LMFDB - Embedded newform 1050.3.p.i.901.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(451,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1050.451");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 $ x^16 + 92x^14 - 112x^13 + 5846x^12 - 7728x^11 + 197216x^10 - 298200x^9 + 4836403x^8 - 6808704x^7 + 64376800x^6 - 91953512x^5 + 595763862x^4 - 630430976x^3 + 1087013404x^2 + 294123256x + 101626561
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4}\cdot 7 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.2
Root			$-0.141814 - 0.245629i$ of defining polynomial
Character	$\chi$	$=$	1050.901
Dual form			1050.3.p.i.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-4.24494 - 5.56601i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-4.24494 - 5.56601i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(5.42967 + 9.40447i) q^{11} +(-3.00000 - 1.73205i) q^{12} +0.772061i q^{13} +(9.81857 - 1.26320i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-16.7760 + 9.68565i) q^{17} +(2.12132 + 3.67423i) q^{18} +(22.5766 + 13.0346i) q^{19} +(-11.1877 - 4.67280i) q^{21} -15.3574 q^{22} +(-6.84734 + 11.8599i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-0.945577 - 0.545929i) q^{26} -5.19615i q^{27} +(-5.39568 + 12.9185i) q^{28} -6.99131 q^{29} +(22.7559 - 13.1381i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(16.2890 + 9.40447i) q^{33} -27.3952i q^{34} -6.00000 q^{36} +(32.3004 - 55.9459i) q^{37} +(-31.9281 + 18.4337i) q^{38} +(0.668624 + 1.15809i) q^{39} +5.54839i q^{41} +(13.6339 - 10.3979i) q^{42} +68.9320 q^{43} +(10.8593 - 18.8089i) q^{44} +(-9.68361 - 16.7725i) q^{46} +(19.5817 + 11.3055i) q^{47} +6.92820i q^{48} +(-12.9610 + 47.2548i) q^{49} +(-16.7760 + 29.0570i) q^{51} +(1.33725 - 0.772061i) q^{52} +(37.2820 + 64.5742i) q^{53} +(6.36396 + 3.67423i) q^{54} +(-12.0065 - 15.7431i) q^{56} +45.1532 q^{57} +(4.94360 - 8.56257i) q^{58} +(96.6595 - 55.8064i) q^{59} +(-46.9572 - 27.1108i) q^{61} +37.1603i q^{62} +(-20.8283 + 2.67965i) q^{63} +8.00000 q^{64} +(-23.0362 + 13.2999i) q^{66} +(-22.1273 - 38.3255i) q^{67} +(33.5521 + 19.3713i) q^{68} +23.7199i q^{69} +31.9550 q^{71} +(4.24264 - 7.34847i) q^{72} +(92.6322 - 53.4812i) q^{73} +(45.6797 + 79.1195i) q^{74} -52.1384i q^{76} +(29.2968 - 70.1430i) q^{77} -1.89115 q^{78} +(-14.8408 + 25.7050i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-6.79536 - 3.92330i) q^{82} +15.8151i q^{83} +(3.09419 + 24.0505i) q^{84} +(-48.7423 + 84.4242i) q^{86} +(-10.4870 + 6.05465i) q^{87} +(15.3574 + 26.5999i) q^{88} +(-31.8358 - 18.3804i) q^{89} +(4.29730 - 3.27735i) q^{91} +27.3894 q^{92} +(22.7559 - 39.4144i) q^{93} +(-27.6926 + 15.9884i) q^{94} +(-8.48528 - 4.89898i) q^{96} +134.212i q^{97} +(-48.7102 - 49.2881i) q^{98} +32.5780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9}+O(q^{10}) $ 16 * q + 24 * q^3 - 16 * q^4 - 4 * q^7 + 24 * q^9	$ 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9} - 4 q^{11} - 48 q^{12} + 8 q^{14} - 32 q^{16} - 12 q^{17} - 72 q^{19} - 24 q^{21} + 48 q^{22} + 12 q^{23} - 32 q^{28} + 72 q^{29} + 120 q^{31} - 12 q^{33} - 96 q^{36} - 44 q^{37} + 72 q^{38} + 36 q^{39} + 24 q^{42} + 56 q^{43} - 8 q^{44} + 8 q^{46} + 24 q^{47} - 40 q^{49} - 12 q^{51} + 72 q^{52} - 32 q^{53} + 16 q^{56} - 144 q^{57} + 88 q^{58} + 132 q^{59} + 96 q^{61} - 60 q^{63} + 128 q^{64} + 72 q^{66} + 164 q^{67} + 24 q^{68} - 136 q^{71} + 348 q^{73} - 112 q^{74} - 96 q^{77} + 280 q^{79} - 72 q^{81} - 264 q^{82} - 24 q^{84} - 88 q^{86} + 108 q^{87} - 48 q^{88} - 300 q^{89} - 272 q^{91} - 48 q^{92} + 120 q^{93} - 384 q^{98} - 24 q^{99}+O(q^{100}) $ 16 * q + 24 * q^3 - 16 * q^4 - 4 * q^7 + 24 * q^9 - 4 * q^11 - 48 * q^12 + 8 * q^14 - 32 * q^16 - 12 * q^17 - 72 * q^19 - 24 * q^21 + 48 * q^22 + 12 * q^23 - 32 * q^28 + 72 * q^29 + 120 * q^31 - 12 * q^33 - 96 * q^36 - 44 * q^37 + 72 * q^38 + 36 * q^39 + 24 * q^42 + 56 * q^43 - 8 * q^44 + 8 * q^46 + 24 * q^47 - 40 * q^49 - 12 * q^51 + 72 * q^52 - 32 * q^53 + 16 * q^56 - 144 * q^57 + 88 * q^58 + 132 * q^59 + 96 * q^61 - 60 * q^63 + 128 * q^64 + 72 * q^66 + 164 * q^67 + 24 * q^68 - 136 * q^71 + 348 * q^73 - 112 * q^74 - 96 * q^77 + 280 * q^79 - 72 * q^81 - 264 * q^82 - 24 * q^84 - 88 * q^86 + 108 * q^87 - 48 * q^88 - 300 * q^89 - 272 * q^91 - 48 * q^92 + 120 * q^93 - 384 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$2$	−0.707107	+	1.22474i	−0.353553	+	0.612372i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−4.24494	−	5.56601i	−0.606420	−	0.795145i
$7$	−4.24494	−	5.56601i	−0.606420	−	0.795145i
$8$	2.82843			0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	5.42967	+	9.40447i	0.493607	+	0.854952i	0.999973	−	0.00736658i	$-0.00234488\pi$
$11$	5.42967	+	9.40447i	0.493607	+	0.854952i	−0.506366	+	0.862319i	$0.669012\pi$
$12$	−3.00000	−	1.73205i	−0.250000	−	0.144338i
$13$			0.772061i			0.0593893i	0.999559	+	0.0296946i	$0.00945349\pi$
$13$			0.772061i			0.0593893i	−0.999559	+	0.0296946i	$0.990547\pi$
$14$	9.81857	−	1.26320i	0.701326	−	0.0902284i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−16.7760	+	9.68565i	−0.986826	+	0.569744i	−0.904324	−	0.426847i	$-0.859624\pi$
$17$	−16.7760	+	9.68565i	−0.986826	+	0.569744i	−0.0825021	+	0.996591i	$0.526291\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	22.5766	+	13.0346i	1.18824	+	0.686032i	0.957907	−	0.287079i	$-0.0926844\pi$
$19$	22.5766	+	13.0346i	1.18824	+	0.686032i	0.230335	+	0.973111i	$0.426018\pi$
$20$		0			0
$21$	−11.1877	−	4.67280i	−0.532748	−	0.222514i
$22$	−15.3574			−0.698065
$23$	−6.84734	+	11.8599i	−0.297711	+	0.515650i	−0.975612	−	0.219503i	$-0.929556\pi$
$23$	−6.84734	+	11.8599i	−0.297711	+	0.515650i	0.677901	+	0.735153i	$0.262890\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$		0			0
$26$	−0.945577	−	0.545929i	−0.0363684	−	0.0209973i
$27$		−	5.19615i		−	0.192450i
$28$	−5.39568	+	12.9185i	−0.192703	+	0.461374i
$29$	−6.99131			−0.241080			−0.120540	−	0.992708i	$-0.538463\pi$
$29$	−6.99131			−0.241080			−0.120540	+	0.992708i	$0.538463\pi$
$30$		0			0
$31$	22.7559	−	13.1381i	0.734062	−	0.423811i	−0.0858441	−	0.996309i	$-0.527359\pi$
$31$	22.7559	−	13.1381i	0.734062	−	0.423811i	0.819906	+	0.572497i	$0.194025\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	16.2890	+	9.40447i	0.493607	+	0.284984i
$34$		−	27.3952i		−	0.805740i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	32.3004	−	55.9459i	0.872984	−	1.51205i	0.0140890	−	0.999901i	$-0.495515\pi$
$37$	32.3004	−	55.9459i	0.872984	−	1.51205i	0.858895	−	0.512152i	$-0.171151\pi$
$38$	−31.9281	+	18.4337i	−0.840214	+	0.485098i
$39$	0.668624	+	1.15809i	0.0171442	+	0.0296946i
$40$		0			0
$41$			5.54839i			0.135327i	0.997708	+	0.0676633i	$0.0215544\pi$
$41$			5.54839i			0.135327i	−0.997708	+	0.0676633i	$0.978446\pi$
$42$	13.6339	−	10.3979i	0.324617	−	0.247570i
$43$	68.9320			1.60307			0.801535	−	0.597948i	$-0.204017\pi$
$43$	68.9320			1.60307			0.801535	+	0.597948i	$0.204017\pi$
$44$	10.8593	−	18.8089i	0.246803	−	0.427476i
$45$		0			0
$46$	−9.68361	−	16.7725i	−0.210513	−	0.364620i
$47$	19.5817	+	11.3055i	0.416631	+	0.240542i	0.693635	−	0.720327i	$-0.256008\pi$
$47$	19.5817	+	11.3055i	0.416631	+	0.240542i	−0.277004	+	0.960869i	$0.589342\pi$
$48$			6.92820i			0.144338i
$49$	−12.9610	+	47.2548i	−0.264511	+	0.964383i
$50$		0			0
$51$	−16.7760	+	29.0570i	−0.328942	+	0.569744i
$52$	1.33725	−	0.772061i	0.0257163	−	0.0148473i
$53$	37.2820	+	64.5742i	0.703433	+	1.21838i	0.967254	+	0.253810i	$0.0816839\pi$
$53$	37.2820	+	64.5742i	0.703433	+	1.21838i	−0.263821	+	0.964572i	$0.584983\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		0			0
$56$	−12.0065	−	15.7431i	−0.214402	−	0.281126i
$57$	45.1532			0.792161
$58$	4.94360	−	8.56257i	0.0852345	−	0.147631i
$59$	96.6595	−	55.8064i	1.63830	−	0.945871i	0.656878	−	0.753997i	$-0.271877\pi$
$59$	96.6595	−	55.8064i	1.63830	−	0.945871i	0.981420	−	0.191874i	$-0.0614566\pi$
$60$		0			0
$61$	−46.9572	−	27.1108i	−0.769790	−	0.444439i	0.0630096	−	0.998013i	$-0.479930\pi$
$61$	−46.9572	−	27.1108i	−0.769790	−	0.444439i	−0.832800	+	0.553574i	$0.813263\pi$
$62$			37.1603i			0.599359i
$63$	−20.8283	+	2.67965i	−0.330608	+	0.0425341i
$64$	8.00000			0.125000
$65$		0			0
$66$	−23.0362	+	13.2999i	−0.349033	+	0.201514i
$67$	−22.1273	−	38.3255i	−0.330258	−	0.572023i	0.652305	−	0.757957i	$-0.273802\pi$
$67$	−22.1273	−	38.3255i	−0.330258	−	0.572023i	−0.982562	+	0.185934i	$0.940469\pi$
$68$	33.5521	+	19.3713i	0.493413	+	0.284872i
$69$			23.7199i			0.343767i
$70$		0			0
$71$	31.9550			0.450071			0.225035	−	0.974351i	$-0.427750\pi$
$71$	31.9550			0.450071			0.225035	+	0.974351i	$0.427750\pi$
$72$	4.24264	−	7.34847i	0.0589256	−	0.102062i
$73$	92.6322	−	53.4812i	1.26893	−	0.732619i	0.294147	−	0.955760i	$-0.404964\pi$
$73$	92.6322	−	53.4812i	1.26893	−	0.732619i	0.974786	+	0.223141i	$0.0716310\pi$
$74$	45.6797	+	79.1195i	0.617293	+	1.06918i
$75$		0			0
$76$		−	52.1384i		−	0.686032i
$77$	29.2968	−	70.1430i	0.380478	−	0.910949i
$78$	−1.89115			−0.0242456
$79$	−14.8408	+	25.7050i	−0.187858	+	0.325380i	−0.944536	−	0.328408i	$-0.893488\pi$
$79$	−14.8408	+	25.7050i	−0.187858	+	0.325380i	0.756678	+	0.653788i	$0.226821\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−6.79536	−	3.92330i	−0.0828702	−	0.0478451i
$83$			15.8151i			0.190543i	0.995451	+	0.0952717i	$0.0303720\pi$
$83$			15.8151i			0.190543i	−0.995451	+	0.0952717i	$0.969628\pi$
$84$	3.09419	+	24.0505i	0.0368356	+	0.286315i
$85$		0			0
$86$	−48.7423	+	84.4242i	−0.566771	+	0.981676i
$87$	−10.4870	+	6.05465i	−0.120540	+	0.0695937i
$88$	15.3574	+	26.5999i	0.174516	+	0.302271i
$89$	−31.8358	−	18.3804i	−0.357706	−	0.206521i	0.310368	−	0.950616i	$-0.399548\pi$
$89$	−31.8358	−	18.3804i	−0.357706	−	0.206521i	−0.668074	+	0.744095i	$0.732881\pi$
$90$		0			0
$91$	4.29730	−	3.27735i	0.0472231	−	0.0360148i
$92$	27.3894			0.297711
$93$	22.7559	−	39.4144i	0.244687	−	0.423811i
$94$	−27.6926	+	15.9884i	−0.294603	+	0.170089i
$95$		0			0
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$			134.212i			1.38363i	0.722077	+	0.691813i	$0.243188\pi$
$97$			134.212i			1.38363i	−0.722077	+	0.691813i	$0.756812\pi$
$98$	−48.7102	−	49.2881i	−0.497043	−	0.502940i
$99$	32.5780			0.329071
$100$		0			0
$101$	132.760	−	76.6490i	1.31445	−	0.758901i	0.331624	−	0.943412i	$-0.392404\pi$
$101$	132.760	−	76.6490i	1.31445	−	0.758901i	0.982830	+	0.184511i	$0.0590702\pi$
$102$	−23.7249	−	41.0927i	−0.232597	−	0.402870i
$103$	54.8504	+	31.6679i	0.532529	+	0.307456i	0.742046	−	0.670349i	$-0.233856\pi$
$103$	54.8504	+	31.6679i	0.532529	+	0.307456i	−0.209517	+	0.977805i	$0.567189\pi$
$104$			2.18372i			0.0209973i
$105$		0			0
$106$	−105.449			−0.994805
$107$	−21.9277	+	37.9800i	−0.204932	+	0.354953i	−0.950111	−	0.311912i	$-0.899031\pi$
$107$	−21.9277	+	37.9800i	−0.204932	+	0.354953i	0.745179	+	0.666865i	$0.232364\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	−2.64166	−	4.57549i	−0.0242354	−	0.0419770i	0.853653	−	0.520842i	$-0.174382\pi$
$109$	−2.64166	−	4.57549i	−0.0242354	−	0.0419770i	−0.877889	+	0.478865i	$0.841048\pi$
$110$		0			0
$111$		−	111.892i		−	1.00804i
$112$	27.7711	−	3.57286i	0.247956	−	0.0319006i
$113$	106.725			0.944469			0.472234	−	0.881473i	$-0.343448\pi$
$113$	106.725			0.944469			0.472234	+	0.881473i	$0.343448\pi$
$114$	−31.9281	+	55.3011i	−0.280071	+	0.485098i
$115$		0			0
$116$	6.99131	+	12.1093i	0.0602699	+	0.104391i
$117$	2.00587	+	1.15809i	0.0171442	+	0.00989821i
$118$			157.844i			1.33766i
$119$	125.124	+	52.2607i	1.05146	+	0.439166i
$120$		0			0
$121$	1.53727	−	2.66262i	0.0127047	−	0.0220051i
$122$	66.4075	−	38.3404i	0.544324	−	0.314266i
$123$	4.80504	+	8.32258i	0.0390654	+	0.0676633i
$124$	−45.5119	−	26.2763i	−0.367031	−	0.211906i
$125$		0			0
$126$	11.4460	−	27.4042i	0.0908410	−	0.217494i
$127$	−203.641			−1.60348			−0.801738	−	0.597676i	$-0.796091\pi$
$127$	−203.641			−1.60348			−0.801738	+	0.597676i	$0.796091\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	103.398	−	59.6969i	0.801535	−	0.462767i
$130$		0			0
$131$	−67.2791	−	38.8436i	−0.513581	−	0.296516i	0.220724	−	0.975336i	$-0.429158\pi$
$131$	−67.2791	−	38.8436i	−0.513581	−	0.296516i	−0.734304	+	0.678820i	$0.762491\pi$
$132$		−	37.6179i		−	0.284984i
$133$	−23.2854	−	180.993i	−0.175078	−	1.36085i
$134$	62.5853			0.467055
$135$		0			0
$136$	−47.4498	+	27.3952i	−0.348896	+	0.201435i
$137$	114.504	+	198.326i	0.835794	+	1.44764i	0.893382	+	0.449297i	$0.148326\pi$
$137$	114.504	+	198.326i	0.835794	+	1.44764i	−0.0575883	+	0.998340i	$0.518341\pi$
$138$	−29.0508	−	16.7725i	−0.210513	−	0.121540i
$139$			61.7421i			0.444188i	0.975025	+	0.222094i	$0.0712892\pi$
$139$			61.7421i			0.444188i	−0.975025	+	0.222094i	$0.928711\pi$
$140$		0			0
$141$	39.1633			0.277754
$142$	−22.5956	+	39.1368i	−0.159124	+	0.275611i
$143$	−7.26082	+	4.19204i	−0.0507750	+	0.0293149i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$		0			0
$146$			151.268i			1.03608i
$147$	21.4823	+	82.1067i	0.146138	+	0.558549i
$148$	−129.202			−0.872984
$149$	14.6523	−	25.3785i	0.0983373	−	0.170325i	−0.812659	−	0.582739i	$-0.801981\pi$
$149$	14.6523	−	25.3785i	0.0983373	−	0.170325i	0.910997	+	0.412414i	$0.135314\pi$
$150$		0			0
$151$	−81.8479	−	141.765i	−0.542039	−	0.938839i	−0.998787	−	0.0492431i	$-0.984319\pi$
$151$	−81.8479	−	141.765i	−0.542039	−	0.938839i	0.456748	−	0.889596i	$-0.349014\pi$
$152$	63.8563	+	36.8674i	0.420107	+	0.242549i
$153$			58.1139i			0.379830i
$154$	65.1914	+	85.4797i	0.423320	+	0.555063i
$155$		0			0
$156$	1.33725	−	2.31618i	0.00857210	−	0.0148473i
$157$	−180.741	+	104.351i	−1.15122	+	0.664657i	−0.949184	−	0.314722i	$-0.898089\pi$
$157$	−180.741	+	104.351i	−1.15122	+	0.664657i	−0.202035	+	0.979378i	$0.564755\pi$
$158$	−20.9880	−	36.3524i	−0.132836	−	0.230078i
$159$	111.846	+	64.5742i	0.703433	+	0.406127i
$160$		0			0
$161$	95.0792	−	12.2323i	0.590554	−	0.0759771i
$162$	12.7279			0.0785674
$163$	69.5841	−	120.523i	0.426896	−	0.739406i	−0.569699	−	0.821853i	$-0.692940\pi$
$163$	69.5841	−	120.523i	0.426896	−	0.739406i	0.996595	+	0.0824475i	$0.0262737\pi$
$164$	9.61009	−	5.54839i	0.0585981	−	0.0338316i
$165$		0			0
$166$	−19.3695	−	11.1830i	−0.116683	−	0.0673672i
$167$			54.4023i			0.325762i	0.986646	+	0.162881i	$0.0520787\pi$
$167$			54.4023i			0.325762i	−0.986646	+	0.162881i	$0.947921\pi$
$168$	−31.6436	−	13.2167i	−0.188355	−	0.0786707i
$169$	168.404			0.996473
$170$		0			0
$171$	67.7298	−	39.1038i	0.396081	−	0.228677i
$172$	−68.9320	−	119.394i	−0.400768	−	0.694150i
$173$	−54.3723	−	31.3918i	−0.314291	−	0.181456i	0.334554	−	0.942376i	$-0.391414\pi$
$173$	−54.3723	−	31.3918i	−0.314291	−	0.181456i	−0.648845	+	0.760921i	$0.724748\pi$
$174$		−	17.1251i		−	0.0984203i
$175$		0			0
$176$	−43.4374			−0.246803
$177$	96.6595	−	167.419i	0.546099	−	0.945871i
$178$	45.0226	−	25.9938i	0.252936	−	0.146033i
$179$	70.3978	+	121.933i	0.393284	+	0.681187i	0.992880	−	0.119115i	$-0.0380057\pi$
$179$	70.3978	+	121.933i	0.393284	+	0.681187i	−0.599597	+	0.800302i	$0.704672\pi$
$180$		0			0
$181$			222.987i			1.23197i	0.787757	+	0.615986i	$0.211242\pi$
$181$			222.987i			1.23197i	−0.787757	+	0.615986i	$0.788758\pi$
$182$	0.975265	+	7.58053i	0.00535860	+	0.0416513i
$183$	−93.9144			−0.513193
$184$	−19.3672	+	33.5450i	−0.105257	+	0.182310i
$185$		0			0
$186$	32.1817	+	55.7404i	0.173020	+	0.299680i
$187$	−182.177	−	105.180i	−0.974208	−	0.562459i
$188$		−	45.2219i		−	0.240542i
$189$	−28.9219	+	22.0573i	−0.153026	+	0.116705i
$190$		0			0
$191$	−66.5069	+	115.193i	−0.348204	+	0.603106i	−0.985930	−	0.167156i	$-0.946542\pi$
$191$	−66.5069	+	115.193i	−0.348204	+	0.603106i	0.637727	+	0.770263i	$0.279875\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	142.611	+	247.010i	0.738919	+	1.27984i	0.952983	+	0.303025i	$0.0979967\pi$
$193$	142.611	+	247.010i	0.738919	+	1.27984i	−0.214064	+	0.976820i	$0.568670\pi$
$194$	−164.375	−	94.9020i	−0.847295	−	0.489186i
$195$		0			0
$196$	94.8087	−	24.8056i	0.483718	−	0.126559i
$197$	307.784			1.56236			0.781178	−	0.624309i	$-0.214619\pi$
$197$	307.784			1.56236			0.781178	+	0.624309i	$0.214619\pi$
$198$	−23.0362	+	39.8998i	−0.116344	+	0.201514i
$199$	−8.39167	+	4.84493i	−0.0421692	+	0.0243464i	−0.520936	−	0.853595i	$-0.674417\pi$
$199$	−8.39167	+	4.84493i	−0.0421692	+	0.0243464i	0.478767	+	0.877942i	$0.341084\pi$
$200$		0			0
$201$	−66.3818	−	38.3255i	−0.330258	−	0.190674i
$202$			216.796i			1.07325i
$203$	29.6777	+	38.9137i	0.146195	+	0.191693i
$204$	67.1042			0.328942
$205$		0			0
$206$	−77.5702	+	44.7852i	−0.376555	+	0.217404i
$207$	20.5420	+	35.5798i	0.0992369	+	0.171883i
$208$	−2.67450	−	1.54412i	−0.0128582	−	0.00742366i
$209$			283.095i			1.35452i
$210$		0			0
$211$	175.954			0.833903			0.416952	−	0.908929i	$-0.363098\pi$
$211$	175.954			0.833903			0.416952	+	0.908929i	$0.363098\pi$
$212$	74.5639	−	129.148i	0.351717	−	0.609191i
$213$	47.9326	−	27.6739i	0.225035	−	0.129924i
$214$	−31.0105	−	53.7118i	−0.144909	−	0.250990i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−169.725	−	70.8893i	−0.782141	−	0.326679i
$218$	7.47174			0.0342740
$219$	92.6322	−	160.444i	0.422978	−	0.732619i
$220$		0			0
$221$	−7.47791	−	12.9521i	−0.0338367	−	0.0586069i
$222$	137.039	+	79.1195i	0.617293	+	0.356394i
$223$			50.0854i			0.224598i	0.993674	+	0.112299i	$0.0358215\pi$
$223$			50.0854i			0.224598i	−0.993674	+	0.112299i	$0.964178\pi$
$224$	−15.2613	+	36.5389i	−0.0681308	+	0.163120i
$225$		0			0
$226$	−75.4659	+	130.711i	−0.333920	+	0.578366i
$227$	−264.301	+	152.594i	−1.16432	+	0.672221i	−0.952336	−	0.305052i	$-0.901326\pi$
$227$	−264.301	+	152.594i	−1.16432	+	0.672221i	−0.211985	+	0.977273i	$0.567993\pi$
$228$	−45.1532	−	78.2076i	−0.198040	−	0.343016i
$229$	−353.428	−	204.052i	−1.54335	−	0.891055i	−0.998624	−	0.0524421i	$-0.983299\pi$
$229$	−353.428	−	204.052i	−1.54335	−	0.891055i	−0.544728	−	0.838613i	$-0.683367\pi$
$230$		0			0
$231$	−16.8004	−	130.586i	−0.0727292	−	0.565309i
$232$	−19.7744			−0.0852345
$233$	108.404	−	187.762i	0.465255	−	0.805846i	−0.533958	−	0.845511i	$-0.679296\pi$
$233$	108.404	−	187.762i	0.465255	−	0.805846i	0.999213	+	0.0396654i	$0.0126292\pi$
$234$	−2.83673	+	1.63779i	−0.0121228	+	0.00699909i
$235$		0			0
$236$	−193.319	−	111.613i	−0.819149	−	0.472936i
$237$			51.4100i			0.216920i
$238$	−152.482	+	116.291i	−0.640680	+	0.488617i
$239$	−389.739			−1.63071			−0.815354	−	0.578963i	$-0.803457\pi$
$239$	−389.739			−1.63071			−0.815354	+	0.578963i	$0.803457\pi$
$240$		0			0
$241$	60.0686	−	34.6806i	0.249247	−	0.143903i	−0.370172	−	0.928963i	$-0.620701\pi$
$241$	60.0686	−	34.6806i	0.249247	−	0.143903i	0.619419	+	0.785060i	$0.287368\pi$
$242$	2.17402	+	3.76552i	0.00898356	+	0.0155600i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$			108.443i			0.444439i
$245$		0			0
$246$	−13.5907			−0.0552468
$247$	−10.0635	+	17.4305i	−0.0407429	+	0.0705688i
$248$	64.3635	−	37.1603i	0.259530	−	0.149840i
$249$	13.6963	+	23.7226i	0.0550051	+	0.0952717i
$250$		0			0
$251$			256.631i			1.02244i	0.859451	+	0.511218i	$0.170805\pi$
$251$			256.631i			1.02244i	−0.859451	+	0.511218i	$0.829195\pi$
$252$	25.4696	+	33.3961i	0.101070	+	0.132524i
$253$	−148.715			−0.587808
$254$	143.996	−	249.409i	0.566914	−	0.981924i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	173.998	+	100.458i	0.677034	+	0.390886i	0.798737	−	0.601681i	$-0.205502\pi$
$257$	173.998	+	100.458i	0.677034	+	0.390886i	−0.121703	+	0.992567i	$0.538835\pi$
$258$			168.848i			0.654451i
$259$	−448.509	+	57.7025i	−1.73170	+	0.222789i
$260$		0			0
$261$	−10.4870	+	18.1640i	−0.0401799	+	0.0695937i
$262$	95.1470	−	54.9331i	0.363156	−	0.209668i
$263$	251.495	+	435.602i	0.956256	+	1.65628i	0.731469	+	0.681875i	$0.238835\pi$
$263$	251.495	+	435.602i	0.956256	+	1.65628i	0.224787	+	0.974408i	$0.427831\pi$
$264$	46.0723	+	26.5999i	0.174516	+	0.100757i
$265$		0			0
$266$	238.135	+	99.4625i	0.895245	+	0.373919i
$267$	−63.6716			−0.238470
$268$	−44.2545	+	76.6511i	−0.165129	+	0.286012i
$269$	−121.754	+	70.2945i	−0.452616	+	0.261318i	−0.708934	−	0.705275i	$-0.750824\pi$
$269$	−121.754	+	70.2945i	−0.452616	+	0.261318i	0.256318	+	0.966592i	$0.417490\pi$
$270$		0			0
$271$	103.808	+	59.9334i	0.383054	+	0.221157i	0.679146	−	0.734003i	$-0.262350\pi$
$271$	103.808	+	59.9334i	0.383054	+	0.221157i	−0.296092	+	0.955159i	$0.595684\pi$
$272$		−	77.4852i		−	0.284872i
$273$	3.60768	−	8.63759i	0.0132150	−	0.0316395i
$274$	−323.866			−1.18199
$275$		0			0
$276$	41.0841	−	23.7199i	0.148855	−	0.0859416i
$277$	−53.5034	−	92.6706i	−0.193153	−	0.334551i	0.753140	−	0.657860i	$-0.228538\pi$
$277$	−53.5034	−	92.6706i	−0.193153	−	0.334551i	−0.946293	+	0.323309i	$0.895205\pi$
$278$	−75.6183	−	43.6583i	−0.272008	−	0.157044i
$279$		−	78.8289i		−	0.282541i
$280$		0			0
$281$	−85.5187			−0.304337			−0.152169	−	0.988355i	$-0.548626\pi$
$281$	−85.5187			−0.304337			−0.152169	+	0.988355i	$0.548626\pi$
$282$	−27.6926	+	47.9651i	−0.0982008	+	0.170089i
$283$	339.501	−	196.011i	1.19965	−	0.692619i	0.239173	−	0.970977i	$-0.423124\pi$
$283$	339.501	−	196.011i	1.19965	−	0.692619i	0.960477	+	0.278358i	$0.0897902\pi$
$284$	−31.9550	−	55.3477i	−0.112518	−	0.194886i
$285$		0			0
$286$		−	11.8569i		−	0.0414576i
$287$	30.8824	−	23.5526i	0.107604	−	0.0820646i
$288$	−16.9706			−0.0589256
$289$	43.1238	−	74.6926i	0.149217	−	0.258452i
$290$		0			0
$291$	116.231	+	201.318i	0.399419	+	0.691813i
$292$	−185.264	−	106.962i	−0.634467	−	0.366310i
$293$		−	500.595i		−	1.70851i	−0.519850	−	0.854257i	$-0.674012\pi$
$293$		−	500.595i		−	1.70851i	0.519850	−	0.854257i	$-0.325988\pi$
$294$	−115.750	−	31.7479i	−0.393708	−	0.107986i
$295$		0			0
$296$	91.3593	−	158.239i	0.308646	−	0.534591i
$297$	48.8671	−	28.2134i	0.164536	−	0.0949947i
$298$	20.7214	+	35.8906i	0.0695350	+	0.120438i
$299$	−9.15660	−	5.28656i	−0.0306241	−	0.0176808i
$300$		0			0
$301$	−292.612	−	383.677i	−0.972133	−	1.27467i
$302$	231.501			0.766559
$303$	132.760	−	229.947i	0.438151	−	0.758901i
$304$	−90.3064	+	52.1384i	−0.297061	+	0.171508i
$305$		0			0
$306$	−71.1747	−	41.0927i	−0.232597	−	0.134290i
$307$		−	398.171i		−	1.29698i	−0.761225	−	0.648488i	$-0.775402\pi$
$307$		−	398.171i		−	1.29698i	0.761225	−	0.648488i	$-0.224598\pi$
$308$	−150.788	+	19.3995i	−0.489572	+	0.0629853i
$309$	109.701			0.355019
$310$		0			0
$311$	322.107	−	185.968i	1.03571	−	0.597969i	0.117097	−	0.993120i	$-0.462641\pi$
$311$	322.107	−	185.968i	1.03571	−	0.597969i	0.918616	+	0.395151i	$0.129308\pi$
$312$	1.89115	+	3.27558i	0.00606139	+	0.0104986i
$313$	−365.884	−	211.243i	−1.16896	−	0.674899i	−0.215524	−	0.976499i	$-0.569146\pi$
$313$	−365.884	−	211.243i	−1.16896	−	0.674899i	−0.953435	+	0.301600i	$0.902479\pi$
$314$		−	295.149i		−	0.939966i
$315$		0			0
$316$	59.3632			0.187858
$317$	108.091	−	187.219i	0.340981	−	0.590597i	−0.643634	−	0.765333i	$-0.722574\pi$
$317$	108.091	−	187.219i	0.340981	−	0.590597i	0.984615	+	0.174737i	$0.0559075\pi$
$318$	−158.174	+	91.3218i	−0.497402	+	0.287175i
$319$	−37.9605	−	65.7496i	−0.118999	−	0.206112i
$320$		0			0
$321$			75.9599i			0.236635i
$322$	−52.2497	+	125.097i	−0.162266	+	0.388501i
$323$	−504.995			−1.56345
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	98.4067	+	170.445i	0.301861	+	0.522839i
$327$	−7.92498	−	4.57549i	−0.0242354	−	0.0139923i
$328$			15.6932i			0.0478451i
$329$	−20.1965	−	156.983i	−0.0613874	−	0.477151i
$330$		0			0
$331$	−105.730	+	183.130i	−0.319426	+	0.553262i	−0.980368	−	0.197175i	$-0.936823\pi$
$331$	−105.730	+	183.130i	−0.319426	+	0.553262i	0.660942	+	0.750437i	$0.270157\pi$
$332$	27.3926	−	15.8151i	0.0825077	−	0.0476358i
$333$	−96.9012	−	167.838i	−0.290995	−	0.504018i
$334$	−66.6289	−	38.4682i	−0.199488	−	0.115174i
$335$		0			0
$336$	38.5625	−	29.4098i	0.114769	−	0.0875291i
$337$	−260.379			−0.772639			−0.386319	−	0.922365i	$-0.626254\pi$
$337$	−260.379			−0.772639			−0.386319	+	0.922365i	$0.626254\pi$
$338$	−119.080	+	206.252i	−0.352306	+	0.610213i
$339$	160.087	−	92.4265i	0.472234	−	0.272645i
$340$		0			0
$341$	247.115	+	142.672i	0.724676	+	0.418392i
$342$			110.602i			0.323399i
$343$	318.039	−	128.452i	0.927228	−	0.374496i
$344$	194.969			0.566771
$345$		0			0
$346$	76.8940	−	44.3948i	0.222237	−	0.128309i
$347$	−255.968	−	443.350i	−0.737661	−	1.27767i	−0.953546	−	0.301247i	$-0.902597\pi$
$347$	−255.968	−	443.350i	−0.737661	−	1.27767i	0.215885	−	0.976419i	$-0.430736\pi$
$348$	20.9739	+	12.1093i	0.0602699	+	0.0347968i
$349$		−	527.872i		−	1.51253i	−0.654266	−	0.756264i	$-0.727022\pi$
$349$		−	527.872i		−	1.51253i	0.654266	−	0.756264i	$-0.272978\pi$
$350$		0			0
$351$	4.01174			0.0114295
$352$	30.7149	−	53.1997i	0.0872582	−	0.151136i
$353$	−118.226	+	68.2579i	−0.334918	+	0.193365i	−0.658023	−	0.752998i	$-0.728607\pi$
$353$	−118.226	+	68.2579i	−0.334918	+	0.193365i	0.323104	+	0.946363i	$0.395274\pi$
$354$	136.697	+	236.767i	0.386150	+	0.668832i
$355$		0			0
$356$			73.5216i			0.206521i
$357$	232.945	−	29.9693i	0.652506	−	0.0839475i
$358$	−199.115			−0.556187
$359$	278.525	−	482.419i	0.775835	−	1.34379i	−0.158490	−	0.987361i	$-0.550662\pi$
$359$	278.525	−	482.419i	0.775835	−	1.34379i	0.934324	−	0.356424i	$-0.116004\pi$
$360$		0			0
$361$	159.302	+	275.919i	0.441279	+	0.764318i
$362$	−273.102	−	157.676i	−0.754426	−	0.435568i
$363$		−	5.32525i		−	0.0146701i
$364$	−9.97383	−	4.16579i	−0.0274006	−	0.0114445i
$365$		0			0
$366$	66.4075	−	115.021i	0.181441	−	0.314266i
$367$	−102.210	+	59.0110i	−0.278502	+	0.160793i	−0.632745	−	0.774360i	$-0.718072\pi$
$367$	−102.210	+	59.0110i	−0.278502	+	0.160793i	0.354243	+	0.935153i	$0.384738\pi$
$368$	−27.3894	−	47.4398i	−0.0744276	−	0.128912i
$369$	14.4151	+	8.32258i	0.0390654	+	0.0225544i
$370$		0			0
$371$	201.162	−	481.625i	0.542215	−	1.29818i
$372$	−91.0237			−0.244687
$373$	−159.186	+	275.718i	−0.426772	+	0.739191i	−0.996584	−	0.0825840i	$-0.973683\pi$
$373$	−159.186	+	275.718i	−0.426772	+	0.739191i	0.569812	+	0.821775i	$0.307016\pi$
$374$	257.637	−	148.747i	0.688869	−	0.397719i
$375$		0			0
$376$	55.3853	+	31.9767i	0.147301	+	0.0850444i
$377$		−	5.39771i		−	0.0143175i
$378$	−6.56377	−	51.0188i	−0.0173645	−	0.134970i
$379$	−579.699			−1.52955			−0.764774	−	0.644299i	$-0.777149\pi$
$379$	−579.699			−1.52955			−0.764774	+	0.644299i	$0.777149\pi$
$380$		0			0
$381$	−305.462	+	176.359i	−0.801738	+	0.462883i
$382$	−94.0549	−	162.908i	−0.246217	−	0.426461i
$383$	−526.581	−	304.022i	−1.37488	−	0.793790i	−0.383346	−	0.923605i	$-0.625228\pi$
$383$	−526.581	−	304.022i	−1.37488	−	0.793790i	−0.991538	+	0.129815i	$0.958562\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−403.366			−1.04499
$387$	103.398	−	179.091i	0.267178	−	0.462767i
$388$	232.462	−	134.212i	0.599128	−	0.345907i
$389$	−57.5081	−	99.6069i	−0.147836	−	0.256059i	0.782592	−	0.622535i	$-0.213897\pi$
$389$	−57.5081	−	99.6069i	−0.147836	−	0.256059i	−0.930427	+	0.366476i	$0.880564\pi$
$390$		0			0
$391$		−	265.284i		−	0.678476i
$392$	−36.6593	+	133.657i	−0.0935187	+	0.340961i
$393$	−134.558			−0.342387
$394$	−217.636	+	376.957i	−0.552376	+	0.956744i
$395$		0			0
$396$	−32.5780	−	56.4268i	−0.0822678	−	0.142492i
$397$	139.249	+	80.3952i	0.350752	+	0.202507i	0.665016	−	0.746829i	$-0.268425\pi$
$397$	139.249	+	80.3952i	0.350752	+	0.202507i	−0.314264	+	0.949336i	$0.601758\pi$
$398$		−	13.7035i		−	0.0344310i
$399$	−191.672	−	251.323i	−0.480382	−	0.629883i
$400$		0			0
$401$	29.4028	−	50.9272i	0.0733238	−	0.127000i	−0.827032	−	0.562154i	$-0.809973\pi$
$401$	29.4028	−	50.9272i	0.0733238	−	0.127000i	0.900356	+	0.435154i	$0.143306\pi$
$402$	93.8780	−	54.2005i	0.233527	−	0.134827i
$403$	10.1434	+	17.5690i	0.0251698	+	0.0435954i
$404$	−265.520	−	153.298i	−0.657227	−	0.379450i
$405$		0			0
$406$	−68.6447	+	8.83141i	−0.169076	+	0.0217522i
$407$	701.523			1.72364
$408$	−47.4498	+	82.1855i	−0.116299	+	0.201435i
$409$	182.052	−	105.108i	0.445114	−	0.256987i	−0.260650	−	0.965433i	$-0.583937\pi$
$409$	182.052	−	105.108i	0.445114	−	0.256987i	0.705765	+	0.708446i	$0.250604\pi$
$410$		0			0
$411$	343.511	+	198.326i	0.835794	+	0.482546i
$412$		−	126.672i		−	0.307456i
$413$	−720.933	−	301.114i	−1.74560	−	0.729089i
$414$	−58.1016			−0.140342
$415$		0			0
$416$	3.78231	−	2.18372i	0.00909209	−	0.00524932i
$417$	53.4702	+	92.6132i	0.128226	+	0.222094i
$418$	−346.719	−	200.178i	−0.829471	−	0.478895i
$419$			690.319i			1.64754i	0.566924	+	0.823770i	$0.308133\pi$
$419$			690.319i			1.64754i	−0.566924	+	0.823770i	$0.691867\pi$
$420$		0			0
$421$	407.084			0.966945			0.483472	−	0.875360i	$-0.339375\pi$
$421$	407.084			0.966945			0.483472	+	0.875360i	$0.339375\pi$
$422$	−124.418	+	215.498i	−0.294829	+	0.510659i
$423$	58.7450	−	33.9164i	0.138877	−	0.0801807i
$424$	105.449	+	182.644i	0.248701	+	0.430763i
$425$		0			0
$426$			78.2735i			0.183741i
$427$	48.4315	+	376.448i	0.113423	+	0.881611i
$428$	87.7110			0.204932
$429$	−7.26082	+	12.5761i	−0.0169250	+	0.0293149i
$430$		0			0
$431$	28.0096	+	48.5141i	0.0649875	+	0.112562i	0.896688	−	0.442662i	$-0.145966\pi$
$431$	28.0096	+	48.5141i	0.0649875	+	0.112562i	−0.831701	+	0.555224i	$0.812633\pi$
$432$	18.0000	+	10.3923i	0.0416667	+	0.0240563i
$433$			71.4593i			0.165033i	0.996590	+	0.0825165i	$0.0262957\pi$
$433$			71.4593i			0.165033i	−0.996590	+	0.0825165i	$0.973704\pi$
$434$	206.835	−	157.743i	0.476578	−	0.363463i
$435$		0			0
$436$	−5.28332	+	9.15098i	−0.0121177	+	0.0209885i
$437$	−309.179	+	178.505i	−0.707504	+	0.408478i
$438$	131.002	+	226.902i	0.299091	+	0.518040i
$439$	−691.975	−	399.512i	−1.57625	−	0.910050i	−0.995376	−	0.0960592i	$-0.969376\pi$
$439$	−691.975	−	399.512i	−1.57625	−	0.910050i	−0.580878	−	0.813991i	$-0.697290\pi$
$440$		0			0
$441$	103.330	+	104.556i	0.234308	+	0.237088i
$442$	21.1507			0.0478523
$443$	−406.200	+	703.559i	−0.916930	+	1.58817i	−0.112879	+	0.993609i	$0.536007\pi$
$443$	−406.200	+	703.559i	−0.916930	+	1.58817i	−0.804051	+	0.594561i	$0.797326\pi$
$444$	−193.802	+	111.892i	−0.436492	+	0.252009i
$445$		0			0
$446$	−61.3419	−	35.4157i	−0.137538	−	0.0794075i
$447$		−	50.7569i		−	0.113550i
$448$	−33.9595	−	44.5281i	−0.0758024	−	0.0993931i
$449$	434.785			0.968340			0.484170	−	0.874974i	$-0.339122\pi$
$449$	434.785			0.968340			0.484170	+	0.874974i	$0.339122\pi$
$450$		0			0
$451$	−52.1797	+	30.1259i	−0.115698	+	0.0667981i
$452$	−106.725	−	184.853i	−0.236117	−	0.408967i
$453$	−245.544	−	141.765i	−0.542039	−	0.312946i
$454$		−	431.601i		−	0.950663i
$455$		0			0
$456$	127.713			0.280071
$457$	−372.524	+	645.231i	−0.815151	+	1.41188i	0.0940682	+	0.995566i	$0.470013\pi$
$457$	−372.524	+	645.231i	−0.815151	+	1.41188i	−0.909219	+	0.416317i	$0.863320\pi$
$458$	499.822	−	288.572i	1.09131	−	0.630071i
$459$	50.3281	+	87.1709i	0.109647	+	0.189915i
$460$		0			0
$461$		−	516.757i		−	1.12095i	−0.828172	−	0.560474i	$-0.810619\pi$
$461$		−	516.757i		−	1.12095i	0.828172	−	0.560474i	$-0.189381\pi$
$462$	171.815	+	71.7622i	0.371893	+	0.155329i
$463$	538.823			1.16376			0.581882	−	0.813273i	$-0.302316\pi$
$463$	538.823			1.16376			0.581882	+	0.813273i	$0.302316\pi$
$464$	13.9826	−	24.2186i	0.0301350	−	0.0521953i
$465$		0			0
$466$	153.307	+	265.536i	0.328985	+	0.569819i
$467$	−549.839	−	317.450i	−1.17739	−	0.679764i	−0.221977	−	0.975052i	$-0.571251\pi$
$467$	−549.839	−	317.450i	−1.17739	−	0.679764i	−0.955408	+	0.295288i	$0.904584\pi$
$468$		−	4.63236i		−	0.00989821i
$469$	−119.392	+	285.850i	−0.254566	+	0.609489i
$470$		0			0
$471$	−180.741	+	313.053i	−0.383740	+	0.664657i
$472$	273.394	−	157.844i	0.579226	−	0.334416i
$473$	374.279	+	648.269i	0.791286	+	1.37055i
$474$	−62.9641	−	36.3524i	−0.132836	−	0.0766928i
$475$		0			0
$476$	−34.6055	−	268.981i	−0.0727007	−	0.565087i
$477$	223.692			0.468955
$478$	275.587	−	477.331i	0.576542	−	0.998600i
$479$	−427.580	+	246.863i	−0.892650	+	0.515372i	−0.874809	−	0.484469i	$-0.839013\pi$
$479$	−427.580	+	246.863i	−0.892650	+	0.515372i	−0.0178420	+	0.999841i	$0.505680\pi$
$480$		0			0
$481$	43.1937	+	24.9379i	0.0897997	+	0.0518459i
$482$			98.0915i			0.203509i
$483$	132.025	−	100.689i	0.273344	−	0.208467i
$484$	−6.14906			−0.0127047
$485$		0			0
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	−165.873	−	287.301i	−0.340603	−	0.589941i	0.643942	−	0.765074i	$-0.277298\pi$
$487$	−165.873	−	287.301i	−0.340603	−	0.589941i	−0.984545	+	0.175133i	$0.943964\pi$
$488$	−132.815	−	76.6808i	−0.272162	−	0.157133i
$489$		−	241.046i		−	0.492937i
$490$		0			0
$491$	−744.294			−1.51587			−0.757937	−	0.652328i	$-0.773793\pi$
$491$	−744.294			−1.51587			−0.757937	+	0.652328i	$0.773793\pi$
$492$	9.61009	−	16.6452i	0.0195327	−	0.0338316i
$493$	117.287	−	67.7154i	0.237904	−	0.137354i
$494$	−14.2319	−	24.6505i	−0.0288096	−	0.0498997i
$495$		0			0
$496$			105.105i			0.211906i
$497$	−135.647	−	177.862i	−0.272932	−	0.357872i
$498$	−38.7389			−0.0777890
$499$	252.414	−	437.194i	0.505840	−	0.876141i	−0.494137	−	0.869384i	$-0.664516\pi$
$499$	252.414	−	437.194i	0.505840	−	0.876141i	0.999977	−	0.00675693i	$-0.00215081\pi$
$500$		0			0
$501$	47.1138	+	81.6034i	0.0940394	+	0.162881i
$502$	−314.308	−	181.466i	−0.626111	−	0.361486i
$503$			402.412i			0.800024i	0.916510	+	0.400012i	$0.130994\pi$
$503$			402.412i			0.800024i	−0.916510	+	0.400012i	$0.869006\pi$
$504$	−58.9114	+	7.57919i	−0.116888	+	0.0150381i
$505$		0			0
$506$	105.158	−	182.138i	0.207821	−	0.359957i
$507$	252.606	−	145.842i	0.498236	−	0.287657i
$508$	203.641	+	352.717i	0.400869	+	0.694325i
$509$	409.218	+	236.262i	0.803965	+	0.464169i	0.844856	−	0.534994i	$-0.179686\pi$
$509$	409.218	+	236.262i	0.803965	+	0.464169i	−0.0408910	+	0.999164i	$0.513020\pi$
$510$		0			0
$511$	−690.895	−	288.568i	−1.35204	−	0.564712i
$512$	22.6274			0.0441942
$513$	67.7298	−	117.311i	0.132027	−	0.228677i
$514$	−246.070	+	142.069i	−0.478735	+	0.276398i
$515$		0			0
$516$	−206.796	−	119.394i	−0.400768	−	0.231383i
$517$			245.540i			0.474933i
$518$	246.473	−	590.111i	0.475817	−	1.13921i
$519$	−108.745			−0.209527
$520$		0			0
$521$	48.2368	−	27.8496i	0.0925851	−	0.0534540i	−0.452993	−	0.891514i	$-0.649644\pi$
$521$	48.2368	−	27.8496i	0.0925851	−	0.0534540i	0.545578	+	0.838060i	$0.316310\pi$
$522$	−14.8308	−	25.6877i	−0.0284115	−	0.0492102i
$523$	−459.405	−	265.238i	−0.878403	−	0.507146i	−0.00827171	−	0.999966i	$-0.502633\pi$
$523$	−459.405	−	265.238i	−0.878403	−	0.507146i	−0.870132	+	0.492819i	$0.835966\pi$
$524$			155.374i			0.296516i
$525$		0			0
$526$	−711.336			−1.35235
$527$	−254.503	+	440.812i	−0.482928	+	0.836456i
$528$	−65.1561	+	37.6179i	−0.123402	+	0.0712460i
$529$	170.728	+	295.709i	0.322737	+	0.558997i
$530$		0			0
$531$		−	334.838i		−	0.630581i
$532$	−290.203	+	221.324i	−0.545495	+	0.416023i
$533$	−4.28369			−0.00803694
$534$	45.0226	−	77.9815i	0.0843120	−	0.146033i
$535$		0			0
$536$	−62.5853	−	108.401i	−0.116764	−	0.202241i
$537$	211.193	+	121.933i	0.393284	+	0.227062i
$538$		−	198.823i		−	0.369559i
$539$	−514.780	+	134.686i	−0.955065	+	0.249882i
$540$		0			0
$541$	−222.070	+	384.636i	−0.410480	+	0.710972i	−0.994942	−	0.100449i	$-0.967972\pi$
$541$	−222.070	+	384.636i	−0.410480	+	0.710972i	0.584462	+	0.811421i	$0.301306\pi$
$542$	−146.806	+	84.7586i	−0.270860	+	0.156381i
$543$	193.112	+	334.480i	0.355640	+	0.615986i
$544$	94.8996	+	54.7903i	0.174448	+	0.100718i
$545$		0			0
$546$	8.02783	+	10.5262i	0.0147030	+	0.0192787i
$547$	308.345			0.563702			0.281851	−	0.959458i	$-0.409052\pi$
$547$	308.345			0.563702			0.281851	+	0.959458i	$0.409052\pi$
$548$	229.008	−	396.653i	0.417897	−	0.723819i
$549$	−140.872	+	81.3323i	−0.256597	+	0.148146i
$550$		0			0
$551$	−157.840	−	91.1289i	−0.286461	−	0.165388i
$552$			67.0900i			0.121540i
$553$	206.073	−	26.5121i	0.372645	−	0.0479422i
$554$	151.330			0.273160
$555$		0			0
$556$	106.940	−	61.7421i	0.192339	−	0.111047i
$557$	223.840	+	387.702i	0.401867	+	0.696054i	0.993951	−	0.109822i	$-0.0350281\pi$
$557$	223.840	+	387.702i	0.401867	+	0.696054i	−0.592084	+	0.805876i	$0.701695\pi$
$558$	96.5452	+	55.7404i	0.173020	+	0.0998932i
$559$			53.2197i			0.0952052i
$560$		0			0
$561$	−364.354			−0.649472
$562$	60.4709	−	104.739i	0.107599	−	0.186368i
$563$	733.087	−	423.248i	1.30211	−	0.751773i	0.321343	−	0.946963i	$-0.395866\pi$
$563$	733.087	−	423.248i	1.30211	−	0.751773i	0.980765	+	0.195190i	$0.0625324\pi$
$564$	−39.1633	−	67.8328i	−0.0694385	−	0.120271i
$565$		0			0
$566$			554.403i			0.979511i
$567$	−24.2806	+	58.1331i	−0.0428229	+	0.102527i
$568$	90.3825			0.159124
$569$	−175.038	+	303.174i	−0.307623	+	0.532819i	−0.977842	−	0.209345i	$-0.932867\pi$
$569$	−175.038	+	303.174i	−0.307623	+	0.532819i	0.670219	+	0.742164i	$0.266200\pi$
$570$		0			0
$571$	382.891	+	663.186i	0.670562	+	1.16145i	0.977745	+	0.209797i	$0.0672803\pi$
$571$	382.891	+	663.186i	0.670562	+	1.16145i	−0.307183	+	0.951650i	$0.599386\pi$
$572$	14.5216	+	8.38408i	0.0253875	+	0.0146575i
$573$			230.387i			0.402071i
$574$	7.00871	+	54.4772i	0.0122103	+	0.0949081i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	91.9471	−	53.0857i	0.159354	−	0.0920029i	−0.418203	−	0.908354i	$-0.637340\pi$
$577$	91.9471	−	53.0857i	0.159354	−	0.0920029i	0.577556	+	0.816351i	$0.304006\pi$
$578$	60.9862	+	105.631i	0.105512	+	0.182753i
$579$	427.834	+	247.010i	0.738919	+	0.426615i
$580$		0			0
$581$	88.0271	−	67.1341i	0.151510	−	0.115549i
$582$	−328.750			−0.564863
$583$	−404.858	+	701.234i	−0.694439	+	1.20280i
$584$	262.003	−	151.268i	0.448636	−	0.259020i
$585$		0			0
$586$	613.101	+	353.974i	1.04625	+	0.604051i
$587$		−	802.707i		−	1.36747i	−0.729729	−	0.683737i	$-0.760354\pi$
$587$		−	802.707i		−	1.36747i	0.729729	−	0.683737i	$-0.239646\pi$
$588$	120.731	−	119.315i	0.205324	−	0.202917i
$589$	685.002			1.16299
$590$		0			0
$591$	461.676	−	266.549i	0.781178	−	0.451013i
$592$	129.202	+	223.784i	0.218246	+	0.378013i
$593$	73.6360	+	42.5138i	0.124175	+	0.0716927i	0.560801	−	0.827951i	$-0.310493\pi$
$593$	73.6360	+	42.5138i	0.124175	+	0.0716927i	−0.436626	+	0.899643i	$0.643827\pi$
$594$			79.7996i			0.134343i
$595$		0			0
$596$	−58.6090			−0.0983373
$597$	−8.39167	+	14.5348i	−0.0140564	+	0.0243464i
$598$	12.9494	−	7.47633i	0.0216545	−	0.0125022i
$599$	−185.040	−	320.498i	−0.308914	−	0.535055i	0.669211	−	0.743072i	$-0.266632\pi$
$599$	−185.040	−	320.498i	−0.308914	−	0.535055i	−0.978125	+	0.208017i	$0.933299\pi$
$600$		0			0
$601$			462.547i			0.769628i	0.922994	+	0.384814i	$0.125734\pi$
$601$			462.547i			0.769628i	−0.922994	+	0.384814i	$0.874266\pi$
$602$	676.814	−	87.0748i	1.12428	−	0.144643i
$603$	−132.764			−0.220172
$604$	−163.696	+	283.529i	−0.271020	+	0.469420i
$605$		0			0
$606$	187.751	+	325.194i	0.309820	+	0.536624i
$607$	598.134	+	345.333i	0.985394	+	0.568918i	0.903894	−	0.427756i	$-0.140696\pi$
$607$	598.134	+	345.333i	0.985394	+	0.568918i	0.0814998	+	0.996673i	$0.474029\pi$
$608$		−	147.470i		−	0.242549i
$609$	78.2168	+	32.6690i	0.128435	+	0.0536436i
$610$		0			0
$611$	−8.72851	+	15.1182i	−0.0142856	+	0.0247434i
$612$	100.656	−	58.1139i	0.164471	−	0.0949574i
$613$	−49.1726	−	85.1695i	−0.0802163	−	0.138939i	0.823126	−	0.567858i	$-0.192228\pi$
$613$	−49.1726	−	85.1695i	−0.0802163	−	0.138939i	−0.903343	+	0.428919i	$0.858894\pi$
$614$	487.658	+	281.550i	0.794232	+	0.458550i
$615$		0			0
$616$	82.8639	−	198.394i	0.134519	−	0.322069i
$617$	794.667			1.28795			0.643976	−	0.765045i	$-0.277283\pi$
$617$	794.667			1.28795			0.643976	+	0.765045i	$0.277283\pi$
$618$	−77.5702	+	134.356i	−0.125518	+	0.217404i
$619$	−114.032	+	65.8365i	−0.184220	+	0.106359i	−0.589274	−	0.807933i	$-0.700586\pi$
$619$	−114.032	+	65.8365i	−0.184220	+	0.106359i	0.405054	+	0.914293i	$0.367253\pi$
$620$		0			0
$621$	61.6261	+	35.5798i	0.0992369	+	0.0572944i
$622$			525.998i			0.845656i
$623$	32.8353	+	255.222i	0.0527052	+	0.409666i
$624$	−5.34899			−0.00857210
$625$		0			0
$626$	517.438	−	298.743i	0.826579	−	0.477225i
$627$	245.167	+	424.642i	0.391016	+	0.677260i
$628$	361.483	+	208.702i	0.575609	+	0.332328i
$629$			1251.40i			1.98951i
$630$		0			0
$631$	−1086.67			−1.72213			−0.861067	−	0.508492i	$-0.830203\pi$
$631$	−1086.67			−1.72213			−0.861067	+	0.508492i	$0.830203\pi$
$632$	−41.9761	+	72.7047i	−0.0664179	+	0.115039i
$633$	263.930	−	152.380i	0.416952	−	0.240727i
$634$	152.864	+	264.768i	0.241110	+	0.417615i
$635$		0			0
$636$		−	258.297i		−	0.406127i
$637$	−36.4835	−	10.0067i	−0.0572740	−	0.0157091i
$638$	107.369			0.168289
$639$	47.9326	−	83.0216i	0.0750118	−	0.129924i
$640$		0			0
$641$	310.496	+	537.795i	0.484393	+	0.838993i	0.999839	−	0.0179287i	$-0.00570718\pi$
$641$	310.496	+	537.795i	0.484393	+	0.838993i	−0.515446	+	0.856922i	$0.672374\pi$
$642$	−93.0316	−	53.7118i	−0.144909	−	0.0836632i
$643$		−	75.8433i		−	0.117952i	−0.998259	−	0.0589761i	$-0.981216\pi$
$643$		−	75.8433i		−	0.117952i	0.998259	−	0.0589761i	$-0.0187836\pi$
$644$	−116.266	−	152.450i	−0.180538	−	0.236723i
$645$		0			0
$646$	357.085	−	618.490i	0.552763	−	0.957414i
$647$	−136.611	+	78.8723i	−0.211145	+	0.121905i	−0.601843	−	0.798614i	$-0.705567\pi$
$647$	−136.611	+	78.8723i	−0.211145	+	0.121905i	0.390698	+	0.920519i	$0.372234\pi$
$648$	−12.7279	−	22.0454i	−0.0196419	−	0.0340207i
$649$	1049.66	+	606.021i	1.61735	+	0.933777i
$650$		0			0
$651$	−315.979	+	40.6519i	−0.485374	+	0.0624453i
$652$	−278.336			−0.426896
$653$	−359.691	+	623.004i	−0.550829	+	0.954064i	0.447386	+	0.894341i	$0.352355\pi$
$653$	−359.691	+	623.004i	−0.550829	+	0.954064i	−0.998215	+	0.0597229i	$0.980978\pi$
$654$	11.2076	−	6.47072i	0.0171370	−	0.00989407i
$655$		0			0
$656$	−19.2202	−	11.0968i	−0.0292991	−	0.0169158i
$657$		−	320.887i		−	0.488413i
$658$	206.545	+	86.2681i	0.313898	+	0.131106i
$659$	−10.5090			−0.0159469			−0.00797343	−	0.999968i	$-0.502538\pi$
$659$	−10.5090			−0.0159469			−0.00797343	+	0.999968i	$0.502538\pi$
$660$		0			0
$661$	1040.86	−	600.938i	1.57467	−	0.909135i	0.579083	−	0.815268i	$-0.303411\pi$
$661$	1040.86	−	600.938i	1.57467	−	0.909135i	0.995585	−	0.0938667i	$-0.0299227\pi$
$662$	−149.525	−	258.985i	−0.225868	−	0.391215i
$663$	−22.4337	−	12.9521i	−0.0338367	−	0.0195356i
$664$			44.7318i			0.0673672i
$665$		0			0
$666$	274.078			0.411529
$667$	47.8719	−	82.9166i	0.0717720	−	0.124313i
$668$	94.2275	−	54.4023i	0.141059	−	0.0814405i
$669$	43.3753	+	75.1282i	0.0648360	+	0.112299i
$670$		0			0
$671$		−	588.810i		−	0.877512i
$672$	8.75169	+	68.0251i	0.0130234	+	0.101228i
$673$	−1070.49			−1.59062			−0.795310	−	0.606203i	$-0.792692\pi$
$673$	−1070.49			−1.59062			−0.795310	+	0.606203i	$0.792692\pi$
$674$	184.116	−	318.898i	0.273169	−	0.473143i
$675$		0			0
$676$	−168.404	−	291.684i	−0.249118	−	0.431485i
$677$	517.691	+	298.889i	0.764685	+	0.441491i	0.830975	−	0.556309i	$-0.187783\pi$
$677$	517.691	+	298.889i	0.764685	+	0.441491i	−0.0662906	+	0.997800i	$0.521116\pi$
$678$			261.422i			0.385578i
$679$	747.024	−	569.720i	1.10018	−	0.839058i
$680$		0			0
$681$	−264.301	+	457.782i	−0.388107	+	0.672221i
$682$	−349.473	+	201.768i	−0.512424	+	0.295848i
$683$	261.801	+	453.453i	0.383310	+	0.663913i	0.991533	−	0.129853i	$-0.0414506\pi$
$683$	261.801	+	453.453i	0.383310	+	0.663913i	−0.608223	+	0.793766i	$0.708117\pi$
$684$	−135.460	−	78.2076i	−0.198040	−	0.114339i
$685$		0			0
$686$	−67.5667	+	480.346i	−0.0984937	+	0.700214i
$687$	−706.855			−1.02890
$688$	−137.864	+	238.788i	−0.200384	+	0.347075i
$689$	−49.8552	+	28.7839i	−0.0723588	+	0.0417764i
$690$		0			0
$691$	170.271	+	98.3059i	0.246412	+	0.142266i	0.618120	−	0.786083i	$-0.287894\pi$
$691$	170.271	+	98.3059i	0.246412	+	0.142266i	−0.371708	+	0.928350i	$0.621228\pi$
$692$			125.567i			0.181456i
$693$	−138.292	−	181.330i	−0.199555	−	0.261659i
$694$	723.988			1.04321
$695$		0			0
$696$	−29.6616	+	17.1251i	−0.0426173	+	0.0246051i
$697$	−53.7398	−	93.0800i	−0.0771015	−	0.133544i
$698$	646.509	+	373.262i	0.926231	+	0.534760i
$699$		−	375.524i		−	0.537231i
$700$		0			0
$701$	132.968			0.189683			0.0948414	−	0.995492i	$-0.469766\pi$
$701$	132.968			0.189683			0.0948414	+	0.995492i	$0.469766\pi$
$702$	−2.83673	+	4.91336i	−0.00404093	+	0.00699909i
$703$	1458.47	−	842.046i	2.07463	−	1.19779i
$704$	43.4374	+	75.2358i	0.0617008	+	0.106869i
$705$		0			0
$706$		−	193.062i		−	0.273460i
$707$	−990.186	−	413.573i	−1.40055	−	0.584969i
$708$	−386.638			−0.546099
$709$	−151.618	+	262.609i	−0.213847	+	0.370394i	−0.952915	−	0.303237i	$-0.901933\pi$
$709$	−151.618	+	262.609i	−0.213847	+	0.370394i	0.739068	+	0.673631i	$0.235266\pi$
$710$		0			0
$711$	44.5224	+	77.1150i	0.0626194	+	0.108460i
$712$	−90.0453	−	51.9877i	−0.126468	−	0.0730164i
$713$			359.846i			0.504692i
$714$	−128.012	+	306.489i	−0.179289	+	0.429257i
$715$		0			0
$716$	140.796	−	243.865i	0.196642	−	0.340594i
$717$	−584.608	+	337.524i	−0.815354	+	0.470745i
$718$	393.893	+	682.243i	0.548598	+	0.950200i
$719$	−118.785	−	68.5808i	−0.165209	−	0.0953835i	0.415116	−	0.909769i	$-0.363741\pi$
$719$	−118.785	−	68.5808i	−0.165209	−	0.0953835i	−0.580325	+	0.814385i	$0.697074\pi$
$720$		0			0
$721$	−56.5726	−	439.727i	−0.0784640	−	0.609884i
$722$	−450.574			−0.624063
$723$	60.0686	−	104.042i	0.0830824	−	0.143903i
$724$	386.225	−	222.987i	0.533460	−	0.307993i
$725$		0			0
$726$	6.52207	+	3.76552i	0.00898356	+	0.00518666i
$727$		−	741.058i		−	1.01934i	−0.860371	−	0.509669i	$-0.829768\pi$
$727$		−	741.058i		−	1.01934i	0.860371	−	0.509669i	$-0.170232\pi$
$728$	12.1546	−	9.26974i	0.0166959	−	0.0127332i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−1156.41	+	667.652i	−1.58195	+	0.913340i
$732$	93.9144	+	162.665i	0.128298	+	0.222219i
$733$	−124.538	−	71.9021i	−0.169902	−	0.0980929i	0.412638	−	0.910895i	$-0.364608\pi$
$733$	−124.538	−	71.9021i	−0.169902	−	0.0980929i	−0.582540	+	0.812802i	$0.697941\pi$
$734$		−	166.908i		−	0.227396i
$735$		0			0
$736$	77.4688			0.105257
$737$	240.288	−	416.190i	0.326035	−	0.564709i
$738$	−20.3861	+	11.7699i	−0.0276234	+	0.0159484i
$739$	522.722	+	905.381i	0.707337	+	1.22514i	0.965842	+	0.259133i	$0.0834368\pi$
$739$	522.722	+	905.381i	0.707337	+	1.22514i	−0.258505	+	0.966010i	$0.583230\pi$
$740$		0			0
$741$			34.8610i			0.0470459i
$742$	447.626	+	586.932i	0.603269	+	0.791014i
$743$	−660.175			−0.888526			−0.444263	−	0.895896i	$-0.646534\pi$
$743$	−660.175			−0.888526			−0.444263	+	0.895896i	$0.646534\pi$
$744$	64.3635	−	111.481i	0.0865101	−	0.149840i
$745$		0			0
$746$	−225.123	−	389.925i	−0.301774	−	0.522687i
$747$	41.0888	+	23.7226i	0.0550051	+	0.0317572i
$748$			420.720i			0.562459i
$749$	304.479	−	39.1724i	0.406514	−	0.0522996i
$750$		0			0
$751$	−79.4795	+	137.663i	−0.105832	+	0.183306i	−0.914078	−	0.405539i	$-0.867084\pi$
$751$	−79.4795	+	137.663i	−0.105832	+	0.183306i	0.808246	+	0.588845i	$0.200417\pi$
$752$	−78.3266	+	45.2219i	−0.104158	+	0.0601355i
$753$	222.249	+	384.947i	0.295152	+	0.511218i
$754$	6.61082	+	3.81676i	0.00876767	+	0.00506202i
$755$		0			0
$756$	67.1263	+	28.0368i	0.0887914	+	0.0370857i
$757$	777.212			1.02670			0.513350	−	0.858179i	$-0.328404\pi$
$757$	777.212			1.02670			0.513350	+	0.858179i	$0.328404\pi$
$758$	409.909	−	709.983i	0.540777	−	0.936653i
$759$	−223.073	+	128.791i	−0.293904	+	0.169686i
$760$		0			0
$761$	−989.290	−	571.167i	−1.29999	−	0.750548i	−0.319585	−	0.947558i	$-0.603544\pi$
$761$	−989.290	−	571.167i	−1.29999	−	0.750548i	−0.980401	+	0.197010i	$0.936877\pi$
$762$		−	498.817i		−	0.654616i
$763$	−14.2536	+	34.1262i	−0.0186809	+	0.0447263i
$764$	266.028			0.348204
$765$		0			0
$766$	744.698	−	429.951i	0.972190	−	0.561294i
$767$	43.0859	+	74.6270i	0.0561746	+	0.0972973i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$		−	166.927i		−	0.217070i	−0.994093	−	0.108535i	$-0.965384\pi$
$769$		−	166.927i		−	0.217070i	0.994093	−	0.108535i	$-0.0346159\pi$
$770$		0			0
$771$	347.995			0.451356
$772$	285.223	−	494.020i	0.369459	−	0.639922i
$773$	−293.663	+	169.546i	−0.379901	+	0.219336i	−0.677775	−	0.735269i	$-0.737056\pi$
$773$	−293.663	+	169.546i	−0.379901	+	0.219336i	0.297874	+	0.954605i	$0.403722\pi$
$774$	146.227	+	253.272i	0.188924	+	0.327225i
$775$		0			0
$776$			379.608i			0.489186i
$777$	−622.792	+	474.974i	−0.801534	+	0.611292i
$778$	162.657			0.209071
$779$	−72.3210	+	125.264i	−0.0928383	+	0.160801i
$780$		0			0
$781$	173.505	+	300.520i	0.222158	+	0.384789i
$782$	324.905	+	187.584i	0.415480	+	0.239877i
$783$			36.3279i			0.0463958i
$784$	−137.773	−	139.408i	−0.175731	−	0.177816i
$785$		0			0
$786$	95.1470	−	164.799i	0.121052	−	0.209668i
$787$	−302.268	+	174.514i	−0.384076	+	0.221746i	−0.679590	−	0.733592i	$-0.737842\pi$
$787$	−302.268	+	174.514i	−0.384076	+	0.221746i	0.295514	+	0.955338i	$0.404509\pi$
$788$	−307.784	−	533.098i	−0.390589	−	0.676520i
$789$	754.486	+	435.602i	0.956256	+	0.552094i
$790$		0			0
$791$	−453.041	−	594.033i	−0.572744	−	0.750989i
$792$	92.1446			0.116344
$793$	20.9311	−	36.2538i	0.0263949	−	0.0457173i
$794$	−196.927	+	113.696i	−0.248019	+	0.143194i
$795$		0			0
$796$	16.7833	+	9.68987i	0.0210846	+	0.0121732i
$797$		−	137.702i		−	0.172776i	−0.996262	−	0.0863878i	$-0.972468\pi$
$797$		−	137.702i		−	0.172776i	0.996262	−	0.0863878i	$-0.0275324\pi$
$798$	443.340	−	57.0374i	0.555564	−	0.0714755i
$799$	−438.004			−0.548190
$800$		0			0
$801$	−95.5074	+	55.1412i	−0.119235	+	0.0688405i
$802$	41.5819	+	72.0219i	0.0518477	+	0.0898029i
$803$	1005.92	+	580.771i	1.25271	+	0.723252i
$804$			153.302i			0.190674i
$805$		0			0
$806$	−28.6900			−0.0355955
$807$	−121.754	+	210.884i	−0.150872	+	0.261318i
$808$	375.502	−	216.796i	0.464730	−	0.268312i
$809$	474.092	+	821.151i	0.586022	+	1.01502i	0.994747	+	0.102362i	$0.0326400\pi$
$809$	474.092	+	821.151i	0.586022	+	1.01502i	−0.408726	+	0.912657i	$0.634027\pi$
$810$		0			0
$811$			434.987i			0.536359i	0.963369	+	0.268180i	$0.0864221\pi$
$811$			434.987i			0.536359i	−0.963369	+	0.268180i	$0.913578\pi$
$812$	37.7229	−	90.3169i	0.0464568	−	0.111228i
$813$	207.615			0.255370
$814$	−496.052	+	859.186i	−0.609400	+	1.05551i
$815$		0			0
$816$	−67.1042	−	116.228i	−0.0822355	−	0.142436i
$817$	1556.25	+	898.502i	1.90484	+	1.09976i
$818$			297.289i			0.363434i
$819$	−2.06885	−	16.0807i	−0.00252607	−	0.0196346i
$820$		0			0
$821$	−497.701	+	862.043i	−0.606213	+	1.04999i	0.385646	+	0.922647i	$0.373979\pi$
$821$	−497.701	+	862.043i	−0.606213	+	1.04999i	−0.991859	+	0.127344i	$0.959355\pi$
$822$	−485.798	+	280.476i	−0.590996	+	0.341211i
$823$	117.517	+	203.545i	0.142791	+	0.247321i	0.928547	−	0.371216i	$-0.121059\pi$
$823$	117.517	+	203.545i	0.142791	+	0.247321i	−0.785756	+	0.618537i	$0.787726\pi$
$824$	155.140	+	89.5704i	0.188277	+	0.108702i
$825$		0			0
$826$	878.564	−	670.039i	1.06364	−	0.811186i
$827$	−267.742			−0.323751			−0.161876	−	0.986811i	$-0.551754\pi$
$827$	−267.742			−0.323751			−0.161876	+	0.986811i	$0.551754\pi$
$828$	41.0841	−	71.1597i	0.0496184	−	0.0859416i
$829$	1367.65	−	789.613i	1.64976	−	0.952489i	0.672593	−	0.740013i	$-0.265181\pi$
$829$	1367.65	−	789.613i	1.64976	−	0.952489i	0.977166	−	0.212476i	$-0.0681527\pi$
$830$		0			0
$831$	−160.510	−	92.6706i	−0.193153	−	0.111517i
$832$			6.17648i			0.00742366i
$833$	−240.258	−	918.284i	−0.288425	−	1.10238i
$834$	−151.237			−0.181339
$835$		0			0
$836$	490.334	−	283.095i	0.586524	−	0.338630i
$837$	−68.2678	−	118.243i	−0.0815625	−	0.141270i
$838$	−845.465	−	488.129i	−1.00891	−	0.582493i
$839$			502.512i			0.598942i	0.954105	+	0.299471i	$0.0968102\pi$
$839$			502.512i			0.598942i	−0.954105	+	0.299471i	$0.903190\pi$
$840$		0			0
$841$	−792.122			−0.941881
$842$	−287.852	+	498.574i	−0.341867	+	0.592130i
$843$	−128.278	+	74.0614i	−0.152169	+	0.0878545i
$844$	−175.954	−	304.761i	−0.208476	−	0.361091i
$845$		0			0
$846$			95.9301i			0.113393i
$847$	−21.3458	+	2.74622i	−0.0252016	+	0.00324229i
$848$	−298.256			−0.351717
$849$	339.501	−	588.033i	0.399884	−	0.692619i
$850$		0			0
$851$	442.344	+	766.162i	0.519793	+	0.900308i
$852$	−95.8651	−	55.3477i	−0.112518	−	0.0649621i
$853$			880.120i			1.03179i	0.856651	+	0.515897i	$0.172541\pi$
$853$			880.120i			1.03179i	−0.856651	+	0.515897i	$0.827459\pi$
$854$	−495.299	−	206.873i	−0.579975	−	0.242240i
$855$		0			0
$856$	−62.0210	+	107.424i	−0.0724545	+	0.125495i
$857$	316.900	−	182.962i	0.369778	−	0.213492i	−0.303583	−	0.952805i	$-0.598183\pi$
$857$	316.900	−	182.962i	0.369778	−	0.213492i	0.673362	+	0.739313i	$0.264850\pi$
$858$	−10.2684	−	17.7853i	−0.0119678	−	0.0207288i
$859$	−957.688	−	552.921i	−1.11489	−	0.643680i	−0.174796	−	0.984605i	$-0.555927\pi$
$859$	−957.688	−	552.921i	−1.11489	−	0.643680i	−0.940091	+	0.340924i	$0.889260\pi$
$860$		0			0
$861$	25.9265	−	62.0738i	0.0301121	−	0.0720950i
$862$	−79.2231			−0.0919062
$863$	490.021	−	848.741i	0.567811	−	0.983477i	−0.428971	−	0.903318i	$-0.641124\pi$
$863$	490.021	−	848.741i	0.567811	−	0.983477i	0.996782	−	0.0801589i	$-0.0255428\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$		0			0
$866$	−87.5194	−	50.5293i	−0.101062	−	0.0583480i
$867$		−	149.385i		−	0.172301i
$868$	46.9408	+	364.861i	0.0540793	+	0.420347i
$869$	−322.323			−0.370912
$870$		0			0
$871$	29.5896	−	17.0836i	0.0339720	−	0.0196138i
$872$	−7.47174	−	12.9414i	−0.00856851	−	0.0148411i
$873$	348.692	+	201.318i	0.399419	+	0.230604i
$874$		−	504.888i		−	0.577675i
$875$		0			0
$876$	−370.529			−0.422978
$877$	695.577	−	1204.77i	0.793132	−	1.37374i	−0.130887	−	0.991397i	$-0.541782\pi$
$877$	695.577	−	1204.77i	0.793132	−	1.37374i	0.924019	−	0.382347i	$-0.124884\pi$
$878$	978.601	−	564.995i	1.11458	−	0.643503i
$879$	−433.528	−	750.892i	−0.493206	−	0.854257i
$880$		0			0
$881$		−	234.790i		−	0.266504i	−0.991082	−	0.133252i	$-0.957458\pi$
$881$		−	234.790i		−	0.266504i	0.991082	−	0.133252i	$-0.0425419\pi$
$882$	−201.120	+	52.6206i	−0.228027	+	0.0596606i
$883$	−977.996			−1.10758			−0.553791	−	0.832655i	$-0.686820\pi$
$883$	−977.996			−1.10758			−0.553791	+	0.832655i	$0.686820\pi$
$884$	−14.9558	+	25.9042i	−0.0169184	+	0.0293034i
$885$		0			0
$886$	−574.454	−	994.983i	−0.648367	−	1.12301i
$887$	−1196.32	−	690.695i	−1.34872	−	0.778686i	−0.360655	−	0.932699i	$-0.617447\pi$
$887$	−1196.32	−	690.695i	−1.34872	−	0.778686i	−0.988069	+	0.154013i	$0.950780\pi$
$888$		−	316.478i		−	0.356394i
$889$	864.445	+	1133.47i	0.972379	+	1.27500i
$890$		0			0
$891$	48.8671	−	84.6403i	0.0548452	−	0.0949947i
$892$	86.7505	−	50.0854i	0.0972539	−	0.0561496i
$893$	294.725	+	510.478i	0.330039	+	0.571644i
$894$	62.1643	+	35.8906i	0.0695350	+	0.0401460i
$895$		0			0
$896$	78.5486	−	10.1056i	0.0876658	−	0.0112786i
$897$	−18.3132			−0.0204160
$898$	−307.439	+	532.501i	−0.342360	+	0.592985i
$899$	−159.094	+	91.8528i	−0.176967	+	0.102172i
$900$		0			0
$901$	−1250.89	−	722.200i	−1.38833	−	0.801554i
$902$		−	85.2090i		−	0.0944668i
$903$	−771.192	−	322.105i	−0.854033	−	0.356706i
$904$	301.864			0.333920
$905$		0			0
$906$	347.251	−	200.486i	0.383280	−	0.221287i
$907$	−523.235	−	906.269i	−0.576885	−	0.999194i	−0.995834	−	0.0911843i	$-0.970935\pi$
$907$	−523.235	−	906.269i	−0.576885	−	0.999194i	0.418949	−	0.908010i	$-0.362399\pi$
$908$	528.601	+	305.188i	0.582160	+	0.336110i
$909$		−	459.894i		−	0.505934i
$910$		0			0
$911$	−942.221			−1.03427			−0.517136	−	0.855903i	$-0.673002\pi$
$911$	−942.221			−1.03427			−0.517136	+	0.855903i	$0.673002\pi$
$912$	−90.3064	+	156.415i	−0.0990202	+	0.171508i
$913$	−148.733	+	85.8708i	−0.162905	+	0.0940535i
$914$	−526.829	−	912.494i	−0.576399	−	0.998352i
$915$		0			0
$916$			816.206i			0.891055i
$917$	69.3914	+	539.365i	0.0756722	+	0.588184i
$918$	−142.349			−0.155065
$919$	−218.878	+	379.108i	−0.238170	+	0.412522i	−0.960189	−	0.279350i	$-0.909881\pi$
$919$	−218.878	+	379.108i	−0.238170	+	0.412522i	0.722019	+	0.691873i	$0.243214\pi$
$920$		0			0
$921$	−344.827	−	597.257i	−0.374405	−	0.648488i
$922$	632.896	+	365.403i	0.686438	+	0.396315i
$923$			24.6712i			0.0267294i
$924$	−209.382	+	159.686i	−0.226604	+	0.172820i
$925$		0			0
$926$	−381.005	+	659.921i	−0.411453	+	0.712657i
$927$	164.551	−	95.0038i	0.177510	−	0.102485i
$928$	19.7744	+	34.2503i	0.0213086	+	0.0369076i
$929$	−1326.88	−	766.072i	−1.42828	−	0.824620i	−0.431299	−	0.902209i	$-0.641944\pi$
$929$	−1326.88	−	766.072i	−1.42828	−	0.824620i	−0.996985	+	0.0775890i	$0.975278\pi$
$930$		0			0
$931$	−908.563	+	897.910i	−0.975900	+	0.964457i
$932$	−433.618			−0.465255
$933$	322.107	−	557.905i	0.345238	−	0.597969i
$934$	777.590	−	448.942i	0.832537	−	0.480666i
$935$		0			0
$936$	5.67346	+	3.27558i	0.00606139	+	0.00349955i
$937$		−	987.468i		−	1.05386i	−0.849908	−	0.526931i	$-0.823343\pi$
$937$		−	987.468i		−	1.05386i	0.849908	−	0.526931i	$-0.176657\pi$
$938$	−265.671	−	348.351i	−0.283231	−	0.371376i
$939$	−731.768			−0.779306
$940$		0			0
$941$	1441.57	−	832.293i	1.53196	−	0.884477i	0.532687	−	0.846312i	$-0.321182\pi$
$941$	1441.57	−	832.293i	1.53196	−	0.884477i	0.999271	−	0.0381649i	$-0.0121512\pi$
$942$	−255.607	−	442.724i	−0.271345	−	0.469983i
$943$	−65.8036	−	37.9917i	−0.0697811	−	0.0402881i
$944$			446.451i			0.472936i
$945$		0			0
$946$	−1058.62			−1.11905
$947$	−341.603	+	591.674i	−0.360721	+	0.624788i	−0.988080	−	0.153943i	$-0.950803\pi$
$947$	−341.603	+	591.674i	−0.360721	+	0.624788i	0.627358	+	0.778731i	$0.284136\pi$
$948$	89.0448	−	51.4100i	0.0939291	−	0.0542300i
$949$	41.2907	+	71.5176i	0.0435097	+	0.0753610i
$950$		0			0
$951$		−	374.438i		−	0.393731i
$952$	353.903	+	147.816i	0.371747	+	0.155269i
$953$	−705.451			−0.740243			−0.370121	−	0.928983i	$-0.620684\pi$
$953$	−705.451			−0.740243			−0.370121	+	0.928983i	$0.620684\pi$
$954$	−158.174	+	273.965i	−0.165801	+	0.287175i
$955$		0			0
$956$	389.739	+	675.048i	0.407677	+	0.706117i
$957$	−113.882	−	65.7496i	−0.118999	−	0.0687038i
$958$		−	698.235i		−	0.728846i
$959$	617.826	−	1479.21i	0.644240	−	1.54245i
$960$		0			0
$961$	−135.278	+	234.309i	−0.140768	+	0.243818i
$962$	−61.0851	+	35.2675i	−0.0634980	+	0.0366606i
$963$	65.7832	+	113.940i	0.0683107	+	0.118318i
$964$	−120.137	−	69.3612i	−0.124624	−	0.0719515i
$965$		0			0
$966$	29.9629	+	232.895i	0.0310175	+	0.241093i
$967$	187.828			0.194238			0.0971188	−	0.995273i	$-0.469037\pi$
$967$	187.828			0.194238			0.0971188	+	0.995273i	$0.469037\pi$
$968$	4.34804	−	7.53103i	0.00449178	−	0.00777999i
$969$	−757.492	+	437.338i	−0.781725	+	0.451329i
$970$		0			0
$971$	244.015	+	140.882i	0.251303	+	0.145090i	0.620361	−	0.784317i	$-0.286986\pi$
$971$	244.015	+	140.882i	0.251303	+	0.145090i	−0.369058	+	0.929406i	$0.620320\pi$
$972$			31.1769i			0.0320750i
$973$	343.658	−	262.091i	0.353194	−	0.269364i
$974$	469.161			0.481685
$975$		0			0
$976$	187.829	−	108.443i	0.192448	−	0.111110i
$977$	434.096	+	751.877i	0.444316	+	0.769577i	0.998004	−	0.0631464i	$-0.0201135\pi$
$977$	434.096	+	751.877i	0.444316	+	0.769577i	−0.553689	+	0.832724i	$0.686780\pi$
$978$	295.220	+	170.445i	0.301861	+	0.174280i
$979$		−	399.199i		−	0.407762i
$980$		0			0
$981$	−15.8500			−0.0161569
$982$	526.296	−	911.571i	0.535943	−	0.928280i
$983$	29.8262	−	17.2202i	0.0303420	−	0.0175180i	−0.484752	−	0.874652i	$-0.661090\pi$
$983$	29.8262	−	17.2202i	0.0303420	−	0.0175180i	0.515094	+	0.857134i	$0.327757\pi$
$984$	13.5907	+	23.5398i	0.0138117	+	0.0239226i
$985$		0			0
$986$			191.528i			0.194248i
$987$	−166.246	−	217.983i	−0.168435	−	0.220855i
$988$	40.2540			0.0407429
$989$	−472.001	+	817.530i	−0.477251	+	0.826623i
$990$		0			0
$991$	225.801	+	391.098i	0.227851	+	0.394650i	0.957171	−	0.289523i	$-0.0934967\pi$
$991$	225.801	+	391.098i	0.227851	+	0.394650i	−0.729320	+	0.684173i	$0.760163\pi$
$992$	−128.727	−	74.3206i	−0.129765	−	0.0749199i
$993$			366.259i			0.368841i
$994$	313.753	−	40.3655i	0.315647	−	0.0406092i
$995$		0			0
$996$	27.3926	−	47.4453i	0.0275026	−	0.0476358i
$997$	1412.73	−	815.641i	1.41698	−	0.818095i	0.420949	−	0.907084i	$-0.361697\pi$
$997$	1412.73	−	815.641i	1.41698	−	0.818095i	0.996033	+	0.0889893i	$0.0283637\pi$
$998$	356.968	+	618.286i	0.357683	+	0.619525i
$999$	−290.704	−	167.838i	−0.290995	−	0.168006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.i.901.2		16
5.2	odd	4		1050.3.q.e.649.5		32
5.3	odd	4		1050.3.q.e.649.11		32
5.4	even	2		210.3.o.b.61.8	yes	16
7.3	odd	6	inner	1050.3.p.i.451.2		16
15.14	odd	2		630.3.v.c.271.2		16
35.3	even	12		1050.3.q.e.199.5		32
35.9	even	6		1470.3.f.d.391.1		16
35.17	even	12		1050.3.q.e.199.11		32
35.19	odd	6		1470.3.f.d.391.7		16
35.24	odd	6		210.3.o.b.31.8	✓	16
105.59	even	6		630.3.v.c.451.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.8	✓	16	35.24	odd	6
210.3.o.b.61.8	yes	16	5.4	even	2
630.3.v.c.271.2		16	15.14	odd	2
630.3.v.c.451.2		16	105.59	even	6
1050.3.p.i.451.2		16	7.3	odd	6	inner
1050.3.p.i.901.2		16	1.1	even	1	trivial
1050.3.q.e.199.5		32	35.3	even	12
1050.3.q.e.199.11		32	35.17	even	12
1050.3.q.e.649.5		32	5.2	odd	4
1050.3.q.e.649.11		32	5.3	odd	4
1470.3.f.d.391.1		16	35.9	even	6
1470.3.f.d.391.7		16	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-4.24494 - 5.56601i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-4.24494 - 5.56601i) q^{7} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(5.42967 + 9.40447i) q^{11} +(-3.00000 - 1.73205i) q^{12} +0.772061i q^{13} +(9.81857 - 1.26320i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-16.7760 + 9.68565i) q^{17} +(2.12132 + 3.67423i) q^{18} +(22.5766 + 13.0346i) q^{19} +(-11.1877 - 4.67280i) q^{21} -15.3574 q^{22} +(-6.84734 + 11.8599i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-0.945577 - 0.545929i) q^{26} -5.19615i q^{27} +(-5.39568 + 12.9185i) q^{28} -6.99131 q^{29} +(22.7559 - 13.1381i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(16.2890 + 9.40447i) q^{33} -27.3952i q^{34} -6.00000 q^{36} +(32.3004 - 55.9459i) q^{37} +(-31.9281 + 18.4337i) q^{38} +(0.668624 + 1.15809i) q^{39} +5.54839i q^{41} +(13.6339 - 10.3979i) q^{42} +68.9320 q^{43} +(10.8593 - 18.8089i) q^{44} +(-9.68361 - 16.7725i) q^{46} +(19.5817 + 11.3055i) q^{47} +6.92820i q^{48} +(-12.9610 + 47.2548i) q^{49} +(-16.7760 + 29.0570i) q^{51} +(1.33725 - 0.772061i) q^{52} +(37.2820 + 64.5742i) q^{53} +(6.36396 + 3.67423i) q^{54} +(-12.0065 - 15.7431i) q^{56} +45.1532 q^{57} +(4.94360 - 8.56257i) q^{58} +(96.6595 - 55.8064i) q^{59} +(-46.9572 - 27.1108i) q^{61} +37.1603i q^{62} +(-20.8283 + 2.67965i) q^{63} +8.00000 q^{64} +(-23.0362 + 13.2999i) q^{66} +(-22.1273 - 38.3255i) q^{67} +(33.5521 + 19.3713i) q^{68} +23.7199i q^{69} +31.9550 q^{71} +(4.24264 - 7.34847i) q^{72} +(92.6322 - 53.4812i) q^{73} +(45.6797 + 79.1195i) q^{74} -52.1384i q^{76} +(29.2968 - 70.1430i) q^{77} -1.89115 q^{78} +(-14.8408 + 25.7050i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-6.79536 - 3.92330i) q^{82} +15.8151i q^{83} +(3.09419 + 24.0505i) q^{84} +(-48.7423 + 84.4242i) q^{86} +(-10.4870 + 6.05465i) q^{87} +(15.3574 + 26.5999i) q^{88} +(-31.8358 - 18.3804i) q^{89} +(4.29730 - 3.27735i) q^{91} +27.3894 q^{92} +(22.7559 - 39.4144i) q^{93} +(-27.6926 + 15.9884i) q^{94} +(-8.48528 - 4.89898i) q^{96} +134.212i q^{97} +(-48.7102 - 49.2881i) q^{98} +32.5780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9}+O(q^{10}) \) 16 * q + 24 * q^3 - 16 * q^4 - 4 * q^7 + 24 * q^9	\( 16 q + 24 q^{3} - 16 q^{4} - 4 q^{7} + 24 q^{9} - 4 q^{11} - 48 q^{12} + 8 q^{14} - 32 q^{16} - 12 q^{17} - 72 q^{19} - 24 q^{21} + 48 q^{22} + 12 q^{23} - 32 q^{28} + 72 q^{29} + 120 q^{31} - 12 q^{33} - 96 q^{36} - 44 q^{37} + 72 q^{38} + 36 q^{39} + 24 q^{42} + 56 q^{43} - 8 q^{44} + 8 q^{46} + 24 q^{47} - 40 q^{49} - 12 q^{51} + 72 q^{52} - 32 q^{53} + 16 q^{56} - 144 q^{57} + 88 q^{58} + 132 q^{59} + 96 q^{61} - 60 q^{63} + 128 q^{64} + 72 q^{66} + 164 q^{67} + 24 q^{68} - 136 q^{71} + 348 q^{73} - 112 q^{74} - 96 q^{77} + 280 q^{79} - 72 q^{81} - 264 q^{82} - 24 q^{84} - 88 q^{86} + 108 q^{87} - 48 q^{88} - 300 q^{89} - 272 q^{91} - 48 q^{92} + 120 q^{93} - 384 q^{98} - 24 q^{99}+O(q^{100}) \) 16 * q + 24 * q^3 - 16 * q^4 - 4 * q^7 + 24 * q^9 - 4 * q^11 - 48 * q^12 + 8 * q^14 - 32 * q^16 - 12 * q^17 - 72 * q^19 - 24 * q^21 + 48 * q^22 + 12 * q^23 - 32 * q^28 + 72 * q^29 + 120 * q^31 - 12 * q^33 - 96 * q^36 - 44 * q^37 + 72 * q^38 + 36 * q^39 + 24 * q^42 + 56 * q^43 - 8 * q^44 + 8 * q^46 + 24 * q^47 - 40 * q^49 - 12 * q^51 + 72 * q^52 - 32 * q^53 + 16 * q^56 - 144 * q^57 + 88 * q^58 + 132 * q^59 + 96 * q^61 - 60 * q^63 + 128 * q^64 + 72 * q^66 + 164 * q^67 + 24 * q^68 - 136 * q^71 + 348 * q^73 - 112 * q^74 - 96 * q^77 + 280 * q^79 - 72 * q^81 - 264 * q^82 - 24 * q^84 - 88 * q^86 + 108 * q^87 - 48 * q^88 - 300 * q^89 - 272 * q^91 - 48 * q^92 + 120 * q^93 - 384 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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