LMFDB - Embedded newform 1050.3.p.f.901.4

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 4 x^{11} + 56 x^{10} + 300 x^{9} + 1007 x^{8} + 12456 x^{7} + 209990 x^{6} - 250384 x^{5} + \cdots + 6882692292 $ x^12 - 4x^11 + 56x^10 + 300x^9 + 1007x^8 + 12456x^7 + 209990x^6 - 250384x^5 + 4799806x^4 + 51487320x^3 - 123648876x^2 + 379489320*x + 6882692292
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.4
Root			$-0.0663422 + 7.58000i$ of defining polynomial
Character	$\chi$	$=$	1050.901
Dual form			1050.3.p.f.451.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.80475 - 1.64177i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.80475 - 1.64177i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(8.87741 + 15.3761i) q^{11} +(-3.00000 - 1.73205i) q^{12} -2.00882i q^{13} +(-6.82244 + 7.17317i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-18.3681 + 10.6048i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(-5.70198 - 3.29204i) q^{19} +(-11.6289 + 3.43042i) q^{21} +25.1091 q^{22} +(-19.7033 + 34.1271i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-2.46029 - 1.42045i) q^{26} -5.19615i q^{27} +(3.96111 + 13.4279i) q^{28} -25.1091 q^{29} +(4.76798 - 2.75280i) q^{31} +(2.82843 + 4.89898i) q^{32} +(26.6322 + 15.3761i) q^{33} +29.9950i q^{34} -6.00000 q^{36} +(-5.87580 + 10.1772i) q^{37} +(-8.06382 + 4.65565i) q^{38} +(-1.73969 - 3.01323i) q^{39} -16.8812i q^{41} +(-4.02151 + 16.6682i) q^{42} -27.7474 q^{43} +(17.7548 - 30.7523i) q^{44} +(27.8647 + 48.2631i) q^{46} +(-39.5579 - 22.8388i) q^{47} +6.92820i q^{48} +(43.6092 + 22.3437i) q^{49} +(-18.3681 + 31.8145i) q^{51} +(-3.47938 + 2.00882i) q^{52} +(49.2261 + 85.2621i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(19.2467 + 4.64364i) q^{56} -11.4040 q^{57} +(-17.7548 + 30.7523i) q^{58} +(10.9872 - 6.34348i) q^{59} +(82.0429 + 47.3675i) q^{61} -7.78609i q^{62} +(-14.4726 + 15.2166i) q^{63} +8.00000 q^{64} +(37.6637 - 21.7451i) q^{66} +(4.17603 + 7.23310i) q^{67} +(36.7362 + 21.2096i) q^{68} +68.2543i q^{69} +71.8225 q^{71} +(-4.24264 + 7.34847i) q^{72} +(0.697968 - 0.402972i) q^{73} +(8.30963 + 14.3927i) q^{74} +13.1682i q^{76} +(-35.1644 - 119.205i) q^{77} -4.92058 q^{78} +(-58.1846 + 100.779i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-20.6752 - 11.9368i) q^{82} +50.1243i q^{83} +(17.5706 + 16.7115i) q^{84} +(-19.6204 + 33.9835i) q^{86} +(-37.6637 + 21.7451i) q^{87} +(-25.1091 - 43.4903i) q^{88} +(74.9322 + 43.2621i) q^{89} +(-3.29803 + 13.6695i) q^{91} +78.8133 q^{92} +(4.76798 - 8.25839i) q^{93} +(-55.9433 + 32.2989i) q^{94} +(8.48528 + 4.89898i) q^{96} -165.642i q^{97} +(58.2017 - 37.6107i) q^{98} +53.2645 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9}+O(q^{10}) $ 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9	$ 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9} - 4 q^{11} - 36 q^{12} + 8 q^{14} - 24 q^{16} - 24 q^{17} + 12 q^{19} + 18 q^{21} + 24 q^{22} - 60 q^{23} - 24 q^{26} + 4 q^{28} - 24 q^{29} - 198 q^{31} - 12 q^{33} - 72 q^{36} + 70 q^{37} - 60 q^{38} - 36 q^{39} + 36 q^{42} - 84 q^{43} - 8 q^{44} + 32 q^{46} - 60 q^{47} + 28 q^{49} - 24 q^{51} - 72 q^{52} + 44 q^{53} + 40 q^{56} + 24 q^{57} + 8 q^{58} - 48 q^{59} + 186 q^{61} + 30 q^{63} + 96 q^{64} + 36 q^{66} + 152 q^{67} + 48 q^{68} - 136 q^{71} + 18 q^{73} - 64 q^{74} + 132 q^{77} - 48 q^{78} - 70 q^{79} - 54 q^{81} - 84 q^{82} - 12 q^{84} - 208 q^{86} - 36 q^{87} - 24 q^{88} + 168 q^{89} + 292 q^{91} + 240 q^{92} - 198 q^{93} - 204 q^{94} + 48 q^{98} - 24 q^{99}+O(q^{100}) $ 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9 - 4 * q^11 - 36 * q^12 + 8 * q^14 - 24 * q^16 - 24 * q^17 + 12 * q^19 + 18 * q^21 + 24 * q^22 - 60 * q^23 - 24 * q^26 + 4 * q^28 - 24 * q^29 - 198 * q^31 - 12 * q^33 - 72 * q^36 + 70 * q^37 - 60 * q^38 - 36 * q^39 + 36 * q^42 - 84 * q^43 - 8 * q^44 + 32 * q^46 - 60 * q^47 + 28 * q^49 - 24 * q^51 - 72 * q^52 + 44 * q^53 + 40 * q^56 + 24 * q^57 + 8 * q^58 - 48 * q^59 + 186 * q^61 + 30 * q^63 + 96 * q^64 + 36 * q^66 + 152 * q^67 + 48 * q^68 - 136 * q^71 + 18 * q^73 - 64 * q^74 + 132 * q^77 - 48 * q^78 - 70 * q^79 - 54 * q^81 - 84 * q^82 - 12 * q^84 - 208 * q^86 - 36 * q^87 - 24 * q^88 + 168 * q^89 + 292 * q^91 + 240 * q^92 - 198 * q^93 - 204 * q^94 + 48 * 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
$7$	−6.80475	−	1.64177i	−0.972107	−	0.234539i
$7$	−6.80475	−	1.64177i	−0.972107	−	0.234539i
$8$	−2.82843			−0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	8.87741	+	15.3761i	0.807038	+	1.39783i	0.914907	+	0.403665i	$0.132264\pi$
$11$	8.87741	+	15.3761i	0.807038	+	1.39783i	−0.107869	+	0.994165i	$0.534403\pi$
$12$	−3.00000	−	1.73205i	−0.250000	−	0.144338i
$13$		−	2.00882i		−	0.154525i	−0.997011	−	0.0772623i	$-0.975382\pi$
$13$		−	2.00882i		−	0.154525i	0.997011	−	0.0772623i	$-0.0246179\pi$
$14$	−6.82244	+	7.17317i	−0.487317	+	0.512369i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−18.3681	+	10.6048i	−1.08048	+	0.623813i	−0.931025	−	0.364956i	$-0.881084\pi$
$17$	−18.3681	+	10.6048i	−1.08048	+	0.623813i	−0.149451	+	0.988769i	$0.547751\pi$
$18$	−2.12132	−	3.67423i	−0.117851	−	0.204124i
$19$	−5.70198	−	3.29204i	−0.300104	−	0.173265i	0.342386	−	0.939560i	$-0.388765\pi$
$19$	−5.70198	−	3.29204i	−0.300104	−	0.173265i	−0.642490	+	0.766294i	$0.722098\pi$
$20$		0			0
$21$	−11.6289	+	3.43042i	−0.553759	+	0.163353i
$22$	25.1091			1.14132
$23$	−19.7033	+	34.1271i	−0.856666	+	1.48379i	0.0184250	+	0.999830i	$0.494135\pi$
$23$	−19.7033	+	34.1271i	−0.856666	+	1.48379i	−0.875091	+	0.483959i	$0.839199\pi$
$24$	−4.24264	+	2.44949i	−0.176777	+	0.102062i
$25$		0			0
$26$	−2.46029	−	1.42045i	−0.0946266	−	0.0546327i
$27$		−	5.19615i		−	0.192450i
$28$	3.96111	+	13.4279i	0.141468	+	0.479569i
$29$	−25.1091			−0.865832			−0.432916	−	0.901434i	$-0.642515\pi$
$29$	−25.1091			−0.865832			−0.432916	+	0.901434i	$0.642515\pi$
$30$		0			0
$31$	4.76798	−	2.75280i	0.153806	−	0.0887999i	−0.421122	−	0.907004i	$-0.638363\pi$
$31$	4.76798	−	2.75280i	0.153806	−	0.0887999i	0.574928	+	0.818204i	$0.305030\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$	26.6322	+	15.3761i	0.807038	+	0.465943i
$34$			29.9950i			0.882205i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−5.87580	+	10.1772i	−0.158805	+	0.275059i	−0.934438	−	0.356125i	$-0.884098\pi$
$37$	−5.87580	+	10.1772i	−0.158805	+	0.275059i	0.775633	+	0.631184i	$0.217431\pi$
$38$	−8.06382	+	4.65565i	−0.212206	+	0.122517i
$39$	−1.73969	−	3.01323i	−0.0446074	−	0.0772623i
$40$		0			0
$41$		−	16.8812i		−	0.411737i	−0.978580	−	0.205868i	$-0.933998\pi$
$41$		−	16.8812i		−	0.411737i	0.978580	−	0.205868i	$-0.0660019\pi$
$42$	−4.02151	+	16.6682i	−0.0957502	+	0.396861i
$43$	−27.7474			−0.645290			−0.322645	−	0.946520i	$-0.604572\pi$
$43$	−27.7474			−0.645290			−0.322645	+	0.946520i	$0.604572\pi$
$44$	17.7548	−	30.7523i	0.403519	−	0.698915i
$45$		0			0
$46$	27.8647	+	48.2631i	0.605754	+	1.04920i
$47$	−39.5579	−	22.8388i	−0.841657	−	0.485931i	0.0161700	−	0.999869i	$-0.494853\pi$
$47$	−39.5579	−	22.8388i	−0.841657	−	0.485931i	−0.857827	+	0.513938i	$0.828186\pi$
$48$			6.92820i			0.144338i
$49$	43.6092	+	22.3437i	0.889983	+	0.455994i
$50$		0			0
$51$	−18.3681	+	31.8145i	−0.360159	+	0.623813i
$52$	−3.47938	+	2.00882i	−0.0669111	+	0.0386311i
$53$	49.2261	+	85.2621i	0.928794	+	1.60872i	0.785343	+	0.619061i	$0.212487\pi$
$53$	49.2261	+	85.2621i	0.928794	+	1.60872i	0.143451	+	0.989657i	$0.454180\pi$
$54$	−6.36396	−	3.67423i	−0.117851	−	0.0680414i
$55$		0			0
$56$	19.2467	+	4.64364i	0.343692	+	0.0829221i
$57$	−11.4040			−0.200069
$58$	−17.7548	+	30.7523i	−0.306118	+	0.530211i
$59$	10.9872	−	6.34348i	0.186224	−	0.107517i	−0.403990	−	0.914764i	$-0.632377\pi$
$59$	10.9872	−	6.34348i	0.186224	−	0.107517i	0.590214	+	0.807247i	$0.299043\pi$
$60$		0			0
$61$	82.0429	+	47.3675i	1.34497	+	0.776517i	0.987531	−	0.157422i	$-0.0503182\pi$
$61$	82.0429	+	47.3675i	1.34497	+	0.776517i	0.357435	+	0.933938i	$0.383652\pi$
$62$		−	7.78609i		−	0.125582i
$63$	−14.4726	+	15.2166i	−0.229723	+	0.241533i
$64$	8.00000			0.125000
$65$		0			0
$66$	37.6637	−	21.7451i	0.570662	−	0.329472i
$67$	4.17603	+	7.23310i	0.0623289	+	0.107957i	0.895506	−	0.445049i	$-0.146814\pi$
$67$	4.17603	+	7.23310i	0.0623289	+	0.107957i	−0.833177	+	0.553006i	$0.813481\pi$
$68$	36.7362	+	21.2096i	0.540238	+	0.311907i
$69$			68.2543i			0.989193i
$70$		0			0
$71$	71.8225			1.01158			0.505792	−	0.862655i	$-0.331200\pi$
$71$	71.8225			1.01158			0.505792	+	0.862655i	$0.331200\pi$
$72$	−4.24264	+	7.34847i	−0.0589256	+	0.102062i
$73$	0.697968	−	0.402972i	0.00956121	−	0.00552017i	−0.495212	−	0.868772i	$-0.664910\pi$
$73$	0.697968	−	0.402972i	0.00956121	−	0.00552017i	0.504773	+	0.863252i	$0.331576\pi$
$74$	8.30963	+	14.3927i	0.112292	+	0.194496i
$75$		0			0
$76$			13.1682i			0.173265i
$77$	−35.1644	−	119.205i	−0.456681	−	1.54812i
$78$	−4.92058			−0.0630844
$79$	−58.1846	+	100.779i	−0.736514	+	1.27568i	0.217542	+	0.976051i	$0.430196\pi$
$79$	−58.1846	+	100.779i	−0.736514	+	1.27568i	−0.954056	+	0.299628i	$0.903137\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−20.6752	−	11.9368i	−0.252136	−	0.145571i
$83$			50.1243i			0.603907i	0.953323	+	0.301953i	$0.0976387\pi$
$83$			50.1243i			0.603907i	−0.953323	+	0.301953i	$0.902361\pi$
$84$	17.5706	+	16.7115i	0.209174	+	0.198946i
$85$		0			0
$86$	−19.6204	+	33.9835i	−0.228144	+	0.395158i
$87$	−37.6637	+	21.7451i	−0.432916	+	0.249944i
$88$	−25.1091	−	43.4903i	−0.285331	−	0.494208i
$89$	74.9322	+	43.2621i	0.841935	+	0.486091i	0.857921	−	0.513781i	$-0.171756\pi$
$89$	74.9322	+	43.2621i	0.841935	+	0.486091i	−0.0159868	+	0.999872i	$0.505089\pi$
$90$		0			0
$91$	−3.29803	+	13.6695i	−0.0362420	+	0.150214i
$92$	78.8133			0.856666
$93$	4.76798	−	8.25839i	0.0512687	−	0.0887999i
$94$	−55.9433	+	32.2989i	−0.595141	+	0.343605i
$95$		0			0
$96$	8.48528	+	4.89898i	0.0883883	+	0.0510310i
$97$		−	165.642i		−	1.70765i	−0.520563	−	0.853823i	$-0.674278\pi$
$97$		−	165.642i		−	1.70765i	0.520563	−	0.853823i	$-0.325722\pi$
$98$	58.2017	−	37.6107i	0.593895	−	0.383783i
$99$	53.2645			0.538025
$100$		0			0
$101$	−170.953	+	98.7000i	−1.69261	+	0.977227i	−0.740206	+	0.672380i	$0.765272\pi$
$101$	−170.953	+	98.7000i	−1.69261	+	0.977227i	−0.952401	+	0.304847i	$0.901395\pi$
$102$	25.9764	+	44.9925i	0.254671	+	0.441103i
$103$	−61.2474	−	35.3612i	−0.594635	−	0.343313i	0.172293	−	0.985046i	$-0.444882\pi$
$103$	−61.2474	−	35.3612i	−0.594635	−	0.343313i	−0.766928	+	0.641733i	$0.778216\pi$
$104$			5.68180i			0.0546327i
$105$		0			0
$106$	139.232			1.31351
$107$	15.9804	−	27.6788i	0.149349	−	0.258680i	−0.781638	−	0.623732i	$-0.785615\pi$
$107$	15.9804	−	27.6788i	0.149349	−	0.258680i	0.930987	+	0.365052i	$0.118949\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	−106.026	−	183.643i	−0.972717	−	1.68479i	−0.687273	−	0.726399i	$-0.741192\pi$
$109$	−106.026	−	183.643i	−0.972717	−	1.68479i	−0.285444	−	0.958396i	$-0.592141\pi$
$110$		0			0
$111$			20.3544i			0.183373i
$112$	19.2968	−	20.2888i	0.172293	−	0.181150i
$113$	−91.0393			−0.805657			−0.402829	−	0.915275i	$-0.631973\pi$
$113$	−91.0393			−0.805657			−0.402829	+	0.915275i	$0.631973\pi$
$114$	−8.06382	+	13.9669i	−0.0707352	+	0.122517i
$115$		0			0
$116$	25.1091	+	43.4903i	0.216458	+	0.374916i
$117$	−5.21906	−	3.01323i	−0.0446074	−	0.0257541i
$118$		−	17.9421i		−	0.152051i
$119$	142.401	−	42.0069i	1.19665	−	0.352999i
$120$		0			0
$121$	−97.1170	+	168.212i	−0.802620	+	1.39018i
$122$	116.026	−	66.9878i	0.951035	−	0.549080i
$123$	−14.6195	−	25.3218i	−0.118858	−	0.205868i
$124$	−9.53597	−	5.50559i	−0.0769030	−	0.0444000i
$125$		0			0
$126$	8.40279	+	28.4850i	0.0666888	+	0.226071i
$127$	−160.943			−1.26727			−0.633635	−	0.773632i	$-0.718438\pi$
$127$	−160.943			−1.26727			−0.633635	+	0.773632i	$0.718438\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$	−41.6212	+	24.0300i	−0.322645	+	0.186279i
$130$		0			0
$131$	−14.4620	−	8.34962i	−0.110397	−	0.0637375i	0.443785	−	0.896133i	$-0.353635\pi$
$131$	−14.4620	−	8.34962i	−0.110397	−	0.0637375i	−0.554182	+	0.832396i	$0.686969\pi$
$132$		−	61.5045i		−	0.465943i
$133$	33.3957	+	31.7629i	0.251096	+	0.238818i
$134$	11.8116			0.0881463
$135$		0			0
$136$	51.9528	−	29.9950i	0.382006	−	0.220551i
$137$	−63.2788	−	109.602i	−0.461889	−	0.800015i	0.537166	−	0.843476i	$-0.319495\pi$
$137$	−63.2788	−	109.602i	−0.461889	−	0.800015i	−0.999055	+	0.0434613i	$0.986161\pi$
$138$	83.5941	+	48.2631i	0.605754	+	0.349732i
$139$			135.361i			0.973820i	0.873452	+	0.486910i	$0.161876\pi$
$139$			135.361i			0.973820i	−0.873452	+	0.486910i	$0.838124\pi$
$140$		0			0
$141$	−79.1158			−0.561105
$142$	50.7862	−	87.9643i	0.357649	−	0.619467i
$143$	30.8879	−	17.8331i	0.215999	−	0.124707i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$		0			0
$146$		−	1.13978i		−	0.00780669i
$147$	84.7640	−	4.25108i	0.576626	−	0.0289189i
$148$	23.5032			0.158805
$149$	40.3068	−	69.8135i	0.270516	−	0.468547i	−0.698478	−	0.715631i	$-0.746139\pi$
$149$	40.3068	−	69.8135i	0.270516	−	0.468547i	0.968994	+	0.247084i	$0.0794725\pi$
$150$		0			0
$151$	6.96796	+	12.0689i	0.0461454	+	0.0799262i	0.888176	−	0.459504i	$-0.151973\pi$
$151$	6.96796	+	12.0689i	0.0461454	+	0.0799262i	−0.842030	+	0.539430i	$0.818640\pi$
$152$	16.1276	+	9.31129i	0.106103	+	0.0612585i
$153$			63.6289i			0.415875i
$154$	−170.861	−	41.2235i	−1.10949	−	0.267685i
$155$		0			0
$156$	−3.47938	+	6.02646i	−0.0223037	+	0.0386311i
$157$	21.8815	−	12.6333i	0.139373	−	0.0804669i	−0.428692	−	0.903451i	$-0.641026\pi$
$157$	21.8815	−	12.6333i	0.139373	−	0.0804669i	0.568065	+	0.822984i	$0.307692\pi$
$158$	82.2854	+	142.523i	0.520794	+	0.902041i
$159$	147.678	+	85.2621i	0.928794	+	0.536239i
$160$		0			0
$161$	190.105	−	199.878i	1.18078	−	1.24148i
$162$	−12.7279			−0.0785674
$163$	27.8663	−	48.2658i	0.170959	−	0.296109i	−0.767797	−	0.640694i	$-0.778647\pi$
$163$	27.8663	−	48.2658i	0.170959	−	0.296109i	0.938755	+	0.344585i	$0.111980\pi$
$164$	−29.2391	+	16.8812i	−0.178287	+	0.102934i
$165$		0			0
$166$	61.3895	+	35.4432i	0.369816	+	0.213513i
$167$			262.461i			1.57163i	0.618464	+	0.785813i	$0.287755\pi$
$167$			262.461i			1.57163i	−0.618464	+	0.785813i	$0.712245\pi$
$168$	32.8916	−	9.70270i	0.195783	−	0.0577542i
$169$	164.965			0.976122
$170$		0			0
$171$	−17.1059	+	9.87612i	−0.100035	+	0.0577551i
$172$	27.7474	+	48.0600i	0.161322	+	0.279419i
$173$	137.125	+	79.1694i	0.792632	+	0.457627i	0.840888	−	0.541208i	$-0.182033\pi$
$173$	137.125	+	79.1694i	0.792632	+	0.457627i	−0.0482560	+	0.998835i	$0.515366\pi$
$174$			61.5045i			0.353474i
$175$		0			0
$176$	−71.0193			−0.403519
$177$	10.9872	−	19.0304i	0.0620747	−	0.107517i
$178$	105.970	−	61.1819i	0.595338	−	0.343718i
$179$	5.01415	+	8.68475i	0.0280120	+	0.0485182i	0.879692	−	0.475545i	$-0.157749\pi$
$179$	5.01415	+	8.68475i	0.0280120	+	0.0485182i	−0.851680	+	0.524063i	$0.824416\pi$
$180$		0			0
$181$			318.143i			1.75770i	0.477101	+	0.878848i	$0.341688\pi$
$181$			318.143i			1.75770i	−0.477101	+	0.878848i	$0.658312\pi$
$182$	14.4096	+	13.7050i	0.0791736	+	0.0753024i
$183$	164.086			0.896644
$184$	55.7294	−	96.5261i	0.302877	−	0.524599i
$185$		0			0
$186$	−6.74295	−	11.6791i	−0.0362524	−	0.0627910i
$187$	−326.122	−	188.287i	−1.74397	−	1.00688i
$188$			91.3550i			0.485931i
$189$	−8.53091	+	35.3585i	−0.0451371	+	0.187082i
$190$		0			0
$191$	1.85642	−	3.21541i	0.00971946	−	0.0168346i	−0.861125	−	0.508394i	$-0.830239\pi$
$191$	1.85642	−	3.21541i	0.00971946	−	0.0168346i	0.870844	+	0.491559i	$0.163573\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	−147.770	−	255.946i	−0.765649	−	1.32614i	−0.939903	−	0.341443i	$-0.889084\pi$
$193$	−147.770	−	255.946i	−0.765649	−	1.32614i	0.174253	−	0.984701i	$-0.444249\pi$
$194$	−202.869	−	117.126i	−1.04572	−	0.603744i
$195$		0			0
$196$	−4.90872	−	97.8770i	−0.0250445	−	0.499372i
$197$	−231.134			−1.17327			−0.586635	−	0.809852i	$-0.699548\pi$
$197$	−231.134			−1.17327			−0.586635	+	0.809852i	$0.699548\pi$
$198$	37.6637	−	65.2354i	0.190221	−	0.329472i
$199$	−25.3639	+	14.6438i	−0.127457	+	0.0735871i	−0.562373	−	0.826884i	$-0.690111\pi$
$199$	−25.3639	+	14.6438i	−0.127457	+	0.0735871i	0.434916	+	0.900471i	$0.356778\pi$
$200$		0			0
$201$	12.5281	+	7.23310i	0.0623289	+	0.0359856i
$202$			279.166i			1.38201i
$203$	170.861	+	41.2235i	0.841681	+	0.203071i
$204$	73.4724			0.360159
$205$		0			0
$206$	−86.6169	+	50.0083i	−0.420470	+	0.242759i
$207$	59.1099	+	102.381i	0.285555	+	0.494596i
$208$	6.95875	+	4.01764i	0.0334555	+	0.0193156i
$209$		−	116.899i		−	0.559326i
$210$		0			0
$211$	−254.413			−1.20575			−0.602874	−	0.797836i	$-0.705978\pi$
$211$	−254.413			−1.20575			−0.602874	+	0.797836i	$0.705978\pi$
$212$	98.4522	−	170.524i	0.464397	−	0.804359i
$213$	107.734	−	62.2001i	0.505792	−	0.292019i
$214$	−22.5996	−	39.1437i	−0.105606	−	0.182915i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	−36.9644	+	10.9041i	−0.170343	+	0.0502495i
$218$	−299.887			−1.37563
$219$	0.697968	−	1.20892i	0.00318707	−	0.00552017i
$220$		0			0
$221$	21.3032	+	36.8982i	0.0963944	+	0.166960i
$222$	24.9289	+	14.3927i	0.112292	+	0.0648320i
$223$		−	197.116i		−	0.883927i	−0.897033	−	0.441964i	$-0.854282\pi$
$223$		−	197.116i		−	0.883927i	0.897033	−	0.441964i	$-0.145718\pi$
$224$	−11.2037	−	37.9800i	−0.0500166	−	0.169553i
$225$		0			0
$226$	−64.3745	+	111.500i	−0.284843	+	0.493362i
$227$	248.054	−	143.214i	1.09275	−	0.630900i	0.158443	−	0.987368i	$-0.449352\pi$
$227$	248.054	−	143.214i	1.09275	−	0.630900i	0.934308	+	0.356468i	$0.116019\pi$
$228$	11.4040	+	19.7522i	0.0500174	+	0.0866326i
$229$	−178.628	−	103.131i	−0.780034	−	0.450353i	0.0564084	−	0.998408i	$-0.482035\pi$
$229$	−178.628	−	103.131i	−0.780034	−	0.450353i	−0.836442	+	0.548055i	$0.815368\pi$
$230$		0			0
$231$	−155.982	−	148.355i	−0.675245	−	0.642229i
$232$	71.0193			0.306118
$233$	3.44650	−	5.96951i	0.0147918	−	0.0256202i	−0.858535	−	0.512755i	$-0.828625\pi$
$233$	3.44650	−	5.96951i	0.0147918	−	0.0256202i	0.873327	+	0.487135i	$0.161958\pi$
$234$	−7.38087	+	4.26135i	−0.0315422	+	0.0182109i
$235$		0			0
$236$	−21.9744	−	12.6870i	−0.0931121	−	0.0537583i
$237$			201.557i			0.850453i
$238$	49.2450	−	204.108i	0.206912	−	0.857598i
$239$	289.962			1.21323			0.606615	−	0.794995i	$-0.292527\pi$
$239$	289.962			1.21323			0.606615	+	0.794995i	$0.292527\pi$
$240$		0			0
$241$	282.791	−	163.270i	1.17341	−	0.677467i	0.218927	−	0.975741i	$-0.429744\pi$
$241$	282.791	−	163.270i	1.17341	−	0.677467i	0.954480	+	0.298274i	$0.0964110\pi$
$242$	137.344	+	237.887i	0.567538	+	0.983004i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		−	189.470i		−	0.776517i
$245$		0			0
$246$	−41.3503			−0.168091
$247$	−6.61311	+	11.4542i	−0.0267737	+	0.0463735i
$248$	−13.4859	+	7.78609i	−0.0543786	+	0.0313955i
$249$	43.4089	+	75.1864i	0.174333	+	0.301953i
$250$		0			0
$251$		−	341.759i		−	1.36159i	−0.732474	−	0.680795i	$-0.761634\pi$
$251$		−	341.759i		−	1.36159i	0.732474	−	0.680795i	$-0.238366\pi$
$252$	40.8285	+	9.85064i	0.162018	+	0.0390898i
$253$	−699.658			−2.76545
$254$	−113.804	+	197.115i	−0.448048	+	0.776042i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−168.741	−	97.4226i	−0.656579	−	0.379076i	0.134393	−	0.990928i	$-0.457092\pi$
$257$	−168.741	−	97.4226i	−0.656579	−	0.379076i	−0.790972	+	0.611852i	$0.790425\pi$
$258$			67.9671i			0.263438i
$259$	56.6920	−	59.6064i	0.218888	−	0.230141i
$260$		0			0
$261$	−37.6637	+	65.2354i	−0.144305	+	0.249944i
$262$	−20.4523	+	11.8081i	−0.0780622	+	0.0450692i
$263$	69.0324	+	119.568i	0.262481	+	0.454630i	0.966900	−	0.255154i	$-0.0821261\pi$
$263$	69.0324	+	119.568i	0.262481	+	0.454630i	−0.704420	+	0.709783i	$0.748793\pi$
$264$	−75.3274	−	43.4903i	−0.285331	−	0.164736i
$265$		0			0
$266$	62.5157	−	18.4415i	0.235022	−	0.0693291i
$267$	149.864			0.561290
$268$	8.35207	−	14.4662i	0.0311644	−	0.0539784i
$269$	8.57284	−	4.94953i	0.0318693	−	0.0183998i	−0.483981	−	0.875079i	$-0.660810\pi$
$269$	8.57284	−	4.94953i	0.0318693	−	0.0183998i	0.515850	+	0.856679i	$0.327476\pi$
$270$		0			0
$271$	−16.4712	−	9.50963i	−0.0607792	−	0.0350909i	0.469302	−	0.883037i	$-0.344505\pi$
$271$	−16.4712	−	9.50963i	−0.0607792	−	0.0350909i	−0.530082	+	0.847947i	$0.677839\pi$
$272$		−	84.8386i		−	0.311907i
$273$	6.89110	+	23.3604i	0.0252421	+	0.0855693i
$274$	−178.979			−0.653210
$275$		0			0
$276$	118.220	−	68.2543i	0.428333	−	0.247298i
$277$	102.731	+	177.936i	0.370871	+	0.642367i	0.989700	−	0.143159i	$-0.0457260\pi$
$277$	102.731	+	177.936i	0.370871	+	0.642367i	−0.618829	+	0.785526i	$0.712393\pi$
$278$	165.783	+	95.7147i	0.596340	+	0.344297i
$279$		−	16.5168i		−	0.0591999i
$280$		0			0
$281$	−449.661			−1.60022			−0.800109	−	0.599854i	$-0.795225\pi$
$281$	−449.661			−1.60022			−0.800109	+	0.599854i	$0.795225\pi$
$282$	−55.9433	+	96.8966i	−0.198380	+	0.343605i
$283$	−137.762	+	79.5371i	−0.486792	+	0.281050i	−0.723243	−	0.690594i	$-0.757349\pi$
$283$	−137.762	+	79.5371i	−0.486792	+	0.281050i	0.236450	+	0.971644i	$0.424016\pi$
$284$	−71.8225	−	124.400i	−0.252896	−	0.438029i
$285$		0			0
$286$		−	50.4397i		−	0.176363i
$287$	−27.7151	+	114.872i	−0.0965683	+	0.400252i
$288$	16.9706			0.0589256
$289$	80.4246	−	139.300i	0.278286	−	0.482005i
$290$		0			0
$291$	−143.450	−	248.463i	−0.492955	−	0.853823i
$292$	−1.39594	−	0.805944i	−0.00478060	−	0.00276008i
$293$		−	451.939i		−	1.54245i	−0.636560	−	0.771227i	$-0.719643\pi$
$293$		−	451.939i		−	1.54245i	0.636560	−	0.771227i	$-0.280357\pi$
$294$	54.7307	−	106.820i	0.186159	−	0.363334i
$295$		0			0
$296$	16.6193	−	28.7854i	0.0561462	−	0.0972480i
$297$	79.8967	−	46.1284i	0.269013	−	0.155314i
$298$	−57.0024	−	98.7311i	−0.191283	−	0.331313i
$299$	68.5553	+	39.5804i	0.229282	+	0.132376i
$300$		0			0
$301$	188.814	+	45.5550i	0.627290	+	0.151346i
$302$	19.7084			0.0652595
$303$	−170.953	+	296.100i	−0.564202	+	0.977227i
$304$	22.8079	−	13.1682i	0.0750260	−	0.0433163i
$305$		0			0
$306$	77.9292	+	44.9925i	0.254671	+	0.147034i
$307$			555.454i			1.80930i	0.426158	+	0.904649i	$0.359867\pi$
$307$			555.454i			1.80930i	−0.426158	+	0.904649i	$0.640133\pi$
$308$	−171.305	+	180.112i	−0.556186	+	0.584779i
$309$	−122.495			−0.396423
$310$		0			0
$311$	146.444	−	84.5493i	0.470880	−	0.271863i	−0.245728	−	0.969339i	$-0.579027\pi$
$311$	146.444	−	84.5493i	0.470880	−	0.271863i	0.716608	+	0.697476i	$0.245694\pi$
$312$	4.92058	+	8.52270i	0.0157711	+	0.0273163i
$313$	−507.192	−	292.828i	−1.62042	−	0.935552i	−0.986806	−	0.161905i	$-0.948236\pi$
$313$	−507.192	−	292.828i	−1.62042	−	0.935552i	−0.633617	−	0.773647i	$-0.718430\pi$
$314$		−	35.7324i		−	0.113797i
$315$		0			0
$316$	232.738			0.736514
$317$	−130.614	+	226.230i	−0.412032	+	0.713660i	−0.995112	−	0.0987546i	$-0.968514\pi$
$317$	−130.614	+	226.230i	−0.412032	+	0.713660i	0.583080	+	0.812415i	$0.301847\pi$
$318$	208.849	−	120.579i	0.656756	−	0.379179i
$319$	−222.904	−	386.081i	−0.698759	−	1.21029i
$320$		0			0
$321$		−	55.3576i		−	0.172454i
$322$	−110.375	−	374.165i	−0.342780	−	1.16200i
$323$	139.646			0.432341
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$		0			0
$326$	−39.4088	−	68.2581i	−0.120886	−	0.209381i
$327$	−318.078	−	183.643i	−0.972717	−	0.561598i
$328$			47.7472i			0.145571i
$329$	231.685	+	220.357i	0.704211	+	0.669778i
$330$		0			0
$331$	−95.4984	+	165.408i	−0.288515	+	0.499722i	−0.973455	−	0.228877i	$-0.926495\pi$
$331$	−95.4984	+	165.408i	−0.288515	+	0.499722i	0.684941	+	0.728599i	$0.259828\pi$
$332$	86.8178	−	50.1243i	0.261499	−	0.150977i
$333$	17.6274	+	30.5315i	0.0529351	+	0.0916863i
$334$	321.448	+	185.588i	0.962420	+	0.555654i
$335$		0			0
$336$	11.3745	−	47.1447i	0.0338528	−	0.140312i
$337$	−226.109			−0.670947			−0.335474	−	0.942050i	$-0.608896\pi$
$337$	−226.109			−0.670947			−0.335474	+	0.942050i	$0.608896\pi$
$338$	116.648	−	202.040i	0.345111	−	0.597750i
$339$	−136.559	+	78.8423i	−0.402829	+	0.232573i
$340$		0			0
$341$	84.6548	+	48.8754i	0.248254	+	0.143330i
$342$			27.9339i			0.0816780i
$343$	−260.066	−	223.640i	−0.758210	−	0.652011i
$344$	78.4816			0.228144
$345$		0			0
$346$	193.925	−	111.962i	0.560476	−	0.323591i
$347$	331.636	+	574.410i	0.955723	+	1.65536i	0.732704	+	0.680548i	$0.238258\pi$
$347$	331.636	+	574.410i	0.955723	+	1.65536i	0.223020	+	0.974814i	$0.428409\pi$
$348$	75.3274	+	43.4903i	0.216458	+	0.124972i
$349$			293.777i			0.841769i	0.907114	+	0.420884i	$0.138280\pi$
$349$			293.777i			0.841769i	−0.907114	+	0.420884i	$0.861720\pi$
$350$		0			0
$351$	−10.4381			−0.0297383
$352$	−50.2182	+	86.9805i	−0.142665	+	0.247104i
$353$	310.089	−	179.030i	0.878439	−	0.507167i	0.00829580	−	0.999966i	$-0.497359\pi$
$353$	310.089	−	179.030i	0.878439	−	0.507167i	0.870144	+	0.492798i	$0.164026\pi$
$354$	−15.5383	−	26.9131i	−0.0438934	−	0.0760257i
$355$		0			0
$356$		−	173.048i		−	0.486091i
$357$	177.222	−	186.333i	0.496421	−	0.521942i
$358$	14.1821			0.0396149
$359$	28.2996	−	49.0164i	0.0788291	−	0.136536i	−0.823916	−	0.566712i	$-0.808215\pi$
$359$	28.2996	−	49.0164i	0.0788291	−	0.136536i	0.902745	+	0.430176i	$0.141549\pi$
$360$		0			0
$361$	−158.825	−	275.093i	−0.439958	−	0.762030i
$362$	389.644	+	224.961i	1.07637	+	0.621440i
$363$			336.423i			0.926785i
$364$	26.9743	−	7.95716i	0.0741052	−	0.0218603i
$365$		0			0
$366$	116.026	−	200.963i	0.317012	−	0.549080i
$367$	419.473	−	242.183i	1.14298	−	0.659898i	0.195811	−	0.980642i	$-0.437266\pi$
$367$	419.473	−	242.183i	1.14298	−	0.659898i	0.947166	+	0.320743i	$0.103933\pi$
$368$	−78.8133	−	136.509i	−0.214166	−	0.370947i
$369$	−43.8586	−	25.3218i	−0.118858	−	0.0686228i
$370$		0			0
$371$	−194.990	−	661.005i	−0.525579	−	1.78168i
$372$	−19.0719			−0.0512687
$373$	−176.452	+	305.623i	−0.473061	+	0.819365i	−0.999525	−	0.0308322i	$-0.990184\pi$
$373$	−176.452	+	305.623i	−0.473061	+	0.819365i	0.526464	+	0.850198i	$0.323518\pi$
$374$	−461.207	+	266.278i	−1.23317	+	0.711973i
$375$		0			0
$376$	111.887	+	64.5978i	0.297571	+	0.171803i
$377$			50.4397i			0.133792i
$378$	37.2729	+	35.4504i	0.0986055	+	0.0937842i
$379$	−129.666			−0.342126			−0.171063	−	0.985260i	$-0.554720\pi$
$379$	−129.666			−0.342126			−0.171063	+	0.985260i	$0.554720\pi$
$380$		0			0
$381$	−241.415	+	139.381i	−0.633635	+	0.365830i
$382$	−2.62537	−	4.54727i	−0.00687269	−	0.0119039i
$383$	363.416	+	209.819i	0.948868	+	0.547829i	0.892729	−	0.450594i	$-0.148788\pi$
$383$	363.416	+	209.819i	0.948868	+	0.547829i	0.0561389	+	0.998423i	$0.482121\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−417.958			−1.08279
$387$	−41.6212	+	72.0900i	−0.107548	+	0.186279i
$388$	−286.900	+	165.642i	−0.739433	+	0.426912i
$389$	−49.2202	−	85.2518i	−0.126530	−	0.219156i	0.795800	−	0.605560i	$-0.207051\pi$
$389$	−49.2202	−	85.2518i	−0.126530	−	0.219156i	−0.922330	+	0.386403i	$0.873717\pi$
$390$		0			0
$391$		−	835.801i		−	2.13760i
$392$	−123.345	−	63.1975i	−0.314656	−	0.161218i
$393$	−28.9239			−0.0735978
$394$	−163.437	+	283.080i	−0.414814	+	0.718478i
$395$		0			0
$396$	−53.2645	−	92.2568i	−0.134506	−	0.232972i
$397$	160.707	+	92.7842i	0.404804	+	0.233713i	0.688555	−	0.725185i	$-0.258246\pi$
$397$	160.707	+	92.7842i	0.404804	+	0.233713i	−0.283751	+	0.958898i	$0.591579\pi$
$398$			41.4190i			0.104068i
$399$	77.6010	+	18.7227i	0.194489	+	0.0469241i
$400$		0			0
$401$	93.6753	−	162.250i	0.233604	−	0.404614i	−0.725262	−	0.688473i	$-0.758281\pi$
$401$	93.6753	−	162.250i	0.233604	−	0.404614i	0.958866	+	0.283859i	$0.0916147\pi$
$402$	17.7174	−	10.2292i	0.0440732	−	0.0254457i
$403$	−5.52987	−	9.57802i	−0.0137218	−	0.0237668i
$404$	341.907	+	197.400i	0.846304	+	0.488614i
$405$		0			0
$406$	171.305	−	180.112i	0.421934	−	0.443626i
$407$	−208.648			−0.512648
$408$	51.9528	−	89.9849i	0.127335	−	0.220551i
$409$	−182.953	+	105.628i	−0.447319	+	0.258260i	−0.706697	−	0.707516i	$-0.749816\pi$
$409$	−182.953	+	105.628i	−0.447319	+	0.258260i	0.259378	+	0.965776i	$0.416482\pi$
$410$		0			0
$411$	−189.836	−	109.602i	−0.461889	−	0.266672i
$412$			141.445i			0.343313i
$413$	−85.1798	+	25.1272i	−0.206247	+	0.0608407i
$414$	167.188			0.403836
$415$		0			0
$416$	9.84116	−	5.68180i	0.0236566	−	0.0136582i
$417$	117.226	+	203.041i	0.281118	+	0.486910i
$418$	−143.172	−	82.6602i	−0.342516	−	0.197752i
$419$			48.9505i			0.116827i	0.998292	+	0.0584134i	$0.0186042\pi$
$419$			48.9505i			0.116827i	−0.998292	+	0.0584134i	$0.981396\pi$
$420$		0			0
$421$	−166.539			−0.395581			−0.197790	−	0.980244i	$-0.563376\pi$
$421$	−166.539			−0.395581			−0.197790	+	0.980244i	$0.563376\pi$
$422$	−179.897	+	311.591i	−0.426297	+	0.738367i
$423$	−118.674	+	68.5163i	−0.280552	+	0.161977i
$424$	−139.232	−	241.158i	−0.328378	−	0.568768i
$425$		0			0
$426$		−	175.929i		−	0.412978i
$427$	−480.515	−	457.020i	−1.12533	−	1.07030i
$428$	−63.9214			−0.149349
$429$	30.8879	−	53.4994i	0.0719997	−	0.124707i
$430$		0			0
$431$	−95.9137	−	166.127i	−0.222538	−	0.385446i	0.733040	−	0.680185i	$-0.238101\pi$
$431$	−95.9137	−	166.127i	−0.222538	−	0.385446i	−0.955578	+	0.294739i	$0.904767\pi$
$432$	18.0000	+	10.3923i	0.0416667	+	0.0240563i
$433$		−	509.172i		−	1.17592i	−0.808891	−	0.587958i	$-0.799932\pi$
$433$		−	509.172i		−	1.17592i	0.808891	−	0.587958i	$-0.200068\pi$
$434$	−12.7830	+	52.9823i	−0.0294539	+	0.122079i
$435$		0			0
$436$	−212.052	+	367.285i	−0.486358	+	0.842397i
$437$	224.696	−	129.728i	0.514178	−	0.296861i
$438$	−0.987076	−	1.70967i	−0.00225360	−	0.00390335i
$439$	−459.149	−	265.090i	−1.04590	−	0.603849i	−0.124400	−	0.992232i	$-0.539701\pi$
$439$	−459.149	−	265.090i	−1.04590	−	0.603849i	−0.921498	+	0.388383i	$0.873034\pi$
$440$		0			0
$441$	123.464	−	79.7844i	0.279965	−	0.180917i
$442$	60.2545			0.136322
$443$	−212.946	+	368.834i	−0.480692	+	0.832583i	−0.999755	−	0.0221535i	$-0.992948\pi$
$443$	−212.946	+	368.834i	−0.480692	+	0.832583i	0.519063	+	0.854736i	$0.326281\pi$
$444$	35.2548	−	20.3544i	0.0794027	−	0.0458432i
$445$		0			0
$446$	−241.417	−	139.382i	−0.541293	−	0.312516i
$447$		−	139.627i		−	0.312364i
$448$	−54.4380	−	13.1342i	−0.121513	−	0.0293174i
$449$	−294.520			−0.655946			−0.327973	−	0.944687i	$-0.606365\pi$
$449$	−294.520			−0.655946			−0.327973	+	0.944687i	$0.606365\pi$
$450$		0			0
$451$	259.568	−	149.861i	0.575538	−	0.332287i
$452$	91.0393	+	157.685i	0.201414	+	0.348860i
$453$	20.9039	+	12.0689i	0.0461454	+	0.0266421i
$454$		−	405.071i		−	0.892227i
$455$		0			0
$456$	32.2553			0.0707352
$457$	40.9206	−	70.8765i	0.0895418	−	0.155091i	−0.817776	−	0.575537i	$-0.804793\pi$
$457$	40.9206	−	70.8765i	0.0895418	−	0.155091i	0.907318	+	0.420446i	$0.138126\pi$
$458$	−252.618	+	145.849i	−0.551567	+	0.318448i
$459$	55.1043	+	95.4434i	0.120053	+	0.207938i
$460$		0			0
$461$			759.149i			1.64674i	0.567502	+	0.823372i	$0.307910\pi$
$461$			759.149i			1.64674i	−0.567502	+	0.823372i	$0.692090\pi$
$462$	−291.992	+	86.1349i	−0.632018	+	0.186439i
$463$	394.988			0.853105			0.426552	−	0.904463i	$-0.359728\pi$
$463$	394.988			0.853105			0.426552	+	0.904463i	$0.359728\pi$
$464$	50.2182	−	86.9805i	0.108229	−	0.187458i
$465$		0			0
$466$	−4.87409	−	8.44217i	−0.0104594	−	0.0181162i
$467$	−232.364	−	134.156i	−0.497568	−	0.287271i	0.230140	−	0.973157i	$-0.426081\pi$
$467$	−232.364	−	134.156i	−0.497568	−	0.287271i	−0.727709	+	0.685886i	$0.759415\pi$
$468$			12.0529i			0.0257541i
$469$	−16.5417	−	56.0755i	−0.0352702	−	0.119564i
$470$		0			0
$471$	21.8815	−	37.8999i	0.0464576	−	0.0804669i
$472$	−31.0766	+	17.9421i	−0.0658402	+	0.0380128i
$473$	−246.326	−	426.648i	−0.520773	−	0.902005i
$474$	246.856	+	142.523i	0.520794	+	0.300680i
$475$		0			0
$476$	−215.159	−	204.639i	−0.452015	−	0.429913i
$477$	295.356			0.619196
$478$	205.034	−	355.130i	0.428942	−	0.742949i
$479$	−470.659	+	271.735i	−0.982586	+	0.567296i	−0.903050	−	0.429536i	$-0.858677\pi$
$479$	−470.659	+	271.735i	−0.982586	+	0.567296i	−0.0795360	+	0.996832i	$0.525344\pi$
$480$		0			0
$481$	20.4441	+	11.8034i	0.0425034	+	0.0245393i
$482$		−	461.796i		−	0.958083i
$483$	112.058	−	464.453i	0.232004	−	0.961601i
$484$	388.468			0.802620
$485$		0			0
$486$	−19.0919	+	11.0227i	−0.0392837	+	0.0226805i
$487$	198.261	+	343.398i	0.407107	+	0.705130i	0.994564	−	0.104125i	$-0.0332043\pi$
$487$	198.261	+	343.398i	0.407107	+	0.705130i	−0.587457	+	0.809255i	$0.699871\pi$
$488$	−232.052	−	133.976i	−0.475517	−	0.274540i
$489$		−	96.5315i		−	0.197406i
$490$		0			0
$491$	750.658			1.52883			0.764417	−	0.644722i	$-0.223027\pi$
$491$	750.658			1.52883			0.764417	+	0.644722i	$0.223027\pi$
$492$	−29.2391	+	50.6436i	−0.0594291	+	0.102934i
$493$	461.207	−	266.278i	0.935511	−	0.540117i
$494$	9.35235	+	16.1987i	0.0189319	+	0.0327910i
$495$		0			0
$496$			22.0224i			0.0444000i
$497$	−488.734	−	117.916i	−0.983368	−	0.237256i
$498$	122.779			0.246544
$499$	66.6787	−	115.491i	0.133625	−	0.231445i	−0.791447	−	0.611238i	$-0.790672\pi$
$499$	66.6787	−	115.491i	0.133625	−	0.231445i	0.925071	+	0.379794i	$0.124005\pi$
$500$		0			0
$501$	227.298	+	393.692i	0.453689	+	0.785813i
$502$	−418.568	−	241.660i	−0.833800	−	0.481395i
$503$		−	226.683i		−	0.450661i	−0.974282	−	0.225331i	$-0.927654\pi$
$503$		−	226.683i		−	0.450661i	0.974282	−	0.225331i	$-0.0723462\pi$
$504$	40.9346	−	43.0390i	0.0812195	−	0.0853949i
$505$		0			0
$506$	−494.733	+	856.903i	−0.977733	+	1.69348i
$507$	247.447	−	142.864i	0.488061	−	0.281782i
$508$	160.943	+	278.762i	0.316818	+	0.548744i
$509$	17.6930	+	10.2151i	0.0347603	+	0.0200689i	0.517279	−	0.855817i	$-0.326945\pi$
$509$	17.6930	+	10.2151i	0.0347603	+	0.0200689i	−0.482519	+	0.875885i	$0.660278\pi$
$510$		0			0
$511$	−5.41109	+	1.59622i	−0.0105892	+	0.00312371i
$512$	−22.6274			−0.0441942
$513$	−17.1059	+	29.6284i	−0.0333449	+	0.0577551i
$514$	−238.636	+	137.776i	−0.464272	+	0.268047i
$515$		0			0
$516$	83.2423	+	48.0600i	0.161322	+	0.0931395i
$517$		−	810.996i		−	1.56866i
$518$	−32.9154	−	111.581i	−0.0635432	−	0.215408i
$519$	274.251			0.528422
$520$		0			0
$521$	775.322	−	447.632i	1.48814	−	0.859179i	0.488233	−	0.872713i	$-0.337642\pi$
$521$	775.322	−	447.632i	1.48814	−	0.859179i	0.999908	+	0.0135342i	$0.00430819\pi$
$522$	53.2645	+	92.2568i	0.102039	+	0.176737i
$523$	244.761	+	141.313i	0.467995	+	0.270197i	0.715400	−	0.698715i	$-0.246244\pi$
$523$	244.761	+	141.313i	0.467995	+	0.270197i	−0.247405	+	0.968912i	$0.579578\pi$
$524$			33.3985i			0.0637375i
$525$		0			0
$526$	195.253			0.371204
$527$	−58.3859	+	101.127i	−0.110789	+	0.191892i
$528$	−106.529	+	61.5045i	−0.201759	+	0.116486i
$529$	−511.941	−	886.708i	−0.967753	−	1.67620i
$530$		0			0
$531$		−	38.0609i		−	0.0716777i
$532$	21.6191	−	89.6060i	0.0406375	−	0.168432i
$533$	−33.9113			−0.0636234
$534$	105.970	−	183.546i	0.198446	−	0.343718i
$535$		0			0
$536$	−11.8116	−	20.4583i	−0.0220366	−	0.0381685i
$537$	15.0424	+	8.68475i	0.0280120	+	0.0161727i
$538$		−	13.9994i		−	0.0260212i
$539$	43.5768	+	868.895i	0.0808474	+	1.61205i
$540$		0			0
$541$	−178.897	+	309.858i	−0.330678	+	0.572751i	−0.982645	−	0.185496i	$-0.940611\pi$
$541$	−178.897	+	309.858i	−0.330678	+	0.572751i	0.651967	+	0.758247i	$0.273944\pi$
$542$	−23.2937	+	13.4486i	−0.0429774	+	0.0248130i
$543$	275.520	+	477.215i	0.507403	+	0.878848i
$544$	−103.906	−	59.9899i	−0.191003	−	0.110276i
$545$		0			0
$546$	33.4833	+	8.07848i	0.0613247	+	0.0147958i
$547$	−251.048			−0.458954			−0.229477	−	0.973314i	$-0.573702\pi$
$547$	−251.048			−0.458954			−0.229477	+	0.973314i	$0.573702\pi$
$548$	−126.558	+	219.204i	−0.230944	+	0.400008i
$549$	246.129	−	142.103i	0.448322	−	0.258839i
$550$		0			0
$551$	143.172	+	82.6602i	0.259840	+	0.150019i
$552$		−	193.052i		−	0.349732i
$553$	561.387	−	590.247i	1.01517	−	1.06736i
$554$	290.568			0.524490
$555$		0			0
$556$	234.452	−	135.361i	0.421676	−	0.243455i
$557$	347.274	+	601.496i	0.623472	+	1.07989i	0.988834	+	0.149020i	$0.0476120\pi$
$557$	347.274	+	601.496i	0.623472	+	1.07989i	−0.365362	+	0.930866i	$0.619055\pi$
$558$	−20.2288	−	11.6791i	−0.0362524	−	0.0209303i
$559$			55.7396i			0.0997131i
$560$		0			0
$561$	−652.245			−1.16265
$562$	−317.959	+	550.721i	−0.565763	+	0.979930i
$563$	483.826	−	279.337i	0.859371	−	0.496158i	−0.00443074	−	0.999990i	$-0.501410\pi$
$563$	483.826	−	279.337i	0.859371	−	0.496158i	0.863802	+	0.503832i	$0.168077\pi$
$564$	79.1158	+	137.033i	0.140276	+	0.242965i
$565$		0			0
$566$			224.965i			0.397464i
$567$	17.8250	+	60.4257i	0.0314374	+	0.106571i
$568$	−203.145			−0.357649
$569$	270.266	−	468.114i	0.474983	−	0.822696i	−0.524606	−	0.851345i	$-0.675787\pi$
$569$	270.266	−	468.114i	0.474983	−	0.822696i	0.999590	+	0.0286496i	$0.00912069\pi$
$570$		0			0
$571$	462.071	+	800.331i	0.809232	+	1.40163i	0.913397	+	0.407071i	$0.133450\pi$
$571$	462.071	+	800.331i	0.809232	+	1.40163i	−0.104164	+	0.994560i	$0.533217\pi$
$572$	−61.7757	−	35.6662i	−0.108000	−	0.0623536i
$573$		−	6.43081i		−	0.0112231i
$574$	121.092	+	115.171i	0.210961	+	0.200646i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	838.835	−	484.302i	1.45379	−	0.839344i	0.455093	−	0.890444i	$-0.349606\pi$
$577$	838.835	−	484.302i	1.45379	−	0.839344i	0.998694	+	0.0510997i	$0.0162726\pi$
$578$	−113.738	−	196.999i	−0.196778	−	0.340829i
$579$	−443.311	−	255.946i	−0.765649	−	0.442048i
$580$		0			0
$581$	82.2927	−	341.083i	0.141640	−	0.587062i
$582$	−405.738			−0.697144
$583$	−874.001	+	1513.81i	−1.49914	+	2.59659i
$584$	−1.97415	+	1.13978i	−0.00338040	+	0.00195167i
$585$		0			0
$586$	−553.510	−	319.569i	−0.944556	−	0.545340i
$587$			698.278i			1.18957i	0.803885	+	0.594785i	$0.202763\pi$
$587$			698.278i			1.18957i	−0.803885	+	0.594785i	$0.797237\pi$
$588$	−92.1270	−	142.564i	−0.156679	−	0.242456i
$589$	−36.2493			−0.0615437
$590$		0			0
$591$	−346.701	+	200.168i	−0.586635	+	0.338694i
$592$	−23.5032	−	40.7087i	−0.0397013	−	0.0687647i
$593$	607.963	+	351.007i	1.02523	+	0.591918i	0.915615	−	0.402056i	$-0.131704\pi$
$593$	607.963	+	351.007i	1.02523	+	0.591918i	0.109617	+	0.993974i	$0.465038\pi$
$594$		−	130.471i		−	0.219648i
$595$		0			0
$596$	−161.227			−0.270516
$597$	−25.3639	+	43.9315i	−0.0424855	+	0.0735871i
$598$	96.9518	−	55.9751i	0.162127	−	0.0936039i
$599$	83.1873	+	144.085i	0.138877	+	0.240542i	0.927072	−	0.374884i	$-0.122317\pi$
$599$	83.1873	+	144.085i	0.138877	+	0.240542i	−0.788195	+	0.615426i	$0.788984\pi$
$600$		0			0
$601$			952.482i			1.58483i	0.609983	+	0.792415i	$0.291176\pi$
$601$			952.482i			1.58483i	−0.609983	+	0.792415i	$0.708824\pi$
$602$	189.305	−	199.037i	0.314460	−	0.330627i
$603$	25.0562			0.0415526
$604$	13.9359	−	24.1377i	0.0230727	−	0.0399631i
$605$		0			0
$606$	241.765	+	418.748i	0.398951	+	0.691004i
$607$	694.188	+	400.790i	1.14364	+	0.660279i	0.947329	−	0.320263i	$-0.103771\pi$
$607$	694.188	+	400.790i	1.14364	+	0.660279i	0.196309	+	0.980542i	$0.437105\pi$
$608$		−	37.2452i		−	0.0612585i
$609$	291.992	−	86.1349i	0.479462	−	0.141437i
$610$		0			0
$611$	−45.8789	+	79.4646i	−0.0750883	+	0.130057i
$612$	110.209	−	63.6289i	0.180079	−	0.103969i
$613$	368.775	+	638.737i	0.601591	+	1.04199i	0.992580	+	0.121590i	$0.0387994\pi$
$613$	368.775	+	638.737i	0.601591	+	1.04199i	−0.390990	+	0.920395i	$0.627867\pi$
$614$	680.290	+	392.766i	1.10796	+	0.639683i
$615$		0			0
$616$	99.4600	+	337.164i	0.161461	+	0.547344i
$617$	−244.329			−0.395995			−0.197997	−	0.980203i	$-0.563444\pi$
$617$	−244.329			−0.395995			−0.197997	+	0.980203i	$0.563444\pi$
$618$	−86.6169	+	150.025i	−0.140157	+	0.242759i
$619$	409.586	−	236.475i	0.661690	−	0.382027i	−0.131231	−	0.991352i	$-0.541893\pi$
$619$	409.586	−	236.475i	0.661690	−	0.382027i	0.792920	+	0.609325i	$0.208560\pi$
$620$		0			0
$621$	177.330	+	102.381i	0.285555	+	0.164865i
$622$		−	239.142i		−	0.384472i
$623$	−438.868	−	417.409i	−0.704443	−	0.669999i
$624$	13.9175			0.0223037
$625$		0			0
$626$	−717.278	+	414.121i	−1.14581	+	0.661535i
$627$	−101.238	−	175.349i	−0.161464	−	0.279663i
$628$	−43.7630	−	25.2666i	−0.0696863	−	0.0402334i
$629$		−	249.247i		−	0.396260i
$630$		0			0
$631$	−1204.19			−1.90839			−0.954193	−	0.299191i	$-0.903283\pi$
$631$	−1204.19			−1.90839			−0.954193	+	0.299191i	$0.903283\pi$
$632$	164.571	−	285.045i	0.260397	−	0.451021i
$633$	−381.620	+	220.328i	−0.602874	+	0.348070i
$634$	184.716	+	319.938i	0.291351	+	0.504634i
$635$		0			0
$636$		−	341.048i		−	0.536239i
$637$	44.8845	−	87.6029i	0.0704623	−	0.137524i
$638$	−630.468			−0.988194
$639$	107.734	−	186.600i	0.168597	−	0.292019i
$640$		0			0
$641$	273.033	+	472.908i	0.425949	+	0.737766i	0.996509	−	0.0834907i	$-0.0266069\pi$
$641$	273.033	+	472.908i	0.425949	+	0.737766i	−0.570559	+	0.821256i	$0.693274\pi$
$642$	−67.7989	−	39.1437i	−0.105606	−	0.0609715i
$643$			193.418i			0.300805i	0.988625	+	0.150403i	$0.0480570\pi$
$643$			193.418i			0.300805i	−0.988625	+	0.150403i	$0.951943\pi$
$644$	−536.304	−	129.394i	−0.832771	−	0.200922i
$645$		0			0
$646$	98.7446	−	171.031i	0.152855	−	0.264753i
$647$	−103.099	+	59.5245i	−0.159350	+	0.0920007i	−0.577554	−	0.816352i	$-0.695993\pi$
$647$	−103.099	+	59.5245i	−0.159350	+	0.0920007i	0.418205	+	0.908353i	$0.362660\pi$
$648$	12.7279	+	22.0454i	0.0196419	+	0.0340207i
$649$	195.076	+	112.627i	0.300580	+	0.173540i
$650$		0			0
$651$	−46.0033	+	48.3683i	−0.0706657	+	0.0742985i
$652$	−111.465			−0.170959
$653$	293.854	−	508.970i	0.450006	−	0.779433i	−0.548380	−	0.836229i	$-0.684755\pi$
$653$	293.854	−	508.970i	0.450006	−	0.779433i	0.998386	+	0.0567963i	$0.0180886\pi$
$654$	−449.831	+	259.710i	−0.687815	+	0.397110i
$655$		0			0
$656$	58.4782	+	33.7624i	0.0891436	+	0.0514671i
$657$		−	2.41783i		−	0.00368011i
$658$	433.707	−	127.939i	0.659130	−	0.194437i
$659$	−36.3580			−0.0551714			−0.0275857	−	0.999619i	$-0.508782\pi$
$659$	−36.3580			−0.0551714			−0.0275857	+	0.999619i	$0.508782\pi$
$660$		0			0
$661$	279.780	−	161.531i	0.423268	−	0.244374i	−0.273207	−	0.961955i	$-0.588084\pi$
$661$	279.780	−	161.531i	0.423268	−	0.244374i	0.696475	+	0.717582i	$0.254751\pi$
$662$	135.055	+	233.922i	0.204011	+	0.353357i
$663$	63.9095	+	36.8982i	0.0963944	+	0.0556534i
$664$		−	141.773i		−	0.213513i
$665$		0			0
$666$	49.8578			0.0748616
$667$	494.733	−	856.903i	0.741729	−	1.28471i
$668$	454.597	−	262.461i	0.680534	−	0.392906i
$669$	−170.707	−	295.674i	−0.255168	−	0.441964i
$670$		0			0
$671$			1682.00i			2.50671i
$672$	−49.6972	−	47.2672i	−0.0739541	−	0.0703381i
$673$	705.426			1.04818			0.524091	−	0.851663i	$-0.324405\pi$
$673$	705.426			1.04818			0.524091	+	0.851663i	$0.324405\pi$
$674$	−159.883	+	276.926i	−0.237216	+	0.410870i
$675$		0			0
$676$	−164.965	−	285.727i	−0.244031	−	0.422673i
$677$	−720.152	−	415.780i	−1.06374	−	0.614151i	−0.137276	−	0.990533i	$-0.543835\pi$
$677$	−720.152	−	415.780i	−1.06374	−	0.614151i	−0.926465	+	0.376382i	$0.877168\pi$
$678$			223.000i			0.328908i
$679$	−271.946	+	1127.15i	−0.400510	+	1.66001i
$680$		0			0
$681$	248.054	−	429.643i	0.364250	−	0.630900i
$682$	119.720	−	69.1203i	0.175542	−	0.101349i
$683$	486.271	+	842.246i	0.711964	+	1.23316i	0.964119	+	0.265470i	$0.0855272\pi$
$683$	486.271	+	842.246i	0.711964	+	1.23316i	−0.252155	+	0.967687i	$0.581139\pi$
$684$	34.2119	+	19.7522i	0.0500174	+	0.0288775i
$685$		0			0
$686$	−457.796	+	160.377i	−0.667341	+	0.233786i
$687$	−357.256			−0.520023
$688$	55.4949	−	96.1200i	0.0806612	−	0.139709i
$689$	171.276	−	98.8863i	0.248586	−	0.143521i
$690$		0			0
$691$	443.849	+	256.256i	0.642328	+	0.370848i	0.785511	−	0.618848i	$-0.212400\pi$
$691$	443.849	+	256.256i	0.642328	+	0.370848i	−0.143183	+	0.989696i	$0.545734\pi$
$692$		−	316.678i		−	0.457627i
$693$	−362.451	−	87.4482i	−0.523018	−	0.126188i
$694$	938.008			1.35160
$695$		0			0
$696$	106.529	−	61.5045i	0.153059	−	0.0883686i
$697$	179.022	+	310.076i	0.256847	+	0.444872i
$698$	359.802	+	207.732i	0.515476	+	0.297610i
$699$		−	11.9390i		−	0.0170802i
$700$		0			0
$701$	−259.526			−0.370223			−0.185111	−	0.982718i	$-0.559265\pi$
$701$	−259.526			−0.370223			−0.185111	+	0.982718i	$0.559265\pi$
$702$	−7.38087	+	12.7840i	−0.0105141	+	0.0182109i
$703$	67.0074	−	38.6867i	0.0953163	−	0.0550309i
$704$	71.0193	+	123.009i	0.100880	+	0.174729i
$705$		0			0
$706$		−	506.373i		−	0.717243i
$707$	1325.34	−	390.962i	1.87459	−	0.552987i
$708$	−43.9489			−0.0620747
$709$	−138.685	+	240.210i	−0.195607	+	0.338801i	−0.947099	−	0.320941i	$-0.896001\pi$
$709$	−138.685	+	240.210i	−0.195607	+	0.338801i	0.751492	+	0.659742i	$0.229334\pi$
$710$		0			0
$711$	174.554	+	302.336i	0.245505	+	0.425226i
$712$	−211.940	−	122.364i	−0.297669	−	0.171859i
$713$			216.957i			0.304287i
$714$	−102.895	−	348.810i	−0.144111	−	0.488529i
$715$		0			0
$716$	10.0283	−	17.3695i	0.0140060	−	0.0242591i
$717$	434.943	−	251.115i	0.606615	−	0.350230i
$718$	−40.0217	−	69.3197i	−0.0557406	−	0.0965455i
$719$	1165.19	+	672.723i	1.62057	+	0.935638i	0.986767	+	0.162144i	$0.0518410\pi$
$719$	1165.19	+	672.723i	1.62057	+	0.935638i	0.633805	+	0.773493i	$0.281492\pi$
$720$		0			0
$721$	358.718	+	341.178i	0.497528	+	0.473202i
$722$	−449.225			−0.622195
$723$	282.791	−	489.809i	0.391136	−	0.677467i
$724$	551.040	−	318.143i	0.761105	−	0.439424i
$725$		0			0
$726$	412.032	+	237.887i	0.567538	+	0.327668i
$727$			1143.24i			1.57255i	0.617876	+	0.786275i	$0.287993\pi$
$727$			1143.24i			1.57255i	−0.617876	+	0.786275i	$0.712007\pi$
$728$	9.32823	−	38.6632i	0.0128135	−	0.0531088i
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	509.668	−	294.257i	0.697220	−	0.402540i
$732$	−164.086	−	284.205i	−0.224161	−	0.388258i
$733$	−1181.32	−	682.037i	−1.61163	−	0.930474i	−0.988993	−	0.147961i	$-0.952729\pi$
$733$	−1181.32	−	682.037i	−1.61163	−	0.930474i	−0.622634	−	0.782513i	$-0.713938\pi$
$734$		−	684.996i		−	0.933237i
$735$		0			0
$736$	−222.918			−0.302877
$737$	−74.1448	+	128.423i	−0.100603	+	0.174250i
$738$	−62.0255	+	35.8104i	−0.0840454	+	0.0485236i
$739$	101.096	+	175.103i	0.136801	+	0.236946i	0.926284	−	0.376827i	$-0.122985\pi$
$739$	101.096	+	175.103i	0.136801	+	0.236946i	−0.789483	+	0.613772i	$0.789651\pi$
$740$		0			0
$741$			22.9085i			0.0309156i
$742$	−947.441	−	228.588i	−1.27687	−	0.308070i
$743$	344.793			0.464055			0.232028	−	0.972709i	$-0.425464\pi$
$743$	344.793			0.464055			0.232028	+	0.972709i	$0.425464\pi$
$744$	−13.4859	+	23.3583i	−0.0181262	+	0.0313955i
$745$		0			0
$746$	249.540	+	432.217i	0.334505	+	0.579379i
$747$	130.227	+	75.1864i	0.174333	+	0.100651i
$748$			753.147i			1.00688i
$749$	−154.185	+	162.111i	−0.205854	+	0.216437i
$750$		0			0
$751$	−110.795	+	191.903i	−0.147530	+	0.255530i	−0.930314	−	0.366764i	$-0.880466\pi$
$751$	−110.795	+	191.903i	−0.147530	+	0.255530i	0.782784	+	0.622294i	$0.213799\pi$
$752$	158.232	−	91.3550i	0.210414	−	0.121483i
$753$	−295.972	−	512.639i	−0.393057	−	0.680795i
$754$	61.7757	+	35.6662i	0.0819307	+	0.0473027i
$755$		0			0
$756$	69.7736	−	20.5825i	0.0922932	−	0.0272256i
$757$	−1006.02			−1.32895			−0.664476	−	0.747310i	$-0.731345\pi$
$757$	−1006.02			−1.32895			−0.664476	+	0.747310i	$0.731345\pi$
$758$	−91.6875	+	158.807i	−0.120960	+	0.209508i
$759$	−1049.49	+	605.922i	−1.38272	+	0.798316i
$760$		0			0
$761$	981.832	+	566.861i	1.29019	+	0.744889i	0.978687	−	0.205357i	$-0.0658355\pi$
$761$	981.832	+	566.861i	1.29019	+	0.744889i	0.311499	+	0.950246i	$0.399169\pi$
$762$			394.229i			0.517361i
$763$	419.981	+	1423.71i	0.550434	+	1.86594i
$764$	−7.42566			−0.00971946
$765$		0			0
$766$	513.948	−	296.728i	0.670951	−	0.387374i
$767$	−12.7429	−	22.0713i	−0.0166139	−	0.0287762i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$		−	206.796i		−	0.268915i	−0.990919	−	0.134458i	$-0.957071\pi$
$769$		−	206.796i		−	0.268915i	0.990919	−	0.134458i	$-0.0429292\pi$
$770$		0			0
$771$	−337.482			−0.437719
$772$	−295.541	+	511.891i	−0.382825	+	0.663072i
$773$	663.637	−	383.151i	0.858521	−	0.495668i	−0.00499551	−	0.999988i	$-0.501590\pi$
$773$	663.637	−	383.151i	0.858521	−	0.495668i	0.863517	+	0.504320i	$0.168257\pi$
$774$	58.8612	+	101.951i	0.0760481	+	0.131719i
$775$		0			0
$776$			468.506i			0.603744i
$777$	33.4173	−	138.506i	0.0430081	−	0.178258i
$778$	−139.216			−0.178940
$779$	−55.5736	+	96.2563i	−0.0713396	+	0.123564i
$780$		0			0
$781$	637.598	+	1104.35i	0.816387	+	1.41402i
$782$	−1023.64	−	591.000i	−1.30901	−	0.755755i
$783$			130.471i			0.166629i
$784$	−164.619	+	106.379i	−0.209973	+	0.135688i
$785$		0			0
$786$	−20.4523	+	35.4244i	−0.0260207	+	0.0450692i
$787$	763.935	−	441.058i	0.970693	−	0.560430i	0.0712454	−	0.997459i	$-0.477303\pi$
$787$	763.935	−	441.058i	0.970693	−	0.560430i	0.899447	+	0.437029i	$0.143969\pi$
$788$	231.134	+	400.336i	0.293317	+	0.508041i
$789$	207.097	+	119.568i	0.262481	+	0.151543i
$790$		0			0
$791$	619.499	+	149.466i	0.783185	+	0.188958i
$792$	−150.655			−0.190221
$793$	95.1527	−	164.809i	0.119991	−	0.207830i
$794$	227.274	−	131.217i	0.286239	−	0.165260i
$795$		0			0
$796$	50.7277	+	29.2877i	0.0637283	+	0.0367936i
$797$		−	1202.53i		−	1.50882i	−0.656406	−	0.754408i	$-0.727924\pi$
$797$		−	1202.53i		−	1.50882i	0.656406	−	0.754408i	$-0.272076\pi$
$798$	77.8028	−	81.8025i	0.0974972	−	0.102509i
$799$	968.804			1.21252
$800$		0			0
$801$	224.797	−	129.786i	0.280645	−	0.162030i
$802$	−132.477	−	229.457i	−0.165183	−	0.286106i
$803$	12.3923	+	7.15470i	0.0154325	+	0.00890997i
$804$		−	28.9324i		−	0.0359856i
$805$		0			0
$806$	−15.6408			−0.0194055
$807$	8.57284	−	14.8486i	0.0106231	−	0.0183998i
$808$	483.529	−	279.166i	0.598427	−	0.345502i
$809$	−693.426	−	1201.05i	−0.857140	−	1.48461i	−0.874646	−	0.484763i	$-0.838906\pi$
$809$	−693.426	−	1201.05i	−0.857140	−	1.48461i	0.0175061	−	0.999847i	$-0.494427\pi$
$810$		0			0
$811$		−	987.281i		−	1.21736i	−0.793415	−	0.608681i	$-0.791699\pi$
$811$		−	987.281i		−	1.21736i	0.793415	−	0.608681i	$-0.208301\pi$
$812$	−99.4600	−	337.164i	−0.122488	−	0.415226i
$813$	−32.9423			−0.0405195
$814$	−147.536	+	255.540i	−0.181248	+	0.313931i
$815$		0			0
$816$	−73.4724	−	127.258i	−0.0900397	−	0.155953i
$817$	158.215	+	91.3457i	0.193654	+	0.111806i
$818$			298.762i			0.365234i
$819$	30.5674	+	29.0728i	0.0373228	+	0.0354979i
$820$		0			0
$821$	223.132	−	386.477i	0.271781	−	0.470739i	−0.697537	−	0.716549i	$-0.745721\pi$
$821$	223.132	−	386.477i	0.271781	−	0.470739i	0.969318	+	0.245810i	$0.0790539\pi$
$822$	−268.469	+	155.001i	−0.326605	+	0.188565i
$823$	413.931	+	716.949i	0.502954	+	0.871141i	0.999994	+	0.00341406i	$0.00108673\pi$
$823$	413.931	+	716.949i	0.502954	+	0.871141i	−0.497040	+	0.867727i	$0.665580\pi$
$824$	173.234	+	100.017i	0.210235	+	0.121379i
$825$		0			0
$826$	−29.4568	+	122.091i	−0.0356620	+	0.147810i
$827$	−1333.16			−1.61204			−0.806022	−	0.591885i	$-0.798384\pi$
$827$	−1333.16			−1.61204			−0.806022	+	0.591885i	$0.798384\pi$
$828$	118.220	−	204.763i	0.142778	−	0.247298i
$829$	−1257.72	+	726.147i	−1.51716	+	0.875931i	−0.517360	+	0.855768i	$0.673085\pi$
$829$	−1257.72	+	726.147i	−1.51716	+	0.875931i	−0.999797	+	0.0201631i	$0.993581\pi$
$830$		0			0
$831$	308.194	+	177.936i	0.370871	+	0.214122i
$832$		−	16.0706i		−	0.0193156i
$833$	−1037.97	+	52.0561i	−1.24606	+	0.0624924i
$834$	331.565			0.397560
$835$		0			0
$836$	−202.475	+	116.899i	−0.242195	+	0.139832i
$837$	−14.3040	−	24.7752i	−0.0170896	−	0.0296000i
$838$	59.9518	+	34.6132i	0.0715416	+	0.0413045i
$839$		−	602.259i		−	0.717830i	−0.933370	−	0.358915i	$-0.883147\pi$
$839$		−	602.259i		−	0.717830i	0.933370	−	0.358915i	$-0.116853\pi$
$840$		0			0
$841$	−210.532			−0.250335
$842$	−117.761	+	203.968i	−0.139859	+	0.242243i
$843$	−674.492	+	389.418i	−0.800109	+	0.461943i
$844$	254.413	+	440.656i	0.301437	+	0.522105i
$845$		0			0
$846$			193.793i			0.229070i
$847$	937.022	−	985.193i	1.10628	−	1.16316i
$848$	−393.809			−0.464397
$849$	−137.762	+	238.611i	−0.162264	+	0.281050i
$850$		0			0
$851$	−231.545	−	401.048i	−0.272086	−	0.471267i
$852$	−215.468	−	124.400i	−0.252896	−	0.146010i
$853$		−	487.049i		−	0.570983i	−0.958381	−	0.285492i	$-0.907843\pi$
$853$		−	487.049i		−	0.570983i	0.958381	−	0.285492i	$-0.0921569\pi$
$854$	−899.508	+	265.346i	−1.05329	+	0.310710i
$855$		0			0
$856$	−45.1993	+	78.2875i	−0.0528029	+	0.0914573i
$857$	1199.88	−	692.754i	1.40010	−	0.808347i	0.405696	−	0.914008i	$-0.367029\pi$
$857$	1199.88	−	692.754i	1.40010	−	0.808347i	0.994402	+	0.105661i	$0.0336957\pi$
$858$	−43.6820	−	75.6595i	−0.0509115	−	0.0881813i
$859$	1165.46	+	672.881i	1.35677	+	0.783331i	0.989187	−	0.146660i	$-0.0468523\pi$
$859$	1165.46	+	672.881i	1.35677	+	0.783331i	0.367582	+	0.929991i	$0.380186\pi$
$860$		0			0
$861$	57.9097	+	196.310i	0.0672586	+	0.228003i
$862$	−271.285			−0.314716
$863$	−124.905	+	216.341i	−0.144733	+	0.250685i	−0.929273	−	0.369393i	$-0.879566\pi$
$863$	−124.905	+	216.341i	−0.144733	+	0.250685i	0.784540	+	0.620078i	$0.212899\pi$
$864$	25.4558	−	14.6969i	0.0294628	−	0.0170103i
$865$		0			0
$866$	−623.605	−	360.039i	−0.720099	−	0.415749i
$867$		−	278.599i		−	0.321337i
$868$	55.8509	+	53.1201i	0.0643444	+	0.0611983i
$869$	−2066.11			−2.37758
$870$		0			0
$871$	14.5300	−	8.38890i	0.0166820	−	0.00963134i
$872$	299.887	+	519.420i	0.343907	+	0.595665i
$873$	−430.350	−	248.463i	−0.492955	−	0.284608i
$874$		−	366.927i		−	0.419825i
$875$		0			0
$876$	−2.79187			−0.00318707
$877$	354.104	−	613.327i	0.403768	−	0.699346i	−0.590409	−	0.807104i	$-0.701034\pi$
$877$	354.104	−	613.327i	0.403768	−	0.699346i	0.994177	+	0.107757i	$0.0343670\pi$
$878$	−649.335	+	374.894i	−0.739562	+	0.426986i
$879$	−391.391	−	677.908i	−0.445268	−	0.771227i
$880$		0			0
$881$		−	83.7844i		−	0.0951014i	−0.998869	−	0.0475507i	$-0.984858\pi$
$881$		−	83.7844i		−	0.0951014i	0.998869	−	0.0475507i	$-0.0151416\pi$
$882$	−10.4130	−	207.628i	−0.0118061	−	0.235406i
$883$	1155.05			1.30810			0.654051	−	0.756450i	$-0.273068\pi$
$883$	1155.05			1.30810			0.654051	+	0.756450i	$0.273068\pi$
$884$	42.6063	−	73.7964i	0.0481972	−	0.0834800i
$885$		0			0
$886$	301.152	+	521.610i	0.339900	+	0.588725i
$887$	278.227	+	160.634i	0.313672	+	0.181098i	0.648568	−	0.761157i	$-0.275368\pi$
$887$	278.227	+	160.634i	0.313672	+	0.181098i	−0.334897	+	0.942255i	$0.608701\pi$
$888$		−	57.5708i		−	0.0648320i
$889$	1095.18	+	264.233i	1.23192	+	0.297225i
$890$		0			0
$891$	79.8967	−	138.385i	0.0896709	−	0.155314i
$892$	−341.415	+	197.116i	−0.382752	+	0.220982i
$893$	150.372	+	260.452i	0.168390	+	0.291660i
$894$	−171.007	−	98.7311i	−0.191283	−	0.110438i
$895$		0			0
$896$	−54.5795	+	57.3854i	−0.0609146	+	0.0640462i
$897$	137.111			0.152855
$898$	−208.257	+	360.711i	−0.231912	+	0.401683i
$899$	−119.720	+	69.1203i	−0.133170	+	0.0768858i
$900$		0			0
$901$	−1808.38	−	1044.07i	−2.00708	−	1.15879i
$902$		−	423.872i		−	0.469925i
$903$	322.673	−	95.1855i	0.357335	−	0.105410i
$904$	257.498			0.284843
$905$		0			0
$906$	29.5625	−	17.0679i	0.0326297	−	0.0188388i
$907$	192.833	+	333.996i	0.212605	+	0.368243i	0.952529	−	0.304448i	$-0.0984719\pi$
$907$	192.833	+	333.996i	0.212605	+	0.368243i	−0.739924	+	0.672690i	$0.765139\pi$
$908$	−496.109	−	286.429i	−0.546376	−	0.315450i
$909$			592.200i			0.651485i
$910$		0			0
$911$	544.040			0.597190			0.298595	−	0.954380i	$-0.403482\pi$
$911$	544.040			0.597190			0.298595	+	0.954380i	$0.403482\pi$
$912$	22.8079	−	39.5045i	0.0250087	−	0.0433163i
$913$	−770.718	+	444.974i	−0.844159	+	0.487376i
$914$	−57.8704	−	100.235i	−0.0633156	−	0.109666i
$915$		0			0
$916$			412.523i			0.450353i
$917$	84.7018	+	80.5603i	0.0923684	+	0.0878520i
$918$	155.858			0.169780
$919$	−305.574	+	529.269i	−0.332507	+	0.575919i	−0.983003	−	0.183591i	$-0.941228\pi$
$919$	−305.574	+	529.269i	−0.332507	+	0.575919i	0.650496	+	0.759510i	$0.274561\pi$
$920$		0			0
$921$	481.038	+	833.182i	0.522299	+	0.904649i
$922$	929.764	+	536.799i	1.00842	+	0.582212i
$923$		−	144.278i		−	0.156315i
$924$	−100.977	+	418.523i	−0.109282	+	0.452947i
$925$		0			0
$926$	279.298	−	483.759i	0.301618	−	0.522418i
$927$	−183.742	+	106.084i	−0.198212	+	0.114438i
$928$	−71.0193	−	123.009i	−0.0765294	−	0.132553i
$929$	−744.000	−	429.549i	−0.800862	−	0.462378i	0.0429108	−	0.999079i	$-0.486337\pi$
$929$	−744.000	−	429.549i	−0.800862	−	0.462378i	−0.843772	+	0.536701i	$0.819670\pi$
$930$		0			0
$931$	−175.102	−	270.966i	−0.188080	−	0.291049i
$932$	−13.7860			−0.0147918
$933$	146.444	−	253.648i	0.156960	−	0.271863i
$934$	−328.613	+	189.725i	−0.351834	+	0.203131i
$935$		0			0
$936$	14.7617	+	8.52270i	0.0157711	+	0.00910545i
$937$			1665.22i			1.77718i	0.458700	+	0.888591i	$0.348315\pi$
$937$			1665.22i			1.77718i	−0.458700	+	0.888591i	$0.651685\pi$
$938$	−80.3750	−	19.3920i	−0.0856876	−	0.0206738i
$939$	−1014.38			−1.08028
$940$		0			0
$941$	946.705	−	546.581i	1.00606	−	0.580851i	0.0960266	−	0.995379i	$-0.469387\pi$
$941$	946.705	−	546.581i	1.00606	−	0.580851i	0.910037	+	0.414528i	$0.136053\pi$
$942$	−30.9451	−	53.5985i	−0.0328505	−	0.0568987i
$943$	576.107	+	332.616i	0.610930	+	0.352721i
$944$			50.7478i			0.0537583i
$945$		0			0
$946$	−696.714			−0.736484
$947$	−702.226	+	1216.29i	−0.741527	+	1.28436i	0.210273	+	0.977643i	$0.432565\pi$
$947$	−702.226	+	1216.29i	−0.741527	+	1.28436i	−0.951800	+	0.306720i	$0.900769\pi$
$948$	349.108	−	201.557i	0.368257	−	0.212613i
$949$	−0.809498	−	1.40209i	−0.000853001	−	0.00147744i
$950$		0			0
$951$			452.461i			0.475773i
$952$	−402.771	+	118.813i	−0.423079	+	0.124804i
$953$	−1284.11			−1.34744			−0.673722	−	0.738985i	$-0.735305\pi$
$953$	−1284.11			−1.34744			−0.673722	+	0.738985i	$0.735305\pi$
$954$	208.849	−	361.736i	0.218919	−	0.379179i
$955$		0			0
$956$	−289.962	−	502.229i	−0.303308	−	0.525344i
$957$	−668.712	−	386.081i	−0.698759	−	0.403429i
$958$			768.582i			0.802278i
$959$	250.654	+	849.704i	0.261371	+	0.886031i
$960$		0			0
$961$	−465.344	+	806.000i	−0.484229	+	0.838709i
$962$	28.9123	−	16.6926i	0.0300544	−	0.0173519i
$963$	−47.9411	−	83.0364i	−0.0497831	−	0.0862268i
$964$	−565.582	−	326.539i	−0.586704	−	0.338733i
$965$		0			0
$966$	−489.600	−	465.661i	−0.506832	−	0.482050i
$967$	−437.417			−0.452344			−0.226172	−	0.974087i	$-0.572621\pi$
$967$	−437.417			−0.452344			−0.226172	+	0.974087i	$0.572621\pi$
$968$	274.688	−	475.774i	0.283769	−	0.491502i
$969$	209.469	−	120.937i	0.216170	−	0.124806i
$970$		0			0
$971$	−277.241	−	160.065i	−0.285521	−	0.164846i	0.350399	−	0.936601i	$-0.386046\pi$
$971$	−277.241	−	160.065i	−0.285521	−	0.164846i	−0.635920	+	0.771755i	$0.719379\pi$
$972$			31.1769i			0.0320750i
$973$	222.232	−	921.097i	0.228399	−	0.946657i
$974$	560.767			0.575736
$975$		0			0
$976$	−328.172	+	189.470i	−0.336242	+	0.194129i
$977$	−109.535	−	189.720i	−0.112114	−	0.194187i	0.804509	−	0.593941i	$-0.202429\pi$
$977$	−109.535	−	189.720i	−0.112114	−	0.194187i	−0.916622	+	0.399754i	$0.869095\pi$
$978$	−118.227	−	68.2581i	−0.120886	−	0.0697936i
$979$			1536.22i			1.56918i
$980$		0			0
$981$	−636.157			−0.648478
$982$	530.795	−	919.364i	0.540525	−	0.936216i
$983$	−188.528	+	108.847i	−0.191789	+	0.110729i	−0.592820	−	0.805335i	$-0.701985\pi$
$983$	−188.528	+	108.847i	−0.191789	+	0.110729i	0.401031	+	0.916064i	$0.368652\pi$
$984$	41.3503	+	71.6209i	0.0420227	+	0.0727854i
$985$		0			0
$986$		−	753.147i		−	0.763841i
$987$	538.363	+	129.890i	0.545454	+	0.131601i
$988$	26.4524			0.0267737
$989$	546.717	−	946.941i	0.552798	−	0.957473i
$990$		0			0
$991$	−566.322	−	980.899i	−0.571466	−	0.989808i	−0.996416	−	0.0845907i	$-0.973042\pi$
$991$	−566.322	−	980.899i	−0.571466	−	0.989808i	0.424950	−	0.905217i	$-0.360292\pi$
$992$	26.9718	+	15.5722i	0.0271893	+	0.0156978i
$993$			330.816i			0.333148i
$994$	−490.005	+	515.195i	−0.492962	+	0.518305i
$995$		0			0
$996$	86.8178	−	150.373i	0.0871665	−	0.150977i
$997$	−1350.51	+	779.718i	−1.35458	+	0.782065i	−0.988887	−	0.148672i	$-0.952500\pi$
$997$	−1350.51	+	779.718i	−1.35458	+	0.782065i	−0.365689	+	0.930737i	$0.619167\pi$
$998$	−94.2980	−	163.329i	−0.0944869	−	0.163656i
$999$	52.8822	+	30.5315i	0.0529351	+	0.0305621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.p.f.901.4	yes	12
5.2	odd	4		1050.3.q.d.649.8		24
5.3	odd	4		1050.3.q.d.649.2		24
5.4	even	2		1050.3.p.e.901.3	yes	12
7.3	odd	6	inner	1050.3.p.f.451.4	yes	12
35.3	even	12		1050.3.q.d.199.8		24
35.17	even	12		1050.3.q.d.199.2		24
35.24	odd	6		1050.3.p.e.451.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.p.e.451.3	✓	12	35.24	odd	6
1050.3.p.e.901.3	yes	12	5.4	even	2
1050.3.p.f.451.4	yes	12	7.3	odd	6	inner
1050.3.p.f.901.4	yes	12	1.1	even	1	trivial
1050.3.q.d.199.2		24	35.17	even	12
1050.3.q.d.199.8		24	35.3	even	12
1050.3.q.d.649.2		24	5.3	odd	4
1050.3.q.d.649.8		24	5.2	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.80475 - 1.64177i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-6.80475 - 1.64177i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(8.87741 + 15.3761i) q^{11} +(-3.00000 - 1.73205i) q^{12} -2.00882i q^{13} +(-6.82244 + 7.17317i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-18.3681 + 10.6048i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(-5.70198 - 3.29204i) q^{19} +(-11.6289 + 3.43042i) q^{21} +25.1091 q^{22} +(-19.7033 + 34.1271i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-2.46029 - 1.42045i) q^{26} -5.19615i q^{27} +(3.96111 + 13.4279i) q^{28} -25.1091 q^{29} +(4.76798 - 2.75280i) q^{31} +(2.82843 + 4.89898i) q^{32} +(26.6322 + 15.3761i) q^{33} +29.9950i q^{34} -6.00000 q^{36} +(-5.87580 + 10.1772i) q^{37} +(-8.06382 + 4.65565i) q^{38} +(-1.73969 - 3.01323i) q^{39} -16.8812i q^{41} +(-4.02151 + 16.6682i) q^{42} -27.7474 q^{43} +(17.7548 - 30.7523i) q^{44} +(27.8647 + 48.2631i) q^{46} +(-39.5579 - 22.8388i) q^{47} +6.92820i q^{48} +(43.6092 + 22.3437i) q^{49} +(-18.3681 + 31.8145i) q^{51} +(-3.47938 + 2.00882i) q^{52} +(49.2261 + 85.2621i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(19.2467 + 4.64364i) q^{56} -11.4040 q^{57} +(-17.7548 + 30.7523i) q^{58} +(10.9872 - 6.34348i) q^{59} +(82.0429 + 47.3675i) q^{61} -7.78609i q^{62} +(-14.4726 + 15.2166i) q^{63} +8.00000 q^{64} +(37.6637 - 21.7451i) q^{66} +(4.17603 + 7.23310i) q^{67} +(36.7362 + 21.2096i) q^{68} +68.2543i q^{69} +71.8225 q^{71} +(-4.24264 + 7.34847i) q^{72} +(0.697968 - 0.402972i) q^{73} +(8.30963 + 14.3927i) q^{74} +13.1682i q^{76} +(-35.1644 - 119.205i) q^{77} -4.92058 q^{78} +(-58.1846 + 100.779i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-20.6752 - 11.9368i) q^{82} +50.1243i q^{83} +(17.5706 + 16.7115i) q^{84} +(-19.6204 + 33.9835i) q^{86} +(-37.6637 + 21.7451i) q^{87} +(-25.1091 - 43.4903i) q^{88} +(74.9322 + 43.2621i) q^{89} +(-3.29803 + 13.6695i) q^{91} +78.8133 q^{92} +(4.76798 - 8.25839i) q^{93} +(-55.9433 + 32.2989i) q^{94} +(8.48528 + 4.89898i) q^{96} -165.642i q^{97} +(58.2017 - 37.6107i) q^{98} +53.2645 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9}+O(q^{10}) \) 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9	\( 12 q + 18 q^{3} - 12 q^{4} + 8 q^{7} + 18 q^{9} - 4 q^{11} - 36 q^{12} + 8 q^{14} - 24 q^{16} - 24 q^{17} + 12 q^{19} + 18 q^{21} + 24 q^{22} - 60 q^{23} - 24 q^{26} + 4 q^{28} - 24 q^{29} - 198 q^{31} - 12 q^{33} - 72 q^{36} + 70 q^{37} - 60 q^{38} - 36 q^{39} + 36 q^{42} - 84 q^{43} - 8 q^{44} + 32 q^{46} - 60 q^{47} + 28 q^{49} - 24 q^{51} - 72 q^{52} + 44 q^{53} + 40 q^{56} + 24 q^{57} + 8 q^{58} - 48 q^{59} + 186 q^{61} + 30 q^{63} + 96 q^{64} + 36 q^{66} + 152 q^{67} + 48 q^{68} - 136 q^{71} + 18 q^{73} - 64 q^{74} + 132 q^{77} - 48 q^{78} - 70 q^{79} - 54 q^{81} - 84 q^{82} - 12 q^{84} - 208 q^{86} - 36 q^{87} - 24 q^{88} + 168 q^{89} + 292 q^{91} + 240 q^{92} - 198 q^{93} - 204 q^{94} + 48 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q + 18 * q^3 - 12 * q^4 + 8 * q^7 + 18 * q^9 - 4 * q^11 - 36 * q^12 + 8 * q^14 - 24 * q^16 - 24 * q^17 + 12 * q^19 + 18 * q^21 + 24 * q^22 - 60 * q^23 - 24 * q^26 + 4 * q^28 - 24 * q^29 - 198 * q^31 - 12 * q^33 - 72 * q^36 + 70 * q^37 - 60 * q^38 - 36 * q^39 + 36 * q^42 - 84 * q^43 - 8 * q^44 + 32 * q^46 - 60 * q^47 + 28 * q^49 - 24 * q^51 - 72 * q^52 + 44 * q^53 + 40 * q^56 + 24 * q^57 + 8 * q^58 - 48 * q^59 + 186 * q^61 + 30 * q^63 + 96 * q^64 + 36 * q^66 + 152 * q^67 + 48 * q^68 - 136 * q^71 + 18 * q^73 - 64 * q^74 + 132 * q^77 - 48 * q^78 - 70 * q^79 - 54 * q^81 - 84 * q^82 - 12 * q^84 - 208 * q^86 - 36 * q^87 - 24 * q^88 + 168 * q^89 + 292 * q^91 + 240 * q^92 - 198 * q^93 - 204 * q^94 + 48 * q^98 - 24 * q^99

Introduction

L-functions

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