	−	1.69361i	0.708079	−	0.706133i	$-0.249562\pi$
$878$		0			0
$879$	−47.1518			−1.59039
$880$		0			0
$881$	34.3244			1.15642			0.578210	−	0.815888i	$-0.303752\pi$
$881$	34.3244			1.15642			0.578210	+	0.815888i	$0.303752\pi$
$882$		0			0
$883$	15.3638	−	47.2850i	0.517034	−	1.59127i	−0.262516	−	0.964928i	$-0.584552\pi$
$883$	15.3638	−	47.2850i	0.517034	−	1.59127i	0.779550	−	0.626340i	$-0.215448\pi$
$884$		0			0
$885$	−33.8622	+	24.6023i	−1.13827	+	0.826998i
$886$		0			0
$887$	−3.70249	−	11.3951i	−0.124317	−	0.382610i	0.869459	−	0.494006i	$-0.164468\pi$
$887$	−3.70249	−	11.3951i	−0.124317	−	0.382610i	−0.993776	+	0.111396i	$0.964468\pi$
$888$		0			0
$889$	−44.0450	−	32.0006i	−1.47722	−	1.07327i
$890$		0			0
$891$	−91.7985	−	28.5339i	−3.07537	−	0.955921i
$892$		0			0
$893$	−19.4076	−	14.1005i	−0.649451	−	0.471854i
$894$		0			0
$895$	2.79036	+	8.58784i	0.0932714	+	0.287060i
$896$		0			0
$897$	72.7128	−	52.8290i	2.42781	−	1.76391i
$898$		0			0
$899$	0.0895854	−	0.275716i	0.00298784	−	0.00919563i
$900$		0			0
$901$	−11.0488			−0.368089
$902$		0			0
$903$	83.2301			2.76972
$904$		0			0
$905$	0.354520	−	1.09110i	0.0117846	−	0.0362694i
$906$		0			0
$907$	−38.2401	+	27.7831i	−1.26974	+	0.922522i	−0.999192	−	0.0401839i	$-0.987206\pi$
$907$	−38.2401	+	27.7831i	−1.26974	+	0.922522i	−0.270550	+	0.962706i	$0.587206\pi$
$908$		0			0
$909$	12.9357	+	39.8121i	0.429051	+	1.32048i
$910$		0			0
$911$	7.16223	+	5.20366i	0.237295	+	0.172405i	0.700077	−	0.714067i	$-0.253149\pi$
$911$	7.16223	+	5.20366i	0.237295	+	0.172405i	−0.462782	+	0.886472i	$0.653149\pi$
$912$		0			0
$913$	0.456221	+	35.6539i	0.0150987	+	1.17997i
$914$		0			0
$915$	23.6989	+	17.2182i	0.783461	+	0.569218i
$916$		0			0
$917$	−3.96181	−	12.1932i	−0.130830	−	0.402655i
$918$		0			0
$919$	13.3602	−	9.70674i	0.440712	−	0.320196i	−0.345206	−	0.938527i	$-0.612191\pi$
$919$	13.3602	−	9.70674i	0.440712	−	0.320196i	0.785918	+	0.618331i	$0.212191\pi$
$920$		0			0
$921$	−0.578468	+	1.78034i	−0.0190612	+	0.0586642i
$922$		0			0
$923$	−31.4312			−1.03457
$924$		0			0
$925$	−1.45191			−0.0477384
$926$		0			0
$927$	42.1270	−	129.654i	1.38363	−	4.25838i
$928$		0			0
$929$	9.13367	−	6.63600i	0.299666	−	0.217720i	−0.427784	−	0.903881i	$-0.640705\pi$
$929$	9.13367	−	6.63600i	0.299666	−	0.217720i	0.727450	+	0.686161i	$0.240705\pi$
$930$		0			0
$931$	9.18693	+	28.2745i	0.301089	+	0.926658i
$932$		0			0
$933$	27.1852	+	19.7512i	0.890005	+	0.646626i
$934$		0			0
$935$	−3.15393	−	4.22623i	−0.103145	−	0.138212i
$936$		0			0
$937$	17.4527	+	12.6801i	0.570153	+	0.414241i	0.835161	−	0.550006i	$-0.185374\pi$
$937$	17.4527	+	12.6801i	0.570153	+	0.414241i	−0.265008	+	0.964246i	$0.585374\pi$
$938$		0			0
$939$	9.50017	+	29.2385i	0.310026	+	0.954163i
$940$		0			0
$941$	−40.6986	+	29.5693i	−1.32674	+	0.963930i	−0.326914	+	0.945054i	$0.606009\pi$
$941$	−40.6986	+	29.5693i	−1.32674	+	0.963930i	−0.999822	+	0.0188761i	$0.993991\pi$
$942$		0			0
$943$	12.0896	−	37.2079i	0.393691	−	1.21165i
$944$		0			0
$945$	56.0573			1.82354
$946$		0			0
$947$	−41.7335			−1.35615			−0.678077	−	0.734990i	$-0.737187\pi$
$947$	−41.7335			−1.35615			−0.678077	+	0.734990i	$0.737187\pi$
$948$		0			0
$949$	−9.28145	+	28.5654i	−0.301288	+	0.927271i
$950$		0			0
$951$	−75.3602	+	54.7524i	−2.44372	+	1.77547i
$952$		0			0
$953$	−10.8923	−	33.5229i	−0.352835	−	1.08591i	−0.957254	−	0.289248i	$-0.906595\pi$
$953$	−10.8923	−	33.5229i	−0.352835	−	1.08591i	0.604420	−	0.796666i	$-0.293405\pi$
$954$		0			0
$955$	−12.1245	−	8.80899i	−0.392341	−	0.285052i
$956$		0			0
$957$	−2.40389	+	3.39930i	−0.0777067	+	0.109884i
$958$		0			0
$959$	46.2335	+	33.5906i	1.49296	+	1.08470i
$960$		0			0
$961$	−9.40082	−	28.9327i	−0.303252	−	0.933315i
$962$		0			0
$963$	−22.1943	+	16.1251i	−0.715203	+	0.519625i
$964$		0			0
$965$	4.69151	−	14.4390i	0.151025	−	0.464808i
$966$		0			0
$967$	−21.6156			−0.695111			−0.347556	−	0.937659i	$-0.612988\pi$
$967$	−21.6156			−0.695111			−0.347556	+	0.937659i	$0.612988\pi$
$968$		0			0
$969$	−29.0625			−0.933623
$970$		0			0
$971$	−3.65675	+	11.2543i	−0.117351	+	0.361169i	−0.992430	−	0.122811i	$-0.960809\pi$
$971$	−3.65675	+	11.2543i	−0.117351	+	0.361169i	0.875079	+	0.483980i	$0.160809\pi$
$972$		0			0
$973$	21.3063	−	15.4800i	0.683050	−	0.496265i
$974$		0			0
$975$	4.34617	+	13.3761i	0.139189	+	0.428379i
$976$		0			0
$977$	41.8260	+	30.3884i	1.33813	+	0.972210i	0.999510	+	0.0312874i	$0.00996071\pi$
$977$	41.8260	+	30.3884i	1.33813	+	0.972210i	0.338622	+	0.940923i	$0.390039\pi$
$978$		0			0
$979$	−0.864790	+	1.22289i	−0.0276388	+	0.0390836i
$980$		0			0
$981$	−31.1681	−	22.6449i	−0.995121	−	0.722998i
$982$		0			0
$983$	−15.7983	−	48.6221i	−0.503887	−	1.55080i	−0.802634	−	0.596472i	$-0.796569\pi$
$983$	−15.7983	−	48.6221i	−0.503887	−	1.55080i	0.298747	−	0.954332i	$-0.403431\pi$
$984$		0			0
$985$	−2.39288	+	1.73853i	−0.0762434	+	0.0553940i
$986$		0			0
$987$	−15.4576	+	47.5736i	−0.492021	+	1.51428i
$988$		0			0
$989$	45.9514			1.46117
$990$		0			0
$991$	3.16402			0.100508			0.0502542	−	0.998736i	$-0.483997\pi$
$991$	3.16402			0.100508			0.0502542	+	0.998736i	$0.483997\pi$
$992$		0			0
$993$	5.41183	−	16.6559i	0.171739	−	0.528559i
$994$		0			0
$995$	−4.10959	+	2.98579i	−0.130283	+	0.0946560i
$996$		0			0
$997$	−1.75762	−	5.40939i	−0.0556643	−	0.171317i	0.919359	−	0.393420i	$-0.128708\pi$
$997$	−1.75762	−	5.40939i	−0.0556643	−	0.171317i	−0.975023	+	0.222103i	$0.928708\pi$
$998$		0			0
$999$	−18.7324	−	13.6099i	−0.592667	−	0.430598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.y.c.81.1	✓	12
4.3	odd	2		880.2.bo.i.81.3		12
11.3	even	5	inner	440.2.y.c.201.1	yes	12
11.5	even	5		4840.2.a.bb.1.1		6
11.6	odd	10		4840.2.a.ba.1.1		6
44.3	odd	10		880.2.bo.i.641.3		12
44.27	odd	10		9680.2.a.dc.1.6		6
44.39	even	10		9680.2.a.dd.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.c.81.1	✓	12	1.1	even	1	trivial
440.2.y.c.201.1	yes	12	11.3	even	5	inner
880.2.bo.i.81.3		12	4.3	odd	2
880.2.bo.i.641.3		12	44.3	odd	10
4840.2.a.ba.1.1		6	11.6	odd	10
4840.2.a.bb.1.1		6	11.5	even	5
9680.2.a.dc.1.6		6	44.27	odd	10
9680.2.a.dd.1.6		6	44.39	even	10

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:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01756 + 3.13172i) q^{3} +(0.809017 - 0.587785i) q^{5} +(1.08622 + 3.34304i) q^{7} +(-6.34518 - 4.61004i) q^{9} +O(q^{10})\)	\(q+(-1.01756 + 3.13172i) q^{3} +(0.809017 - 0.587785i) q^{5} +(1.08622 + 3.34304i) q^{7} +(-6.34518 - 4.61004i) q^{9} +(-1.91497 + 2.70793i) q^{11} +(3.45546 + 2.51054i) q^{13} +(1.01756 + 3.13172i) q^{15} +(-1.28632 + 0.934565i) q^{17} +(1.71533 - 5.27925i) q^{19} -11.5747 q^{21} -6.39042 q^{23} +(0.309017 - 0.951057i) q^{25} +(12.9019 - 9.37380i) q^{27} +(-0.117804 - 0.362562i) q^{29} +(0.615229 + 0.446990i) q^{31} +(-6.53187 - 8.75262i) q^{33} +(2.84376 + 2.06611i) q^{35} +(-0.448664 - 1.38085i) q^{37} +(-11.3784 + 8.26690i) q^{39} +(-1.89183 + 5.82245i) q^{41} -7.19067 q^{43} -7.84307 q^{45} +(1.33546 - 4.11012i) q^{47} +(-4.33291 + 3.14804i) q^{49} +(-1.61789 - 4.97936i) q^{51} +(5.62189 + 4.08454i) q^{53} +(0.0424355 + 3.31635i) q^{55} +(14.7877 + 10.7439i) q^{57} +(3.92793 + 12.0889i) q^{59} +(7.19700 - 5.22893i) q^{61} +(8.51929 - 26.2197i) q^{63} +4.27118 q^{65} +12.5135 q^{67} +(6.50261 - 20.0130i) q^{69} +(-5.95347 + 4.32545i) q^{71} +(2.17304 + 6.68793i) q^{73} +(2.66400 + 1.93551i) q^{75} +(-11.1328 - 3.46042i) q^{77} +(5.65811 + 4.11086i) q^{79} +(8.95672 + 27.5660i) q^{81} +(8.69768 - 6.31923i) q^{83} +(-0.491330 + 1.51216i) q^{85} +1.25531 q^{87} +0.451594 q^{89} +(-4.63944 + 14.2787i) q^{91} +(-2.02588 + 1.47189i) q^{93} +(-1.71533 - 5.27925i) q^{95} +(2.24871 + 1.63379i) q^{97} +(24.6345 - 8.35419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} + 3 q^{5} - q^{7} - 10 q^{9}+O(q^{10}) \) 12 * q - q^3 + 3 * q^5 - q^7 - 10 * q^9	\( 12 q - q^{3} + 3 q^{5} - q^{7} - 10 q^{9} + 4 q^{11} + 18 q^{13} + q^{15} + 3 q^{17} + 4 q^{19} - 28 q^{21} - 18 q^{23} - 3 q^{25} + 23 q^{27} + 15 q^{29} - 8 q^{31} + 4 q^{33} + 6 q^{35} + 6 q^{37} - 33 q^{39} + 2 q^{41} - 36 q^{43} - 10 q^{45} - 16 q^{47} - 16 q^{49} - 10 q^{51} + 19 q^{53} + 6 q^{55} + 62 q^{57} + 46 q^{59} + 18 q^{61} - 7 q^{63} + 2 q^{65} - 44 q^{67} - q^{69} - 6 q^{71} + 25 q^{73} + 4 q^{75} + 10 q^{77} + 19 q^{79} + 30 q^{81} - 3 q^{85} + 6 q^{87} - 50 q^{89} - 46 q^{91} - 37 q^{93} - 4 q^{95} - 31 q^{97} + 79 q^{99}+O(q^{100}) \) 12 * q - q^3 + 3 * q^5 - q^7 - 10 * q^9 + 4 * q^11 + 18 * q^13 + q^15 + 3 * q^17 + 4 * q^19 - 28 * q^21 - 18 * q^23 - 3 * q^25 + 23 * q^27 + 15 * q^29 - 8 * q^31 + 4 * q^33 + 6 * q^35 + 6 * q^37 - 33 * q^39 + 2 * q^41 - 36 * q^43 - 10 * q^45 - 16 * q^47 - 16 * q^49 - 10 * q^51 + 19 * q^53 + 6 * q^55 + 62 * q^57 + 46 * q^59 + 18 * q^61 - 7 * q^63 + 2 * q^65 - 44 * q^67 - q^69 - 6 * q^71 + 25 * q^73 + 4 * q^75 + 10 * q^77 + 19 * q^79 + 30 * q^81 - 3 * q^85 + 6 * q^87 - 50 * q^89 - 46 * q^91 - 37 * q^93 - 4 * q^95 - 31 * q^97 + 79 * q^99

Introduction

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