LMFDB - Embedded newform 294.3.g.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,3,Mod(19,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("294.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	294.g (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.01091977219$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.31
Dual form			294.3.g.b.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(5.12132 - 2.95680i) q^{5} -2.44949i q^{6} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(5.12132 - 2.95680i) q^{5} -2.44949i q^{6} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(7.24264 + 4.18154i) q^{10} +(0.878680 - 1.52192i) q^{11} +(3.00000 - 1.73205i) q^{12} -18.7554i q^{13} -10.2426 q^{15} +(-2.00000 - 3.46410i) q^{16} +(20.3345 + 11.7401i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(19.9706 - 11.5300i) q^{19} +11.8272i q^{20} +2.48528 q^{22} +(-9.36396 - 16.2189i) q^{23} +(4.24264 + 2.44949i) q^{24} +(4.98528 - 8.63476i) q^{25} +(22.9706 - 13.2621i) q^{26} -5.19615i q^{27} +30.0000 q^{29} +(-7.24264 - 12.5446i) q^{30} +(7.45584 + 4.30463i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-2.63604 + 1.52192i) q^{33} +33.2061i q^{34} -6.00000 q^{36} +(35.4558 + 61.4113i) q^{37} +(28.2426 + 16.3059i) q^{38} +(-16.2426 + 28.1331i) q^{39} +(-14.4853 + 8.36308i) q^{40} -41.3951i q^{41} +10.4264 q^{43} +(1.75736 + 3.04384i) q^{44} +(15.3640 + 8.87039i) q^{45} +(13.2426 - 22.9369i) q^{46} +(-33.5147 + 19.3497i) q^{47} +6.92820i q^{48} +14.1005 q^{50} +(-20.3345 - 35.2204i) q^{51} +(32.4853 + 18.7554i) q^{52} +(18.5147 - 32.0684i) q^{53} +(6.36396 - 3.67423i) q^{54} -10.3923i q^{55} -39.9411 q^{57} +(21.2132 + 36.7423i) q^{58} +(-84.4264 - 48.7436i) q^{59} +(10.2426 - 17.7408i) q^{60} +(-14.4853 + 8.36308i) q^{61} +12.1753i q^{62} +8.00000 q^{64} +(-55.4558 - 96.0523i) q^{65} +(-3.72792 - 2.15232i) q^{66} +(-30.4853 + 52.8021i) q^{67} +(-40.6690 + 23.4803i) q^{68} +32.4377i q^{69} -110.610 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-49.1543 - 28.3793i) q^{73} +(-50.1421 + 86.8487i) q^{74} +(-14.9558 + 8.63476i) q^{75} +46.1200i q^{76} -45.9411 q^{78} +(34.9117 + 60.4688i) q^{79} +(-20.4853 - 11.8272i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(50.6985 - 29.2708i) q^{82} -6.43583i q^{83} +138.853 q^{85} +(7.37258 + 12.7697i) q^{86} +(-45.0000 - 25.9808i) q^{87} +(-2.48528 + 4.30463i) q^{88} +(36.4523 - 21.0457i) q^{89} +25.0892i q^{90} +37.4558 q^{92} +(-7.45584 - 12.9139i) q^{93} +(-47.3970 - 27.3647i) q^{94} +(68.1838 - 118.098i) q^{95} +(-8.48528 + 4.89898i) q^{96} -51.7153i q^{97} +5.27208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 4 q^{4} + 12 q^{5} + 6 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 - 4 * q^4 + 12 * q^5 + 6 * q^9	$ 4 q - 6 q^{3} - 4 q^{4} + 12 q^{5} + 6 q^{9} + 12 q^{10} + 12 q^{11} + 12 q^{12} - 24 q^{15} - 8 q^{16} - 12 q^{17} + 12 q^{19} - 24 q^{22} - 12 q^{23} - 14 q^{25} + 24 q^{26} + 120 q^{29} - 12 q^{30} - 72 q^{31} - 36 q^{33} - 24 q^{36} + 40 q^{37} + 96 q^{38} - 48 q^{39} - 24 q^{40} - 128 q^{43} + 24 q^{44} + 36 q^{45} + 36 q^{46} - 168 q^{47} + 96 q^{50} + 12 q^{51} + 96 q^{52} + 108 q^{53} - 24 q^{57} - 168 q^{59} + 24 q^{60} - 24 q^{61} + 32 q^{64} - 120 q^{65} + 36 q^{66} - 88 q^{67} + 24 q^{68} - 120 q^{71} + 24 q^{73} - 144 q^{74} + 42 q^{75} - 48 q^{78} - 64 q^{79} - 48 q^{80} - 18 q^{81} + 84 q^{82} + 216 q^{85} + 120 q^{86} - 180 q^{87} + 24 q^{88} + 324 q^{89} + 48 q^{92} + 72 q^{93} + 48 q^{94} + 120 q^{95} + 72 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 - 4 * q^4 + 12 * q^5 + 6 * q^9 + 12 * q^10 + 12 * q^11 + 12 * q^12 - 24 * q^15 - 8 * q^16 - 12 * q^17 + 12 * q^19 - 24 * q^22 - 12 * q^23 - 14 * q^25 + 24 * q^26 + 120 * q^29 - 12 * q^30 - 72 * q^31 - 36 * q^33 - 24 * q^36 + 40 * q^37 + 96 * q^38 - 48 * q^39 - 24 * q^40 - 128 * q^43 + 24 * q^44 + 36 * q^45 + 36 * q^46 - 168 * q^47 + 96 * q^50 + 12 * q^51 + 96 * q^52 + 108 * q^53 - 24 * q^57 - 168 * q^59 + 24 * q^60 - 24 * q^61 + 32 * q^64 - 120 * q^65 + 36 * q^66 - 88 * q^67 + 24 * q^68 - 120 * q^71 + 24 * q^73 - 144 * q^74 + 42 * q^75 - 48 * q^78 - 64 * q^79 - 48 * q^80 - 18 * q^81 + 84 * q^82 + 216 * q^85 + 120 * q^86 - 180 * q^87 + 24 * q^88 + 324 * q^89 + 48 * q^92 + 72 * q^93 + 48 * q^94 + 120 * q^95 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	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
$5$	5.12132	−	2.95680i	1.02426	−	0.591359i	0.108928	−	0.994050i	$-0.465258\pi$
$5$	5.12132	−	2.95680i	1.02426	−	0.591359i	0.915336	+	0.402691i	$0.131925\pi$
$6$		−	2.44949i		−	0.408248i
$7$		0			0
$7$		0			0
$8$	−2.82843			−0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	7.24264	+	4.18154i	0.724264	+	0.418154i
$11$	0.878680	−	1.52192i	0.0798800	−	0.138356i	−0.823318	−	0.567580i	$-0.807880\pi$
$11$	0.878680	−	1.52192i	0.0798800	−	0.138356i	0.903198	+	0.429224i	$0.141213\pi$
$12$	3.00000	−	1.73205i	0.250000	−	0.144338i
$13$		−	18.7554i		−	1.44272i	−0.692559	−	0.721361i	$-0.743517\pi$
$13$		−	18.7554i		−	1.44272i	0.692559	−	0.721361i	$-0.256483\pi$
$14$		0			0
$15$	−10.2426			−0.682843
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	20.3345	+	11.7401i	1.19615	+	0.690597i	0.959694	−	0.281046i	$-0.0906814\pi$
$17$	20.3345	+	11.7401i	1.19615	+	0.690597i	0.236454	+	0.971643i	$0.424015\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	19.9706	−	11.5300i	1.05108	−	0.606843i	0.128130	−	0.991757i	$-0.459102\pi$
$19$	19.9706	−	11.5300i	1.05108	−	0.606843i	0.922952	+	0.384915i	$0.125769\pi$
$20$			11.8272i			0.591359i
$21$		0			0
$22$	2.48528			0.112967
$23$	−9.36396	−	16.2189i	−0.407129	−	0.705168i	0.587438	−	0.809269i	$-0.300137\pi$
$23$	−9.36396	−	16.2189i	−0.407129	−	0.705168i	−0.994567	+	0.104102i	$0.966803\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$	4.98528	−	8.63476i	0.199411	−	0.345390i
$26$	22.9706	−	13.2621i	0.883483	−	0.510079i
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	30.0000			1.03448			0.517241	−	0.855840i	$-0.326959\pi$
$29$	30.0000			1.03448			0.517241	+	0.855840i	$0.326959\pi$
$30$	−7.24264	−	12.5446i	−0.241421	−	0.418154i
$31$	7.45584	+	4.30463i	0.240511	+	0.138859i	0.615412	−	0.788206i	$-0.288990\pi$
$31$	7.45584	+	4.30463i	0.240511	+	0.138859i	−0.374901	+	0.927065i	$0.622323\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	−2.63604	+	1.52192i	−0.0798800	+	0.0461187i
$34$			33.2061i			0.976651i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	35.4558	+	61.4113i	0.958266	+	1.65977i	0.726711	+	0.686944i	$0.241048\pi$
$37$	35.4558	+	61.4113i	0.958266	+	1.65977i	0.231556	+	0.972822i	$0.425619\pi$
$38$	28.2426	+	16.3059i	0.743227	+	0.429103i
$39$	−16.2426	+	28.1331i	−0.416478	+	0.721361i
$40$	−14.4853	+	8.36308i	−0.362132	+	0.209077i
$41$		−	41.3951i		−	1.00964i	−0.863225	−	0.504819i	$-0.831559\pi$
$41$		−	41.3951i		−	1.00964i	0.863225	−	0.504819i	$-0.168441\pi$
$42$		0			0
$43$	10.4264			0.242475			0.121237	−	0.992624i	$-0.461314\pi$
$43$	10.4264			0.242475			0.121237	+	0.992624i	$0.461314\pi$
$44$	1.75736	+	3.04384i	0.0399400	+	0.0691781i
$45$	15.3640	+	8.87039i	0.341421	+	0.197120i
$46$	13.2426	−	22.9369i	0.287883	−	0.498629i
$47$	−33.5147	+	19.3497i	−0.713079	+	0.411696i	−0.812200	−	0.583379i	$-0.801730\pi$
$47$	−33.5147	+	19.3497i	−0.713079	+	0.411696i	0.0991210	+	0.995075i	$0.468397\pi$
$48$			6.92820i			0.144338i
$49$		0			0
$50$	14.1005			0.282010
$51$	−20.3345	−	35.2204i	−0.398716	−	0.690597i
$52$	32.4853	+	18.7554i	0.624717	+	0.360680i
$53$	18.5147	−	32.0684i	0.349334	−	0.605065i	−0.636797	−	0.771031i	$-0.719741\pi$
$53$	18.5147	−	32.0684i	0.349334	−	0.605065i	0.986131	+	0.165967i	$0.0530744\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		−	10.3923i		−	0.188951i
$56$		0			0
$57$	−39.9411			−0.700721
$58$	21.2132	+	36.7423i	0.365745	+	0.633489i
$59$	−84.4264	−	48.7436i	−1.43096	−	0.826163i	−0.433762	−	0.901027i	$-0.642814\pi$
$59$	−84.4264	−	48.7436i	−1.43096	−	0.826163i	−0.997194	+	0.0748645i	$0.976148\pi$
$60$	10.2426	−	17.7408i	0.170711	−	0.295680i
$61$	−14.4853	+	8.36308i	−0.237464	+	0.137100i	−0.614010	−	0.789298i	$-0.710445\pi$
$61$	−14.4853	+	8.36308i	−0.237464	+	0.137100i	0.376547	+	0.926398i	$0.377111\pi$
$62$			12.1753i			0.196376i
$63$		0			0
$64$	8.00000			0.125000
$65$	−55.4558	−	96.0523i	−0.853167	−	1.47773i
$66$	−3.72792	−	2.15232i	−0.0564837	−	0.0326109i
$67$	−30.4853	+	52.8021i	−0.455004	+	0.788090i	−0.998688	−	0.0511995i	$-0.983696\pi$
$67$	−30.4853	+	52.8021i	−0.455004	+	0.788090i	0.543684	+	0.839290i	$0.317029\pi$
$68$	−40.6690	+	23.4803i	−0.598074	+	0.345298i
$69$			32.4377i			0.470112i
$70$		0			0
$71$	−110.610			−1.55789			−0.778945	−	0.627092i	$-0.784245\pi$
$71$	−110.610			−1.55789			−0.778945	+	0.627092i	$0.784245\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	−49.1543	−	28.3793i	−0.673347	−	0.388757i	0.123997	−	0.992283i	$-0.460429\pi$
$73$	−49.1543	−	28.3793i	−0.673347	−	0.388757i	−0.797344	+	0.603526i	$0.793762\pi$
$74$	−50.1421	+	86.8487i	−0.677596	+	1.17363i
$75$	−14.9558	+	8.63476i	−0.199411	+	0.115130i
$76$			46.1200i			0.606843i
$77$		0			0
$78$	−45.9411			−0.588989
$79$	34.9117	+	60.4688i	0.441920	+	0.765428i	0.997832	−	0.0658132i	$-0.0209641\pi$
$79$	34.9117	+	60.4688i	0.441920	+	0.765428i	−0.555912	+	0.831241i	$0.687631\pi$
$80$	−20.4853	−	11.8272i	−0.256066	−	0.147840i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	50.6985	−	29.2708i	0.618274	−	0.356961i
$83$		−	6.43583i		−	0.0775401i	−0.999248	−	0.0387701i	$-0.987656\pi$
$83$		−	6.43583i		−	0.0775401i	0.999248	−	0.0387701i	$-0.0123440\pi$
$84$		0			0
$85$	138.853			1.63356
$86$	7.37258	+	12.7697i	0.0857277	+	0.148485i
$87$	−45.0000	−	25.9808i	−0.517241	−	0.298629i
$88$	−2.48528	+	4.30463i	−0.0282418	+	0.0489163i
$89$	36.4523	−	21.0457i	0.409576	−	0.236469i	−0.281031	−	0.959699i	$-0.590677\pi$
$89$	36.4523	−	21.0457i	0.409576	−	0.236469i	0.690608	+	0.723230i	$0.257343\pi$
$90$			25.0892i			0.278769i
$91$		0			0
$92$	37.4558			0.407129
$93$	−7.45584	−	12.9139i	−0.0801704	−	0.138859i
$94$	−47.3970	−	27.3647i	−0.504223	−	0.291113i
$95$	68.1838	−	118.098i	0.717724	−	1.24313i
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$		−	51.7153i		−	0.533148i	−0.963814	−	0.266574i	$-0.914108\pi$
$97$		−	51.7153i		−	0.533148i	0.963814	−	0.266574i	$-0.0858916\pi$
$98$		0			0
$99$	5.27208			0.0532533
$100$	9.97056	+	17.2695i	0.0997056	+	0.172695i
$101$	5.72435	+	3.30496i	0.0566767	+	0.0327223i	0.528071	−	0.849200i	$-0.322916\pi$
$101$	5.72435	+	3.30496i	0.0566767	+	0.0327223i	−0.471394	+	0.881923i	$0.656249\pi$
$102$	28.7574	−	49.8092i	0.281935	−	0.488326i
$103$	−152.309	+	87.9354i	−1.47872	+	0.853742i	−0.999710	−	0.0240648i	$-0.992339\pi$
$103$	−152.309	+	87.9354i	−1.47872	+	0.853742i	−0.479014	+	0.877807i	$0.659006\pi$
$104$			53.0482i			0.510079i
$105$		0			0
$106$	52.3675			0.494033
$107$	23.1213	+	40.0473i	0.216087	+	0.374274i	0.953608	−	0.301050i	$-0.0973371\pi$
$107$	23.1213	+	40.0473i	0.216087	+	0.374274i	−0.737521	+	0.675324i	$0.764004\pi$
$108$	9.00000	+	5.19615i	0.0833333	+	0.0481125i
$109$	17.9706	−	31.1259i	0.164868	−	0.285559i	−0.771741	−	0.635937i	$-0.780614\pi$
$109$	17.9706	−	31.1259i	0.164868	−	0.285559i	0.936608	+	0.350378i	$0.113947\pi$
$110$	12.7279	−	7.34847i	0.115708	−	0.0668043i
$111$		−	122.823i		−	1.10651i
$112$		0			0
$113$	−73.0294			−0.646278			−0.323139	−	0.946351i	$-0.604738\pi$
$113$	−73.0294			−0.646278			−0.323139	+	0.946351i	$0.604738\pi$
$114$	−28.2426	−	48.9177i	−0.247742	−	0.429103i
$115$	−95.9117	−	55.3746i	−0.834015	−	0.481519i
$116$	−30.0000	+	51.9615i	−0.258621	+	0.447944i
$117$	48.7279	−	28.1331i	0.416478	−	0.240454i
$118$		−	137.868i		−	1.16837i
$119$		0			0
$120$	28.9706			0.241421
$121$	58.9558	+	102.115i	0.487238	+	0.843922i
$122$	−20.4853	−	11.8272i	−0.167912	−	0.0969441i
$123$	−35.8492	+	62.0927i	−0.291457	+	0.504819i
$124$	−14.9117	+	8.60927i	−0.120256	+	0.0694296i
$125$			88.8780i			0.711024i
$126$		0			0
$127$	89.9411			0.708198			0.354099	−	0.935208i	$-0.384788\pi$
$127$	89.9411			0.708198			0.354099	+	0.935208i	$0.384788\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	−15.6396	−	9.02953i	−0.121237	−	0.0699964i
$130$	78.4264	−	135.839i	0.603280	−	1.04491i
$131$	−10.5442	+	6.08767i	−0.0804897	+	0.0464708i	−0.539705	−	0.841854i	$-0.681464\pi$
$131$	−10.5442	+	6.08767i	−0.0804897	+	0.0464708i	0.459215	+	0.888325i	$0.348131\pi$
$132$		−	6.08767i		−	0.0461187i
$133$		0			0
$134$	−86.2254			−0.643473
$135$	−15.3640	−	26.6112i	−0.113807	−	0.197120i
$136$	−57.5147	−	33.2061i	−0.422902	−	0.244163i
$137$	−82.8823	+	143.556i	−0.604980	+	1.04786i	0.387075	+	0.922048i	$0.373486\pi$
$137$	−82.8823	+	143.556i	−0.604980	+	1.04786i	−0.992055	+	0.125808i	$0.959848\pi$
$138$	−39.7279	+	22.9369i	−0.287883	+	0.166210i
$139$			220.514i			1.58643i	0.608941	+	0.793215i	$0.291594\pi$
$139$			220.514i			1.58643i	−0.608941	+	0.793215i	$0.708406\pi$
$140$		0			0
$141$	67.0294			0.475386
$142$	−78.2132	−	135.469i	−0.550797	−	0.954009i
$143$	−28.5442	−	16.4800i	−0.199609	−	0.115245i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$	153.640	−	88.7039i	1.05958	−	0.611751i
$146$		−	80.2687i		−	0.549786i
$147$		0			0
$148$	−141.823			−0.958266
$149$	−105.426	−	182.604i	−0.707560	−	1.22553i	−0.965760	−	0.259438i	$-0.916463\pi$
$149$	−105.426	−	182.604i	−0.707560	−	1.22553i	0.258200	−	0.966091i	$-0.416871\pi$
$150$	−21.1508	−	12.2114i	−0.141005	−	0.0814093i
$151$	36.1838	−	62.6721i	0.239628	−	0.415047i	−0.720980	−	0.692956i	$-0.756308\pi$
$151$	36.1838	−	62.6721i	0.239628	−	0.415047i	0.960607	+	0.277909i	$0.0896413\pi$
$152$	−56.4853	+	32.6118i	−0.371614	+	0.214551i
$153$			70.4409i			0.460398i
$154$		0			0
$155$	50.9117			0.328463
$156$	−32.4853	−	56.2662i	−0.208239	−	0.360680i
$157$	202.368	+	116.837i	1.28897	+	0.744184i	0.978470	−	0.206390i	$-0.0661717\pi$
$157$	202.368	+	116.837i	1.28897	+	0.744184i	0.310495	+	0.950575i	$0.399505\pi$
$158$	−49.3726	+	85.5158i	−0.312485	+	0.541239i
$159$	−55.5442	+	32.0684i	−0.349334	+	0.201688i
$160$		−	33.4523i		−	0.209077i
$161$		0			0
$162$	−12.7279			−0.0785674
$163$	36.5442	+	63.2963i	0.224197	+	0.388321i	0.956078	−	0.293111i	$-0.0946907\pi$
$163$	36.5442	+	63.2963i	0.224197	+	0.388321i	−0.731881	+	0.681432i	$0.761357\pi$
$164$	71.6985	+	41.3951i	0.437186	+	0.252409i
$165$	−9.00000	+	15.5885i	−0.0545455	+	0.0944755i
$166$	7.88225	−	4.55082i	0.0474834	−	0.0274146i
$167$			39.3958i			0.235903i	0.993019	+	0.117951i	$0.0376327\pi$
$167$			39.3958i			0.235903i	−0.993019	+	0.117951i	$0.962367\pi$
$168$		0			0
$169$	−182.765			−1.08145
$170$	98.1838	+	170.059i	0.577552	+	1.00035i
$171$	59.9117	+	34.5900i	0.350361	+	0.202281i
$172$	−10.4264	+	18.0591i	−0.0606186	+	0.104995i
$173$	−20.6360	+	11.9142i	−0.119283	+	0.0688683i	−0.558455	−	0.829535i	$-0.688606\pi$
$173$	−20.6360	+	11.9142i	−0.119283	+	0.0688683i	0.439171	+	0.898403i	$0.355272\pi$
$174$		−	73.4847i		−	0.422326i
$175$		0			0
$176$	−7.02944			−0.0399400
$177$	84.4264	+	146.231i	0.476985	+	0.826163i
$178$	51.5513	+	29.7632i	0.289614	+	0.167209i
$179$	6.45227	−	11.1757i	0.0360462	−	0.0624339i	−0.847439	−	0.530892i	$-0.821857\pi$
$179$	6.45227	−	11.1757i	0.0360462	−	0.0624339i	0.883486	+	0.468458i	$0.155190\pi$
$180$	−30.7279	+	17.7408i	−0.170711	+	0.0985599i
$181$		−	65.3678i		−	0.361148i	−0.983561	−	0.180574i	$-0.942204\pi$
$181$		−	65.3678i		−	0.361148i	0.983561	−	0.180574i	$-0.0577955\pi$
$182$		0			0
$183$	28.9706			0.158309
$184$	26.4853	+	45.8739i	0.143942	+	0.249314i
$185$	363.161	+	209.671i	1.96303	+	1.13336i
$186$	10.5442	−	18.2630i	0.0566890	−	0.0981882i
$187$	35.7351	−	20.6316i	0.191097	−	0.110330i
$188$		−	77.3989i		−	0.411696i
$189$		0			0
$190$	192.853			1.01501
$191$	50.0330	+	86.6597i	0.261953	+	0.453716i	0.966761	−	0.255682i	$-0.0823001\pi$
$191$	50.0330	+	86.6597i	0.261953	+	0.453716i	−0.704808	+	0.709398i	$0.748967\pi$
$192$	−12.0000	−	6.92820i	−0.0625000	−	0.0360844i
$193$	−39.4558	+	68.3395i	−0.204434	+	0.354091i	−0.949952	−	0.312395i	$-0.898869\pi$
$193$	−39.4558	+	68.3395i	−0.204434	+	0.354091i	0.745518	+	0.666486i	$0.232202\pi$
$194$	63.3381	−	36.5683i	0.326485	−	0.188496i
$195$			192.105i			0.985152i
$196$		0			0
$197$	−183.941			−0.933711			−0.466856	−	0.884334i	$-0.654613\pi$
$197$	−183.941			−0.933711			−0.466856	+	0.884334i	$0.654613\pi$
$198$	3.72792	+	6.45695i	0.0188279	+	0.0326109i
$199$	147.250	+	85.0147i	0.739949	+	0.427210i	0.822051	−	0.569414i	$-0.192830\pi$
$199$	147.250	+	85.0147i	0.739949	+	0.427210i	−0.0821020	+	0.996624i	$0.526163\pi$
$200$	−14.1005	+	24.4228i	−0.0705025	+	0.122114i
$201$	91.4558	−	52.8021i	0.455004	−	0.262697i
$202$			9.34783i			0.0462764i
$203$		0			0
$204$	81.3381			0.398716
$205$	−122.397	−	211.998i	−0.597058	−	1.03414i
$206$	−215.397	−	124.359i	−1.04562	−	0.603687i
$207$	28.0919	−	48.6566i	0.135710	−	0.235056i
$208$	−64.9706	+	37.5108i	−0.312358	+	0.180340i
$209$		−	40.5247i		−	0.193898i
$210$		0			0
$211$	21.5736			0.102245			0.0511223	−	0.998692i	$-0.483720\pi$
$211$	21.5736			0.102245			0.0511223	+	0.998692i	$0.483720\pi$
$212$	37.0294	+	64.1369i	0.174667	+	0.302532i
$213$	165.915	+	95.7912i	0.778945	+	0.449724i
$214$	−32.6985	+	56.6354i	−0.152797	+	0.264652i
$215$	53.3970	−	30.8288i	0.248358	−	0.143390i
$216$			14.6969i			0.0680414i
$217$		0			0
$218$	50.8284			0.233158
$219$	49.1543	+	85.1378i	0.224449	+	0.388757i
$220$	18.0000	+	10.3923i	0.0818182	+	0.0472377i
$221$	220.191	−	381.382i	0.996339	−	1.72571i
$222$	150.426	−	86.8487i	0.677596	−	0.391210i
$223$			119.359i			0.535240i	0.963525	+	0.267620i	$0.0862372\pi$
$223$			119.359i			0.535240i	−0.963525	+	0.267620i	$0.913763\pi$
$224$		0			0
$225$	29.9117			0.132941
$226$	−51.6396	−	89.4424i	−0.228494	−	0.395763i
$227$	−147.088	−	84.9215i	−0.647966	−	0.374103i	0.139710	−	0.990192i	$-0.455383\pi$
$227$	−147.088	−	84.9215i	−0.647966	−	0.374103i	−0.787677	+	0.616089i	$0.788716\pi$
$228$	39.9411	−	69.1801i	0.175180	−	0.303421i
$229$	95.2721	−	55.0054i	0.416035	−	0.240198i	−0.277344	−	0.960771i	$-0.589454\pi$
$229$	95.2721	−	55.0054i	0.416035	−	0.240198i	0.693380	+	0.720573i	$0.256121\pi$
$230$		−	156.623i		−	0.680970i
$231$		0			0
$232$	−84.8528			−0.365745
$233$	−28.6325	−	49.5929i	−0.122886	−	0.212845i	0.798019	−	0.602633i	$-0.205882\pi$
$233$	−28.6325	−	49.5929i	−0.122886	−	0.212845i	−0.920905	+	0.389788i	$0.872548\pi$
$234$	68.9117	+	39.7862i	0.294494	+	0.170026i
$235$	−114.426	+	198.192i	−0.486921	+	0.843372i
$236$	168.853	−	97.4872i	0.715478	−	0.413081i
$237$		−	120.938i		−	0.510285i
$238$		0			0
$239$	281.522			1.17792			0.588958	−	0.808164i	$-0.299538\pi$
$239$	281.522			1.17792			0.588958	+	0.808164i	$0.299538\pi$
$240$	20.4853	+	35.4815i	0.0853553	+	0.147840i
$241$	145.757	+	84.1531i	0.604802	+	0.349183i	0.770928	−	0.636922i	$-0.219793\pi$
$241$	145.757	+	84.1531i	0.604802	+	0.349183i	−0.166126	+	0.986105i	$0.553126\pi$
$242$	−83.3762	+	144.412i	−0.344530	+	0.596743i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		−	33.4523i		−	0.137100i
$245$		0			0
$246$	−101.397			−0.412183
$247$	−216.250	−	374.556i	−0.875505	−	1.51642i
$248$	−21.0883	−	12.1753i	−0.0850335	−	0.0490941i
$249$	−5.57359	+	9.65375i	−0.0223839	+	0.0387701i
$250$	−108.853	+	62.8462i	−0.435411	+	0.251385i
$251$		−	106.096i		−	0.422695i	−0.977411	−	0.211348i	$-0.932215\pi$
$251$		−	106.096i		−	0.422695i	0.977411	−	0.211348i	$-0.0677852\pi$
$252$		0			0
$253$	−32.9117			−0.130086
$254$	63.5980	+	110.155i	0.250386	+	0.433681i
$255$	−208.279	−	120.250i	−0.816781	−	0.471569i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	251.548	−	145.231i	0.978785	−	0.565102i	0.0768819	−	0.997040i	$-0.475504\pi$
$257$	251.548	−	145.231i	0.978785	−	0.565102i	0.901903	+	0.431938i	$0.142170\pi$
$258$		−	25.5394i		−	0.0989898i
$259$		0			0
$260$	221.823			0.853167
$261$	45.0000	+	77.9423i	0.172414	+	0.298629i
$262$	−14.9117	−	8.60927i	−0.0569148	−	0.0328598i
$263$	44.5111	−	77.0956i	0.169244	−	0.293139i	−0.768910	−	0.639357i	$-0.779201\pi$
$263$	44.5111	−	77.0956i	0.169244	−	0.293139i	0.938154	+	0.346218i	$0.112534\pi$
$264$	7.45584	−	4.30463i	0.0282418	−	0.0163054i
$265$		−	218.977i		−	0.826328i
$266$		0			0
$267$	−72.9045			−0.273051
$268$	−60.9706	−	105.604i	−0.227502	−	0.394045i
$269$	165.842	+	95.7490i	0.616513	+	0.355944i	0.775510	−	0.631335i	$-0.217493\pi$
$269$	165.842	+	95.7490i	0.616513	+	0.355944i	−0.158997	+	0.987279i	$0.550826\pi$
$270$	21.7279	−	37.6339i	0.0804738	−	0.139385i
$271$	188.309	−	108.720i	0.694866	−	0.401181i	−0.110566	−	0.993869i	$-0.535266\pi$
$271$	188.309	−	108.720i	0.694866	−	0.401181i	0.805432	+	0.592688i	$0.201933\pi$
$272$		−	93.9211i		−	0.345298i
$273$		0			0
$274$	−234.426			−0.855571
$275$	−8.76093	−	15.1744i	−0.0318579	−	0.0551796i
$276$	−56.1838	−	32.4377i	−0.203564	−	0.117528i
$277$	−145.338	+	251.733i	−0.524686	+	0.908783i	0.474901	+	0.880039i	$0.342484\pi$
$277$	−145.338	+	251.733i	−0.524686	+	0.908783i	−0.999587	+	0.0287438i	$0.990849\pi$
$278$	−270.073	+	155.927i	−0.971486	+	0.560888i
$279$			25.8278i			0.0925728i
$280$		0			0
$281$	18.8528			0.0670919			0.0335459	−	0.999437i	$-0.489320\pi$
$281$	18.8528			0.0670919			0.0335459	+	0.999437i	$0.489320\pi$
$282$	47.3970	+	82.0940i	0.168074	+	0.291113i
$283$	−347.912	−	200.867i	−1.22937	−	0.709777i	−0.262472	−	0.964940i	$-0.584538\pi$
$283$	−347.912	−	200.867i	−1.22937	−	0.709777i	−0.966898	+	0.255163i	$0.917871\pi$
$284$	110.610	−	191.582i	0.389472	−	0.674586i
$285$	−204.551	+	118.098i	−0.717724	+	0.414378i
$286$		−	46.6124i		−	0.162980i
$287$		0			0
$288$	16.9706			0.0589256
$289$	131.162	+	227.179i	0.453847	+	0.786087i
$290$	217.279	+	125.446i	0.749239	+	0.432573i
$291$	−44.7868	+	77.5730i	−0.153907	+	0.266574i
$292$	98.3087	−	56.7585i	0.336673	−	0.194379i
$293$			280.893i			0.958679i	0.877629	+	0.479340i	$0.159124\pi$
$293$			280.893i			0.958679i	−0.877629	+	0.479340i	$0.840876\pi$
$294$		0			0
$295$	−576.500			−1.95424
$296$	−100.284	−	173.697i	−0.338798	−	0.586816i
$297$	−7.90812	−	4.56575i	−0.0266267	−	0.0153729i
$298$	149.095	−	258.241i	0.500320	−	0.866580i
$299$	−304.191	+	175.625i	−1.01736	+	0.587374i
$300$		−	34.5390i		−	0.115130i
$301$		0			0
$302$	102.343			0.338885
$303$	−5.72435	−	9.91487i	−0.0188922	−	0.0327223i
$304$	−79.8823	−	46.1200i	−0.262771	−	0.151711i
$305$	−49.4558	+	85.6600i	−0.162150	+	0.280853i
$306$	−86.2721	+	49.8092i	−0.281935	+	0.162775i
$307$		−	152.318i		−	0.496151i	−0.968741	−	0.248076i	$-0.920202\pi$
$307$		−	152.318i		−	0.496151i	0.968741	−	0.248076i	$-0.0797982\pi$
$308$		0			0
$309$	304.617			0.985817
$310$	36.0000	+	62.3538i	0.116129	+	0.201141i
$311$	−245.220	−	141.578i	−0.788490	−	0.455235i	0.0509408	−	0.998702i	$-0.483778\pi$
$311$	−245.220	−	141.578i	−0.788490	−	0.455235i	−0.839431	+	0.543467i	$0.817111\pi$
$312$	45.9411	−	79.5724i	0.147247	−	0.255040i
$313$	−42.0732	+	24.2910i	−0.134419	+	0.0776069i	−0.565702	−	0.824610i	$-0.691395\pi$
$313$	−42.0732	+	24.2910i	−0.134419	+	0.0776069i	0.431282	+	0.902217i	$0.358061\pi$
$314$			330.465i			1.05244i
$315$		0			0
$316$	−139.647			−0.441920
$317$	289.014	+	500.587i	0.911717	+	1.57914i	0.811638	+	0.584161i	$0.198576\pi$
$317$	289.014	+	500.587i	0.911717	+	1.57914i	0.100079	+	0.994980i	$0.468090\pi$
$318$	−78.5513	−	45.3516i	−0.247017	−	0.142615i
$319$	26.3604	−	45.6575i	0.0826345	−	0.143127i
$320$	40.9706	−	23.6544i	0.128033	−	0.0739199i
$321$		−	80.0946i		−	0.249516i
$322$		0			0
$323$	541.456			1.67633
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$	−161.948	−	93.5009i	−0.498302	−	0.287695i
$326$	−51.6812	+	89.5145i	−0.158531	+	0.274584i
$327$	−53.9117	+	31.1259i	−0.164868	+	0.0951863i
$328$			117.083i			0.356961i
$329$		0			0
$330$	−25.4558			−0.0771389
$331$	−166.184	−	287.839i	−0.502066	−	0.869603i	−0.999997	−	0.00238698i	$-0.999240\pi$
$331$	−166.184	−	287.839i	−0.502066	−	0.869603i	0.497931	−	0.867216i	$-0.334093\pi$
$332$	11.1472	+	6.43583i	0.0335759	+	0.0193850i
$333$	−106.368	+	184.234i	−0.319422	+	0.553255i
$334$	−48.2498	+	27.8570i	−0.144460	+	0.0834043i
$335$			360.555i			1.07628i
$336$		0			0
$337$	88.1766			0.261652			0.130826	−	0.991405i	$-0.458237\pi$
$337$	88.1766			0.261652			0.130826	+	0.991405i	$0.458237\pi$
$338$	−129.234	−	223.840i	−0.382349	−	0.662248i
$339$	109.544	+	63.2453i	0.323139	+	0.186564i
$340$	−138.853	+	240.500i	−0.408391	+	0.707353i
$341$	13.1026	−	7.56479i	0.0384240	−	0.0221841i
$342$			97.8354i			0.286068i
$343$		0			0
$344$	−29.4903			−0.0857277
$345$	95.9117	+	166.124i	0.278005	+	0.481519i
$346$	−29.1838	−	16.8493i	−0.0843461	−	0.0486973i
$347$	160.040	−	277.198i	0.461211	−	0.798841i	−0.537811	−	0.843066i	$-0.680749\pi$
$347$	160.040	−	277.198i	0.461211	−	0.798841i	0.999022	+	0.0442250i	$0.0140819\pi$
$348$	90.0000	−	51.9615i	0.258621	−	0.149315i
$349$			333.046i			0.954287i	0.878825	+	0.477143i	$0.158328\pi$
$349$			333.046i			0.954287i	−0.878825	+	0.477143i	$0.841672\pi$
$350$		0			0
$351$	−97.4558			−0.277652
$352$	−4.97056	−	8.60927i	−0.0141209	−	0.0244581i
$353$	−567.864	−	327.856i	−1.60868	−	0.928771i	−0.989666	−	0.143390i	$-0.954200\pi$
$353$	−567.864	−	327.856i	−1.60868	−	0.928771i	−0.619012	−	0.785381i	$-0.712467\pi$
$354$	−119.397	+	206.802i	−0.337280	+	0.584185i
$355$	−566.470	+	327.052i	−1.59569	+	0.921272i
$356$			84.1829i			0.236469i
$357$		0			0
$358$	18.2498			0.0509770
$359$	48.8787	+	84.6604i	0.136152	+	0.235823i	0.926037	−	0.377433i	$-0.123193\pi$
$359$	48.8787	+	84.6604i	0.136152	+	0.235823i	−0.789885	+	0.613255i	$0.789860\pi$
$360$	−43.4558	−	25.0892i	−0.120711	−	0.0696923i
$361$	85.3823	−	147.886i	0.236516	−	0.409658i
$362$	80.0589	−	46.2220i	0.221157	−	0.127685i
$363$		−	204.229i		−	0.562614i
$364$		0			0
$365$	−335.647			−0.919580
$366$	20.4853	+	35.4815i	0.0559707	+	0.0969441i
$367$	−278.044	−	160.529i	−0.757612	−	0.437408i	0.0708255	−	0.997489i	$-0.477437\pi$
$367$	−278.044	−	160.529i	−0.757612	−	0.437408i	−0.828438	+	0.560081i	$0.810770\pi$
$368$	−37.4558	+	64.8754i	−0.101782	+	0.176292i
$369$	107.548	−	62.0927i	0.291457	−	0.168273i
$370$			593.040i			1.60281i
$371$		0			0
$372$	29.8234			0.0801704
$373$	−93.7351	−	162.354i	−0.251300	−	0.435265i	0.712584	−	0.701587i	$-0.247525\pi$
$373$	−93.7351	−	162.354i	−0.251300	−	0.435265i	−0.963884	+	0.266322i	$0.914192\pi$
$374$	50.5370	+	29.1776i	0.135126	+	0.0780149i
$375$	76.9706	−	133.317i	0.205255	−	0.355512i
$376$	94.7939	−	54.7293i	0.252112	−	0.145557i
$377$		−	562.662i		−	1.49247i
$378$		0			0
$379$	−357.103			−0.942223			−0.471112	−	0.882074i	$-0.656147\pi$
$379$	−357.103			−0.942223			−0.471112	+	0.882074i	$0.656147\pi$
$380$	136.368	+	236.195i	0.358862	+	0.621567i
$381$	−134.912	−	77.8913i	−0.354099	−	0.204439i
$382$	−70.7574	+	122.555i	−0.185229	+	0.320826i
$383$	−538.867	+	311.115i	−1.40696	+	0.812311i	−0.995094	−	0.0989320i	$-0.968457\pi$
$383$	−538.867	+	311.115i	−1.40696	+	0.812311i	−0.411870	+	0.911243i	$0.635124\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−111.598			−0.289114
$387$	15.6396	+	27.0886i	0.0404124	+	0.0699964i
$388$	89.5736	+	51.7153i	0.230860	+	0.133287i
$389$	−113.735	+	196.995i	−0.292378	+	0.506414i	−0.974372	−	0.224945i	$-0.927780\pi$
$389$	−113.735	+	196.995i	−0.292378	+	0.506414i	0.681994	+	0.731358i	$0.261113\pi$
$390$	−235.279	+	135.839i	−0.603280	+	0.348304i
$391$		−	439.737i		−	1.12465i
$392$		0			0
$393$	21.0883			0.0536598
$394$	−130.066	−	225.281i	−0.330117	−	0.571779i
$395$	357.588	+	206.453i	0.905286	+	0.522667i
$396$	−5.27208	+	9.13151i	−0.0133133	+	0.0230594i
$397$	−623.823	+	360.165i	−1.57134	+	0.907216i	−0.575339	+	0.817915i	$0.695130\pi$
$397$	−623.823	+	360.165i	−1.57134	+	0.907216i	−0.996005	+	0.0893004i	$0.971537\pi$
$398$			240.458i			0.604166i
$399$		0			0
$400$	−39.8823			−0.0997056
$401$	−348.588	−	603.772i	−0.869296	−	1.50567i	−0.862717	−	0.505687i	$-0.831239\pi$
$401$	−348.588	−	603.772i	−0.869296	−	1.50567i	−0.00657959	−	0.999978i	$-0.502094\pi$
$402$	129.338	+	74.6734i	0.321737	+	0.185755i
$403$	80.7351	−	139.837i	0.200335	−	0.346991i
$404$	−11.4487	+	6.60991i	−0.0283384	+	0.0163612i
$405$			53.2223i			0.131413i
$406$		0			0
$407$	124.617			0.306185
$408$	57.5147	+	99.6184i	0.140967	+	0.244163i
$409$	88.6690	+	51.1931i	0.216795	+	0.125166i	0.604465	−	0.796632i	$-0.293387\pi$
$409$	88.6690	+	51.1931i	0.216795	+	0.125166i	−0.387671	+	0.921798i	$0.626720\pi$
$410$	173.095	−	299.810i	0.422184	−	0.731244i
$411$	248.647	−	143.556i	0.604980	−	0.349285i
$412$		−	351.742i		−	0.853742i
$413$		0			0
$414$	79.4558			0.191922
$415$	−19.0294	−	32.9600i	−0.0458541	−	0.0794216i
$416$	−91.8823	−	53.0482i	−0.220871	−	0.127520i
$417$	190.971	−	330.771i	0.457963	−	0.793215i
$418$	49.6325	−	28.6553i	0.118738	−	0.0685534i
$419$		−	391.426i		−	0.934191i	−0.884207	−	0.467095i	$-0.845300\pi$
$419$		−	391.426i		−	0.934191i	0.884207	−	0.467095i	$-0.154700\pi$
$420$		0			0
$421$	354.441			0.841902			0.420951	−	0.907083i	$-0.361696\pi$
$421$	354.441			0.841902			0.420951	+	0.907083i	$0.361696\pi$
$422$	15.2548	+	26.4221i	0.0361489	+	0.0626117i
$423$	−100.544	−	58.0492i	−0.237693	−	0.137232i
$424$	−52.3675	+	90.7032i	−0.123508	+	0.213923i
$425$	202.747	−	117.056i	0.477051	−	0.275425i
$426$			270.938i			0.636006i
$427$		0			0
$428$	−92.4853			−0.216087
$429$	28.5442	+	49.4399i	0.0665365	+	0.115245i
$430$	75.5147	+	43.5984i	0.175616	+	0.101392i
$431$	−292.643	+	506.873i	−0.678987	+	1.17604i	0.296300	+	0.955095i	$0.404247\pi$
$431$	−292.643	+	506.873i	−0.678987	+	1.17604i	−0.975286	+	0.220944i	$0.929086\pi$
$432$	−18.0000	+	10.3923i	−0.0416667	+	0.0240563i
$433$			392.207i			0.905789i	0.891564	+	0.452895i	$0.149609\pi$
$433$			392.207i			0.905789i	−0.891564	+	0.452895i	$0.850391\pi$
$434$		0			0
$435$	−307.279			−0.706389
$436$	35.9411	+	62.2519i	0.0824338	+	0.142779i
$437$	−374.007	−	215.933i	−0.855852	−	0.494126i
$438$	−69.5147	+	120.403i	−0.158709	+	0.274893i
$439$	339.926	−	196.256i	0.774319	−	0.447053i	−0.0600943	−	0.998193i	$-0.519140\pi$
$439$	339.926	−	196.256i	0.774319	−	0.447053i	0.834413	+	0.551140i	$0.185807\pi$
$440$			29.3939i			0.0668043i
$441$		0			0
$442$	622.794			1.40904
$443$	407.371	+	705.587i	0.919574	+	1.59275i	0.800064	+	0.599915i	$0.204799\pi$
$443$	407.371	+	705.587i	0.919574	+	1.59275i	0.119510	+	0.992833i	$0.461868\pi$
$444$	212.735	+	122.823i	0.479133	+	0.276628i
$445$	124.456	−	215.564i	0.279676	−	0.484413i
$446$	−146.184	+	84.3992i	−0.327766	+	0.189236i
$447$			365.208i			0.817020i
$448$		0			0
$449$	180.323			0.401610			0.200805	−	0.979631i	$-0.435644\pi$
$449$	180.323			0.401610			0.200805	+	0.979631i	$0.435644\pi$
$450$	21.1508	+	36.6342i	0.0470017	+	0.0814093i
$451$	−63.0000	−	36.3731i	−0.139690	−	0.0806498i
$452$	73.0294	−	126.491i	0.161570	−	0.279847i
$453$	−108.551	+	62.6721i	−0.239628	+	0.138349i
$454$		−	240.194i		−	0.529062i
$455$		0			0
$456$	112.971			0.247742
$457$	−140.088	−	242.640i	−0.306539	−	0.530941i	0.671064	−	0.741400i	$-0.265838\pi$
$457$	−140.088	−	242.640i	−0.306539	−	0.530941i	−0.977603	+	0.210459i	$0.932504\pi$
$458$	134.735	+	77.7893i	0.294181	+	0.169846i
$459$	61.0036	−	105.661i	0.132905	−	0.230199i
$460$	191.823	−	110.749i	0.417007	−	0.240759i
$461$		−	406.297i		−	0.881338i	−0.897670	−	0.440669i	$-0.854741\pi$
$461$		−	406.297i		−	0.881338i	0.897670	−	0.440669i	$-0.145259\pi$
$462$		0			0
$463$	457.470			0.988056			0.494028	−	0.869446i	$-0.335524\pi$
$463$	457.470			0.988056			0.494028	+	0.869446i	$0.335524\pi$
$464$	−60.0000	−	103.923i	−0.129310	−	0.223972i
$465$	−76.3675	−	44.0908i	−0.164231	−	0.0948190i
$466$	40.4924	−	70.1349i	0.0868936	−	0.150504i
$467$	557.470	−	321.856i	1.19373	−	0.689198i	0.234577	−	0.972098i	$-0.424630\pi$
$467$	557.470	−	321.856i	1.19373	−	0.689198i	0.959150	+	0.282899i	$0.0912963\pi$
$468$			112.532i			0.240454i
$469$		0			0
$470$	−323.647			−0.688610
$471$	−202.368	−	350.511i	−0.429655	−	0.744184i
$472$	238.794	+	137.868i	0.505919	+	0.292093i
$473$	9.16147	−	15.8681i	0.0193689	−	0.0335479i
$474$	148.118	−	85.5158i	0.312485	−	0.180413i
$475$		−	229.921i		−	0.484045i
$476$		0			0
$477$	111.088			0.232890
$478$	199.066	+	344.792i	0.416456	+	0.721323i
$479$	145.955	+	84.2674i	0.304709	+	0.175924i	0.644556	−	0.764557i	$-0.277042\pi$
$479$	145.955	+	84.2674i	0.304709	+	0.175924i	−0.339848	+	0.940481i	$0.610376\pi$
$480$	−28.9706	+	50.1785i	−0.0603553	+	0.104539i
$481$	1151.79	−	664.988i	2.39458	−	1.38251i
$482$			238.021i			0.493819i
$483$		0			0
$484$	−235.823			−0.487238
$485$	−152.912	−	264.851i	−0.315282	−	0.546084i
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	1.38983	−	2.40725i	0.00285385	−	0.00494302i	−0.864595	−	0.502469i	$-0.832425\pi$
$487$	1.38983	−	2.40725i	0.00285385	−	0.00494302i	0.867449	+	0.497526i	$0.165758\pi$
$488$	40.9706	−	23.6544i	0.0839561	−	0.0484721i
$489$		−	126.593i		−	0.258881i
$490$		0			0
$491$	−247.477			−0.504027			−0.252014	−	0.967724i	$-0.581093\pi$
$491$	−247.477			−0.504027			−0.252014	+	0.967724i	$0.581093\pi$
$492$	−71.6985	−	124.185i	−0.145729	−	0.252409i
$493$	610.036	+	352.204i	1.23739	+	0.714410i
$494$	305.823	−	529.702i	0.619076	−	1.07227i
$495$	27.0000	−	15.5885i	0.0545455	−	0.0314918i
$496$		−	34.4371i		−	0.0694296i
$497$		0			0
$498$	−15.7645			−0.0316556
$499$	241.713	+	418.659i	0.484394	+	0.838996i	0.999839	−	0.0179271i	$-0.00570668\pi$
$499$	241.713	+	418.659i	0.484394	+	0.838996i	−0.515445	+	0.856923i	$0.672373\pi$
$500$	−153.941	−	88.8780i	−0.307882	−	0.177756i
$501$	34.1177	−	59.0937i	0.0680993	−	0.117951i
$502$	129.941	−	75.0215i	0.258847	−	0.149445i
$503$		−	58.7033i		−	0.116706i	−0.998296	−	0.0583532i	$-0.981415\pi$
$503$		−	58.7033i		−	0.116706i	0.998296	−	0.0583532i	$-0.0185849\pi$
$504$		0			0
$505$	39.0883			0.0774026
$506$	−23.2721	−	40.3084i	−0.0459922	−	0.0796609i
$507$	274.147	+	158.279i	0.540723	+	0.312187i
$508$	−89.9411	+	155.783i	−0.177049	+	0.306659i
$509$	−59.6512	+	34.4396i	−0.117193	+	0.0676614i	−0.557451	−	0.830210i	$-0.688220\pi$
$509$	−59.6512	+	34.4396i	−0.117193	+	0.0676614i	0.440258	+	0.897871i	$0.354887\pi$
$510$		−	340.119i		−	0.666899i
$511$		0			0
$512$	−22.6274			−0.0441942
$513$	−59.9117	−	103.770i	−0.116787	−	0.202281i
$514$	355.742	+	205.388i	0.692105	+	0.399587i
$515$	−520.014	+	900.691i	−1.00974	+	1.74891i
$516$	31.2792	−	18.0591i	0.0606186	−	0.0349982i
$517$			68.0089i			0.131545i
$518$		0			0
$519$	41.2721			0.0795223
$520$	156.853	+	271.677i	0.301640	+	0.522456i
$521$	253.503	+	146.360i	0.486570	+	0.280922i	0.723151	−	0.690690i	$-0.242693\pi$
$521$	253.503	+	146.360i	0.486570	+	0.280922i	−0.236580	+	0.971612i	$0.576027\pi$
$522$	−63.6396	+	110.227i	−0.121915	+	0.211163i
$523$	−426.999	+	246.528i	−0.816442	+	0.471373i	−0.849188	−	0.528091i	$-0.822908\pi$
$523$	−426.999	+	246.528i	−0.816442	+	0.471373i	0.0327460	+	0.999464i	$0.489575\pi$
$524$		−	24.3507i		−	0.0464708i
$525$		0			0
$526$	125.897			0.239347
$527$	101.074	+	175.065i	0.191791	+	0.332192i
$528$	10.5442	+	6.08767i	0.0199700	+	0.0115297i
$529$	89.1325	−	154.382i	0.168492	−	0.291837i
$530$	268.191	−	154.840i	0.506021	−	0.292151i
$531$		−	292.462i		−	0.550775i
$532$		0			0
$533$	−776.382			−1.45663
$534$	−51.5513	−	89.2895i	−0.0965380	−	0.167209i
$535$	236.823	+	136.730i	0.442661	+	0.255570i
$536$	86.2254	−	149.347i	0.160868	−	0.278632i
$537$	−19.3568	+	11.1757i	−0.0360462	+	0.0208113i
$538$			270.819i			0.503381i
$539$		0			0
$540$	61.4558			0.113807
$541$	518.926	+	898.806i	0.959198	+	1.66138i	0.724456	+	0.689322i	$0.242091\pi$
$541$	518.926	+	898.806i	0.959198	+	1.66138i	0.234742	+	0.972058i	$0.424575\pi$
$542$	266.309	+	153.753i	0.491344	+	0.283678i
$543$	−56.6102	+	98.0517i	−0.104254	+	0.180574i
$544$	115.029	−	66.4123i	0.211451	−	0.122081i
$545$		−	212.541i		−	0.389984i
$546$		0			0
$547$	−130.530			−0.238629			−0.119314	−	0.992857i	$-0.538070\pi$
$547$	−130.530			−0.238629			−0.119314	+	0.992857i	$0.538070\pi$
$548$	−165.765	−	287.113i	−0.302490	−	0.523928i
$549$	−43.4558	−	25.0892i	−0.0791545	−	0.0456999i
$550$	12.3898	−	21.4598i	0.0225270	−	0.0390178i
$551$	599.117	−	345.900i	1.08733	−	0.627768i
$552$		−	91.7477i		−	0.166210i
$553$		0			0
$554$	−411.078			−0.742018
$555$	−363.161	−	629.014i	−0.654345	−	1.13336i
$556$	−381.941	−	220.514i	−0.686944	−	0.396608i
$557$	−332.574	+	576.034i	−0.597080	+	1.03417i	0.396170	+	0.918177i	$0.370339\pi$
$557$	−332.574	+	576.034i	−0.597080	+	1.03417i	−0.993250	+	0.115996i	$0.962994\pi$
$558$	−31.6325	+	18.2630i	−0.0566890	+	0.0327294i
$559$		−	195.551i		−	0.349823i
$560$		0			0
$561$	−71.4701			−0.127398
$562$	13.3310	+	23.0899i	0.0237206	+	0.0410852i
$563$	718.191	+	414.648i	1.27565	+	0.736497i	0.976045	−	0.217567i	$-0.0698120\pi$
$563$	718.191	+	414.648i	1.27565	+	0.736497i	0.299604	+	0.954064i	$0.403145\pi$
$564$	−67.0294	+	116.098i	−0.118847	+	0.205848i
$565$	−374.007	+	215.933i	−0.661960	+	0.382183i
$566$		−	568.137i		−	1.00378i
$567$		0			0
$568$	312.853			0.550797
$569$	−353.485	−	612.254i	−0.621240	−	1.07602i	−0.989255	−	0.146199i	$-0.953296\pi$
$569$	−353.485	−	612.254i	−0.621240	−	1.07602i	0.368016	−	0.929820i	$-0.380037\pi$
$570$	−289.279	−	167.015i	−0.507507	−	0.293010i
$571$	183.456	−	317.755i	0.321289	−	0.556488i	−0.659466	−	0.751735i	$-0.729217\pi$
$571$	183.456	−	317.755i	0.321289	−	0.556488i	0.980754	+	0.195246i	$0.0625507\pi$
$572$	57.0883	−	32.9600i	0.0998047	−	0.0576223i
$573$		−	173.319i		−	0.302477i
$574$		0			0
$575$	−186.728			−0.324744
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−338.059	−	195.178i	−0.585891	−	0.338264i	0.177580	−	0.984106i	$-0.443173\pi$
$577$	−338.059	−	195.178i	−0.585891	−	0.338264i	−0.763471	+	0.645842i	$0.776506\pi$
$578$	−185.491	+	321.280i	−0.320919	+	0.555847i
$579$	118.368	−	68.3395i	0.204434	−	0.118030i
$580$			354.815i			0.611751i
$581$		0			0
$582$	−126.676			−0.217657
$583$	−32.5370	−	56.3558i	−0.0558096	−	0.0966651i
$584$	139.029	+	80.2687i	0.238064	+	0.137446i
$585$	166.368	−	288.157i	0.284389	−	0.492576i
$586$	−344.022	+	198.621i	−0.587069	+	0.338944i
$587$			702.499i			1.19676i	0.801212	+	0.598381i	$0.204189\pi$
$587$			702.499i			1.19676i	−0.801212	+	0.598381i	$0.795811\pi$
$588$		0			0
$589$	198.530			0.337063
$590$	−407.647	−	706.065i	−0.690927	−	1.19672i
$591$	275.912	+	159.298i	0.466856	+	0.269539i
$592$	141.823	−	245.645i	0.239567	−	0.414941i
$593$	−816.245	+	471.259i	−1.37647	+	0.794704i	−0.991732	−	0.128323i	$-0.959041\pi$
$593$	−816.245	+	471.259i	−1.37647	+	0.794704i	−0.384735	+	0.923027i	$0.625707\pi$
$594$		−	12.9139i		−	0.0217406i
$595$		0			0
$596$	421.706			0.707560
$597$	−147.250	−	255.044i	−0.246650	−	0.427210i
$598$	−430.191	−	248.371i	−0.719383	−	0.415336i
$599$	476.054	−	824.550i	0.794749	−	1.37655i	−0.128250	−	0.991742i	$-0.540936\pi$
$599$	476.054	−	824.550i	0.794749	−	1.37655i	0.922999	−	0.384803i	$-0.125731\pi$
$600$	42.3015	−	24.4228i	0.0705025	−	0.0407047i
$601$		−	729.804i		−	1.21432i	−0.794581	−	0.607158i	$-0.792310\pi$
$601$		−	729.804i		−	1.21432i	0.794581	−	0.607158i	$-0.207690\pi$
$602$		0			0
$603$	−182.912			−0.303336
$604$	72.3675	+	125.344i	0.119814	+	0.207524i
$605$	603.864	+	348.641i	0.998122	+	0.576266i
$606$	8.09545	−	14.0217i	0.0133588	−	0.0231382i
$607$	871.514	−	503.169i	1.43577	−	0.828944i	0.438220	−	0.898868i	$-0.355609\pi$
$607$	871.514	−	503.169i	1.43577	−	0.828944i	0.997552	+	0.0699241i	$0.0222757\pi$
$608$		−	130.447i		−	0.214551i
$609$		0			0
$610$	−139.882			−0.229315
$611$	362.912	+	628.581i	0.593963	+	1.02877i
$612$	−122.007	−	70.4409i	−0.199358	−	0.115099i
$613$	99.7939	−	172.848i	0.162796	−	0.281971i	−0.773074	−	0.634315i	$-0.781282\pi$
$613$	99.7939	−	172.848i	0.162796	−	0.281971i	0.935870	+	0.352344i	$0.114615\pi$
$614$	186.551	−	107.705i	0.303829	−	0.175416i
$615$			423.996i			0.689424i
$616$		0			0
$617$	−353.294			−0.572599			−0.286299	−	0.958140i	$-0.592425\pi$
$617$	−353.294			−0.572599			−0.286299	+	0.958140i	$0.592425\pi$
$618$	215.397	+	373.078i	0.348539	+	0.603687i
$619$	−48.6762	−	28.1032i	−0.0786368	−	0.0454010i	0.460166	−	0.887833i	$-0.347790\pi$
$619$	−48.6762	−	28.1032i	−0.0786368	−	0.0454010i	−0.538803	+	0.842432i	$0.681123\pi$
$620$	−50.9117	+	88.1816i	−0.0821156	+	0.142228i
$621$	−84.2756	+	48.6566i	−0.135710	+	0.0783520i
$622$		−	400.443i		−	0.643799i
$623$		0			0
$624$	129.941			0.208239
$625$	387.426	+	671.041i	0.619882	+	1.07367i
$626$	−59.5004	−	34.3526i	−0.0950486	−	0.0548763i
$627$	−35.0955	+	60.7871i	−0.0559736	+	0.0969491i
$628$	−404.735	+	233.674i	−0.644483	+	0.372092i
$629$			1665.03i			2.64710i
$630$		0			0
$631$	807.322			1.27943			0.639716	−	0.768611i	$-0.279052\pi$
$631$	807.322			1.27943			0.639716	+	0.768611i	$0.279052\pi$
$632$	−98.7452	−	171.032i	−0.156242	−	0.270620i
$633$	−32.3604	−	18.6833i	−0.0511223	−	0.0295154i
$634$	−408.728	+	707.938i	−0.644681	+	1.11662i
$635$	460.617	−	265.938i	0.725382	−	0.418799i
$636$		−	128.274i		−	0.201688i
$637$		0			0
$638$	74.5584			0.116863
$639$	−165.915	−	287.374i	−0.259648	−	0.449724i
$640$	57.9411	+	33.4523i	0.0905330	+	0.0522693i
$641$	−508.176	+	880.186i	−0.792786	+	1.37315i	0.131450	+	0.991323i	$0.458037\pi$
$641$	−508.176	+	880.186i	−0.792786	+	1.37315i	−0.924236	+	0.381823i	$0.875297\pi$
$642$	98.0955	−	56.6354i	0.152797	−	0.0882172i
$643$			404.688i			0.629375i	0.949195	+	0.314687i	$0.101900\pi$
$643$			404.688i			0.629375i	−0.949195	+	0.314687i	$0.898100\pi$
$644$		0			0
$645$	−106.794			−0.165572
$646$	382.867	+	663.145i	0.592674	+	1.02654i
$647$	−814.587	−	470.302i	−1.25902	−	0.726896i	−0.286137	−	0.958189i	$-0.592371\pi$
$647$	−814.587	−	470.302i	−1.25902	−	0.726896i	−0.972884	+	0.231292i	$0.925705\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	−148.368	+	85.6600i	−0.228609	+	0.131988i
$650$		−	264.460i		−	0.406862i
$651$		0			0
$652$	−146.177			−0.224197
$653$	−365.985	−	633.904i	−0.560467	−	0.970757i	−0.997456	−	0.0712901i	$-0.977288\pi$
$653$	−365.985	−	633.904i	−0.560467	−	0.970757i	0.436989	−	0.899467i	$-0.356045\pi$
$654$	−76.2426	−	44.0187i	−0.116579	−	0.0673069i
$655$	−36.0000	+	62.3538i	−0.0549618	+	0.0951967i
$656$	−143.397	+	82.7903i	−0.218593	+	0.126205i
$657$		−	170.276i		−	0.259171i
$658$		0			0
$659$	904.316			1.37225			0.686127	−	0.727481i	$-0.259309\pi$
$659$	904.316			1.37225			0.686127	+	0.727481i	$0.259309\pi$
$660$	−18.0000	−	31.1769i	−0.0272727	−	0.0472377i
$661$	−290.881	−	167.940i	−0.440063	−	0.254070i	0.263562	−	0.964643i	$-0.415103\pi$
$661$	−290.881	−	167.940i	−0.440063	−	0.254070i	−0.703624	+	0.710572i	$0.748436\pi$
$662$	235.019	−	407.065i	0.355014	−	0.614902i
$663$	−660.573	+	381.382i	−0.996339	+	0.575237i
$664$			18.2033i			0.0274146i
$665$		0			0
$666$	−300.853			−0.451731
$667$	−280.919	−	486.566i	−0.421168	−	0.729484i
$668$	−68.2355	−	39.3958i	−0.102149	−	0.0589757i
$669$	103.368	−	179.038i	0.154511	−	0.267620i
$670$	−441.588	+	254.951i	−0.659086	+	0.380524i
$671$			29.3939i			0.0438061i
$672$		0			0
$673$	1191.44			1.77034			0.885171	−	0.465266i	$-0.154041\pi$
$673$	1191.44			1.77034			0.885171	+	0.465266i	$0.154041\pi$
$674$	62.3503	+	107.994i	0.0925078	+	0.160228i
$675$	−44.8675	−	25.9043i	−0.0664704	−	0.0383767i
$676$	182.765	−	316.557i	0.270362	−	0.468280i
$677$	−1048.82	+	605.536i	−1.54922	+	0.894441i	−0.551015	+	0.834495i	$0.685759\pi$
$677$	−1048.82	+	605.536i	−1.54922	+	0.894441i	−0.998202	+	0.0599456i	$0.980907\pi$
$678$			178.885i			0.263842i
$679$		0			0
$680$	−392.735			−0.577552
$681$	147.088	+	254.764i	0.215989	+	0.374103i
$682$	18.5299	+	10.6982i	0.0271699	+	0.0156865i
$683$	616.945	−	1068.58i	0.903287	−	1.56454i	0.0800856	−	0.996788i	$-0.474481\pi$
$683$	616.945	−	1068.58i	0.903287	−	1.56454i	0.823201	−	0.567750i	$-0.192186\pi$
$684$	−119.823	+	69.1801i	−0.175180	+	0.101140i
$685$			980.264i			1.43104i
$686$		0			0
$687$	−190.544			−0.277357
$688$	−20.8528	−	36.1181i	−0.0303093	−	0.0524973i
$689$	−601.456	−	347.251i	−0.872940	−	0.503992i
$690$	−135.640	+	234.935i	−0.196579	+	0.340485i
$691$	75.0883	−	43.3523i	0.108666	−	0.0627384i	−0.444682	−	0.895689i	$-0.646683\pi$
$691$	75.0883	−	43.3523i	0.108666	−	0.0627384i	0.553348	+	0.832950i	$0.313350\pi$
$692$		−	47.6569i		−	0.0688683i
$693$		0			0
$694$	452.662			0.652251
$695$	652.014	+	1129.32i	0.938150	+	1.62492i
$696$	127.279	+	73.4847i	0.182872	+	0.105581i
$697$	485.985	−	841.750i	0.697252	−	1.20768i
$698$	−407.897	+	235.499i	−0.584379	+	0.337391i
$699$			99.1858i			0.141897i
$700$		0			0
$701$	−149.147			−0.212763			−0.106382	−	0.994325i	$-0.533927\pi$
$701$	−149.147			−0.212763			−0.106382	+	0.994325i	$0.533927\pi$
$702$	−68.9117	−	119.359i	−0.0981648	−	0.170026i
$703$	1416.15	+	817.612i	2.01443	+	1.16303i
$704$	7.02944	−	12.1753i	0.00998500	−	0.0172945i
$705$	343.279	−	198.192i	0.486921	−	0.281124i
$706$		−	927.317i		−	1.31348i
$707$		0			0
$708$	−337.706			−0.476985
$709$	−94.8234	−	164.239i	−0.133742	−	0.231649i	0.791374	−	0.611332i	$-0.209366\pi$
$709$	−94.8234	−	164.239i	−0.133742	−	0.231649i	−0.925116	+	0.379684i	$0.876033\pi$
$710$	−801.110	−	462.521i	−1.12832	−	0.651438i
$711$	−104.735	+	181.406i	−0.147307	+	0.255143i
$712$	−103.103	+	59.5263i	−0.144807	+	0.0836044i
$713$		−	161.234i		−	0.226134i
$714$		0			0
$715$	−194.912			−0.272604
$716$	12.9045	+	22.3513i	0.0180231	+	0.0312169i
$717$	−422.283	−	243.805i	−0.588958	−	0.340035i
$718$	−69.1249	+	119.728i	−0.0962742	+	0.166752i
$719$	10.3978	−	6.00319i	0.0144615	−	0.00834937i	−0.492752	−	0.870170i	$-0.664009\pi$
$719$	10.3978	−	6.00319i	0.0144615	−	0.00834937i	0.507213	+	0.861821i	$0.330676\pi$
$720$		−	70.9631i		−	0.0985599i
$721$		0			0
$722$	241.497			0.334484
$723$	−145.757	−	252.459i	−0.201601	−	0.349183i
$724$	113.220	+	65.3678i	0.156382	+	0.0902870i
$725$	149.558	−	259.043i	0.206288	−	0.357300i
$726$	250.128	−	144.412i	0.344530	−	0.198914i
$727$			417.169i			0.573823i	0.957957	+	0.286911i	$0.0926286\pi$
$727$			417.169i			0.573823i	−0.957957	+	0.286911i	$0.907371\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	−237.338	−	411.082i	−0.325121	−	0.563126i
$731$	212.016	+	122.408i	0.290036	+	0.167452i
$732$	−28.9706	+	50.1785i	−0.0395773	+	0.0685498i
$733$	−1114.57	+	643.495i	−1.52055	+	0.877892i	−0.520847	+	0.853650i	$0.674384\pi$
$733$	−1114.57	+	643.495i	−1.52055	+	0.877892i	−0.999706	+	0.0242419i	$0.992283\pi$
$734$		−	454.043i		−	0.618588i
$735$		0			0
$736$	−105.941			−0.143942
$737$	53.5736	+	92.7922i	0.0726914	+	0.125905i
$738$	152.095	+	87.8124i	0.206091	+	0.118987i
$739$	−666.735	+	1154.82i	−0.902213	+	1.56268i	−0.0775967	+	0.996985i	$0.524725\pi$
$739$	−666.735	+	1154.82i	−0.902213	+	1.56268i	−0.824616	+	0.565693i	$0.808609\pi$
$740$	−726.323	+	419.343i	−0.981517	+	0.566679i
$741$			749.111i			1.01095i
$742$		0			0
$743$	−776.476			−1.04506			−0.522528	−	0.852622i	$-0.675011\pi$
$743$	−776.476			−1.04506			−0.522528	+	0.852622i	$0.675011\pi$
$744$	21.0883	+	36.5260i	0.0283445	+	0.0490941i
$745$	−1079.84	−	623.449i	−1.44946	−	0.836844i
$746$	132.561	−	229.603i	0.177696	−	0.307779i
$747$	16.7208	−	9.65375i	0.0223839	−	0.0129234i
$748$			82.5266i			0.110330i
$749$		0			0
$750$	217.706			0.290274
$751$	−24.4193	−	42.2954i	−0.0325157	−	0.0563188i	0.849310	−	0.527895i	$-0.177019\pi$
$751$	−24.4193	−	42.2954i	−0.0325157	−	0.0563188i	−0.881825	+	0.471576i	$0.843685\pi$
$752$	134.059	+	77.3989i	0.178270	+	0.102924i
$753$	−91.8823	+	159.145i	−0.122022	+	0.211348i
$754$	689.117	−	397.862i	0.913948	−	0.527668i
$755$		−	427.952i		−	0.566824i
$756$		0			0
$757$	−1279.47			−1.69019			−0.845093	−	0.534620i	$-0.820455\pi$
$757$	−1279.47			−1.69019			−0.845093	+	0.534620i	$0.820455\pi$
$758$	−252.510	−	437.360i	−0.333126	−	0.576992i
$759$	49.3675	+	28.5024i	0.0650429	+	0.0375525i
$760$	−192.853	+	334.031i	−0.253754	+	0.439514i
$761$	1139.80	−	658.062i	1.49776	−	0.864734i	0.497766	−	0.867311i	$-0.334154\pi$
$761$	1139.80	−	658.062i	1.49776	−	0.864734i	0.999997	+	0.00257751i	$0.000820449\pi$
$762$		−	220.310i		−	0.289121i
$763$		0			0
$764$	−200.132			−0.261953
$765$	208.279	+	360.750i	0.272260	+	0.471569i
$766$	−762.073	−	439.983i	−0.994874	−	0.574391i
$767$	−914.205	+	1583.45i	−1.19192	+	2.06447i
$768$	24.0000	−	13.8564i	0.0312500	−	0.0180422i
$769$			110.324i			0.143464i	0.997424	+	0.0717320i	$0.0228526\pi$
$769$			110.324i			0.143464i	−0.997424	+	0.0717320i	$0.977147\pi$
$770$		0			0
$771$	−503.095			−0.652523
$772$	−78.9117	−	136.679i	−0.102217	−	0.177045i
$773$	−621.489	−	358.817i	−0.803996	−	0.464187i	0.0408706	−	0.999164i	$-0.486987\pi$
$773$	−621.489	−	358.817i	−0.803996	−	0.464187i	−0.844867	+	0.534977i	$0.820320\pi$
$774$	−22.1177	+	38.3091i	−0.0285759	+	0.0494949i
$775$	74.3390	−	42.9196i	0.0959212	−	0.0553802i
$776$			146.273i			0.188496i
$777$		0			0
$778$	−321.691			−0.413485
$779$	−477.286	−	826.684i	−0.612691	−	1.06121i
$780$	−332.735	−	192.105i	−0.426583	−	0.246288i
$781$	−97.1909	+	168.340i	−0.124444	+	0.215544i
$782$	538.566	−	310.941i	0.688703	−	0.397623i
$783$		−	155.885i		−	0.199086i
$784$		0			0
$785$	1381.85			1.76032
$786$	14.9117	+	25.8278i	0.0189716	+	0.0328598i
$787$	−300.676	−	173.595i	−0.382054	−	0.220579i	0.296658	−	0.954984i	$-0.404128\pi$
$787$	−300.676	−	173.595i	−0.382054	−	0.220579i	−0.678711	+	0.734405i	$0.737461\pi$
$788$	183.941	−	318.595i	0.233428	−	0.404309i
$789$	−133.533	+	77.0956i	−0.169244	+	0.0977130i
$790$			583.939i			0.739163i
$791$		0			0
$792$	−14.9117			−0.0188279
$793$	156.853	+	271.677i	0.197797	+	0.342594i
$794$	−882.219	−	509.350i	−1.11111	−	0.641498i
$795$	−189.640	+	328.465i	−0.238540	+	0.413164i
$796$	−294.500	+	170.029i	−0.369974	+	0.213605i
$797$		−	361.246i		−	0.453257i	−0.973981	−	0.226629i	$-0.927230\pi$
$797$		−	361.246i		−	0.453257i	0.973981	−	0.226629i	$-0.0727704\pi$
$798$		0			0
$799$	−908.674			−1.13726
$800$	−28.2010	−	48.8456i	−0.0352513	−	0.0610570i
$801$	109.357	+	63.1372i	0.136525	+	0.0788230i
$802$	492.978	−	853.862i	0.614685	−	1.06467i
$803$	−86.3818	+	49.8726i	−0.107574	+	0.0621078i
$804$			211.208i			0.262697i
$805$		0			0
$806$	228.353			0.283317
$807$	−165.842	−	287.247i	−0.205504	−	0.355944i
$808$	−16.1909	−	9.34783i	−0.0200383	−	0.0115691i
$809$	56.5736	−	97.9883i	0.0699303	−	0.121123i	−0.828940	−	0.559337i	$-0.811056\pi$
$809$	56.5736	−	97.9883i	0.0699303	−	0.121123i	0.898870	+	0.438215i	$0.144389\pi$
$810$	−65.1838	+	37.6339i	−0.0804738	+	0.0464616i
$811$		−	134.182i		−	0.165453i	−0.996572	−	0.0827264i	$-0.973637\pi$
$811$		−	134.182i		−	0.165453i	0.996572	−	0.0827264i	$-0.0263628\pi$
$812$		0			0
$813$	−376.617			−0.463244
$814$	88.1177	+	152.624i	0.108253	+	0.187499i
$815$	374.309	+	216.107i	0.459274	+	0.265162i
$816$	−81.3381	+	140.882i	−0.0996790	+	0.172649i
$817$	208.221	−	120.217i	0.254861	−	0.147144i
$818$			144.796i			0.177012i
$819$		0			0
$820$	489.588			0.597058
$821$	−245.839	−	425.805i	−0.299438	−	0.518642i	0.676570	−	0.736379i	$-0.263466\pi$
$821$	−245.839	−	425.805i	−0.299438	−	0.518642i	−0.976007	+	0.217737i	$0.930132\pi$
$822$	351.640	+	203.019i	0.427785	+	0.246982i
$823$	470.926	−	815.668i	0.572207	−	0.991091i	−0.424132	−	0.905600i	$-0.639421\pi$
$823$	470.926	−	815.668i	0.572207	−	0.991091i	0.996339	−	0.0854906i	$-0.0272458\pi$
$824$	430.794	−	248.719i	0.522808	−	0.301843i
$825$			30.3488i			0.0367864i
$826$		0			0
$827$	966.978			1.16926			0.584630	−	0.811300i	$-0.301240\pi$
$827$	966.978			1.16926			0.584630	+	0.811300i	$0.301240\pi$
$828$	56.1838	+	97.3131i	0.0678548	+	0.117528i
$829$	−1026.70	−	592.764i	−1.23848	−	0.715035i	−0.269694	−	0.962946i	$-0.586923\pi$
$829$	−1026.70	−	592.764i	−1.23848	−	0.715035i	−0.968783	+	0.247911i	$0.920256\pi$
$830$	26.9117	−	46.6124i	0.0324237	−	0.0561595i
$831$	436.014	−	251.733i	0.524686	−	0.302928i
$832$		−	150.043i		−	0.180340i
$833$		0			0
$834$	540.146			0.647657
$835$	116.485	+	201.758i	0.139503	+	0.241627i
$836$	70.1909	+	40.5247i	0.0839604	+	0.0484746i
$837$	22.3675	−	38.7417i	0.0267235	−	0.0462864i
$838$	479.397	−	276.780i	0.572073	−	0.330286i
$839$		−	1376.91i		−	1.64113i	−0.571550	−	0.820567i	$-0.693658\pi$
$839$		−	1376.91i		−	1.64113i	0.571550	−	0.820567i	$-0.306342\pi$
$840$		0			0
$841$	59.0000			0.0701546
$842$	250.627	+	434.099i	0.297657	+	0.515558i
$843$	−28.2792	−	16.3270i	−0.0335459	−	0.0193678i
$844$	−21.5736	+	37.3666i	−0.0255611	+	0.0442732i
$845$	−935.996	+	540.397i	−1.10769	+	0.639523i
$846$		−	164.188i		−	0.194076i
$847$		0			0
$848$	−148.118			−0.174667
$849$	347.912	+	602.601i	0.409790	+	0.709777i
$850$	286.727	+	165.542i	0.337326	+	0.194755i
$851$	664.014	−	1150.11i	0.780275	−	1.35148i
$852$	−331.831	+	191.582i	−0.389472	+	0.224862i
$853$			175.006i			0.205165i	0.994725	+	0.102582i	$0.0327105\pi$
$853$			175.006i			0.205165i	−0.994725	+	0.102582i	$0.967289\pi$
$854$		0			0
$855$	409.103			0.478483
$856$	−65.3970	−	113.271i	−0.0763983	−	0.132326i
$857$	−53.4746	−	30.8736i	−0.0623974	−	0.0360252i	0.468477	−	0.883476i	$-0.344803\pi$
$857$	−53.4746	−	30.8736i	−0.0623974	−	0.0360252i	−0.530874	+	0.847451i	$0.678136\pi$
$858$	−40.3675	+	69.9186i	−0.0470484	+	0.0814902i
$859$	165.676	−	95.6532i	0.192871	−	0.111354i	−0.400455	−	0.916316i	$-0.631148\pi$
$859$	165.676	−	95.6532i	0.192871	−	0.111354i	0.593326	+	0.804962i	$0.297815\pi$
$860$			123.315i			0.143390i
$861$		0			0
$862$	−827.720			−0.960232
$863$	247.253	+	428.255i	0.286504	+	0.496240i	0.972973	−	0.230919i	$-0.0741733\pi$
$863$	247.253	+	428.255i	0.286504	+	0.496240i	−0.686468	+	0.727160i	$0.740840\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$	−70.4558	+	122.033i	−0.0814518	+	0.141079i
$866$	−480.353	+	277.332i	−0.554680	+	0.320245i
$867$		−	454.358i		−	0.524058i
$868$		0			0
$869$	122.705			0.141202
$870$	−217.279	−	376.339i	−0.249746	−	0.432573i
$871$	990.323	+	571.763i	1.13700	+	0.656445i
$872$	−50.8284	+	88.0374i	−0.0582895	+	0.100960i
$873$	134.360	−	77.5730i	0.153907	−	0.0888580i
$874$		−	610.751i		−	0.698800i
$875$		0			0
$876$	−196.617			−0.224449
$877$	227.177	+	393.481i	0.259038	+	0.448668i	0.965985	−	0.258600i	$-0.0832611\pi$
$877$	227.177	+	393.481i	0.259038	+	0.448668i	−0.706946	+	0.707267i	$0.749928\pi$
$878$	480.728	+	277.548i	0.547526	+	0.316114i
$879$	243.260	−	421.340i	0.276747	−	0.479340i
$880$	−36.0000	+	20.7846i	−0.0409091	+	0.0236189i
$881$		−	143.493i		−	0.162875i	−0.996678	−	0.0814375i	$-0.974049\pi$
$881$		−	143.493i		−	0.162875i	0.996678	−	0.0814375i	$-0.0259511\pi$
$882$		0			0
$883$	−927.986			−1.05095			−0.525473	−	0.850810i	$-0.676112\pi$
$883$	−927.986			−1.05095			−0.525473	+	0.850810i	$0.676112\pi$
$884$	440.382	+	762.764i	0.498169	+	0.862855i
$885$	864.749	+	499.263i	0.977118	+	0.564139i
$886$	−576.110	+	997.851i	−0.650237	+	1.12624i
$887$	−829.882	+	479.133i	−0.935606	+	0.540172i	−0.888580	−	0.458721i	$-0.848308\pi$
$887$	−829.882	+	479.133i	−0.935606	+	0.540172i	−0.0470256	+	0.998894i	$0.514974\pi$
$888$			347.395i			0.391210i
$889$		0			0
$890$	352.014			0.395522
$891$	7.90812	+	13.6973i	0.00887555	+	0.0153729i
$892$	−206.735	−	119.359i	−0.231766	−	0.133810i
$893$	−446.205	+	772.850i	−0.499670	+	0.865454i
$894$	−447.286	+	258.241i	−0.500320	+	0.288860i
$895$		−	76.3122i		−	0.0852650i
$896$		0			0
$897$	608.382			0.678241
$898$	127.508	+	220.850i	0.141991	+	0.245935i
$899$	223.675	+	129.139i	0.248805	+	0.143647i
$900$	−29.9117	+	51.8086i	−0.0332352	+	0.0575651i
$901$	752.976	−	434.731i	0.835711	−	0.482498i
$902$		−	102.879i		−	0.114056i
$903$		0			0
$904$	206.558			0.228494
$905$	−193.279	−	334.769i	−0.213568	−	0.369911i
$906$	−153.515	−	88.6318i	−0.169442	−	0.0978276i
$907$	276.360	−	478.670i	0.304697	−	0.527751i	−0.672497	−	0.740100i	$-0.734778\pi$
$907$	276.360	−	478.670i	0.304697	−	0.527751i	0.977194	+	0.212349i	$0.0681114\pi$
$908$	294.177	−	169.843i	0.323983	−	0.187052i
$909$			19.8297i			0.0218149i
$910$		0			0
$911$	142.742			0.156687			0.0783437	−	0.996926i	$-0.475037\pi$
$911$	142.742			0.156687			0.0783437	+	0.996926i	$0.475037\pi$
$912$	79.8823	+	138.360i	0.0875902	+	0.151711i
$913$	−9.79481	−	5.65503i	−0.0107282	−	0.00619390i
$914$	198.115	−	343.145i	0.216756	−	0.375432i
$915$	148.368	−	85.6600i	0.162150	−	0.0936175i
$916$			220.021i			0.240198i
$917$		0			0
$918$	172.544			0.187957
$919$	−543.227	−	940.898i	−0.591107	−	1.02383i	−0.994084	−	0.108617i	$-0.965358\pi$
$919$	−543.227	−	940.898i	−0.591107	−	1.02383i	0.402976	−	0.915210i	$-0.367976\pi$
$920$	271.279	+	156.623i	0.294869	+	0.170243i
$921$	−131.912	+	228.478i	−0.143227	+	0.248076i
$922$	497.610	−	287.295i	0.539707	−	0.311600i
$923$			2074.54i			2.24760i
$924$		0			0
$925$	707.029			0.764356
$926$	323.480	+	560.284i	0.349331	+	0.605059i
$927$	−456.926	−	263.806i	−0.492908	−	0.284581i
$928$	84.8528	−	146.969i	0.0914362	−	0.158372i
$929$	1342.99	−	775.374i	1.44563	−	0.834633i	0.447410	−	0.894329i	$-0.352346\pi$
$929$	1342.99	−	775.374i	1.44563	−	0.834633i	0.998217	+	0.0596956i	$0.0190130\pi$
$930$		−	124.708i		−	0.134094i
$931$		0			0
$932$	114.530			0.122886
$933$	245.220	+	424.734i	0.262830	+	0.455235i
$934$	788.382	+	455.172i	0.844092	+	0.487337i
$935$	122.007	−	211.323i	0.130489	−	0.226013i
$936$	−137.823	+	79.5724i	−0.147247	+	0.0850132i
$937$		−	759.317i		−	0.810370i	−0.914235	−	0.405185i	$-0.867207\pi$
$937$		−	759.317i		−	0.810370i	0.914235	−	0.405185i	$-0.132793\pi$
$938$		0			0
$939$	84.1463			0.0896127
$940$	−228.853	−	396.385i	−0.243460	−	0.421686i
$941$	31.4817	+	18.1760i	0.0334556	+	0.0193156i	0.516635	−	0.856206i	$-0.327185\pi$
$941$	31.4817	+	18.1760i	0.0334556	+	0.0193156i	−0.483179	+	0.875522i	$0.660518\pi$
$942$	286.191	−	495.697i	0.303812	−	0.526218i
$943$	−671.382	+	387.622i	−0.711964	+	0.411052i
$944$			389.949i			0.413081i
$945$		0			0
$946$	25.9126			0.0273917
$947$	−46.2685	−	80.1394i	−0.0488580	−	0.0846245i	0.840562	−	0.541715i	$-0.182225\pi$
$947$	−46.2685	−	80.1394i	−0.0488580	−	0.0846245i	−0.889420	+	0.457091i	$0.848892\pi$
$948$	209.470	+	120.938i	0.220960	+	0.127571i
$949$	−532.264	+	921.908i	−0.560868	+	0.971452i
$950$	281.595	−	162.579i	0.296416	−	0.171136i
$951$		−	1001.17i		−	1.05276i
$952$		0			0
$953$	−1361.29			−1.42843			−0.714215	−	0.699927i	$-0.753216\pi$
$953$	−1361.29			−1.42843			−0.714215	+	0.699927i	$0.753216\pi$
$954$	78.5513	+	136.055i	0.0823389	+	0.142615i
$955$	512.470	+	295.875i	0.536618	+	0.309817i
$956$	−281.522	+	487.610i	−0.294479	+	0.510052i
$957$	−79.0812	+	45.6575i	−0.0826345	+	0.0477090i
$958$			238.344i			0.248794i
$959$		0			0
$960$	−81.9411			−0.0853553
$961$	−443.440	−	768.061i	−0.461436	−	0.799231i
$962$	1628.88	+	940.435i	1.69322	+	0.977583i
$963$	−69.3640	+	120.142i	−0.0720290	+	0.124758i
$964$	−291.515	+	168.306i	−0.302401	+	0.174591i
$965$			466.651i			0.483577i
$966$		0			0
$967$	481.677			0.498115			0.249057	−	0.968489i	$-0.419879\pi$
$967$	481.677			0.498115			0.249057	+	0.968489i	$0.419879\pi$
$968$	−166.752	−	288.823i	−0.172265	−	0.298371i
$969$	−812.184	−	468.915i	−0.838167	−	0.483916i
$970$	216.250	−	374.556i	0.222938	−	0.386140i
$971$	1236.12	−	713.672i	1.27303	−	0.734987i	0.297476	−	0.954729i	$-0.403855\pi$
$971$	1236.12	−	713.672i	1.27303	−	0.734987i	0.975558	+	0.219743i	$0.0705218\pi$
$972$			31.1769i			0.0320750i
$973$		0			0
$974$	3.93102			0.00403596
$975$	161.948	+	280.503i	0.166101	+	0.287695i
$976$	57.9411	+	33.4523i	0.0593659	+	0.0342749i
$977$	678.131	−	1174.56i	0.694095	−	1.20221i	−0.276389	−	0.961046i	$-0.589138\pi$
$977$	678.131	−	1174.56i	0.694095	−	1.20221i	0.970485	−	0.241163i	$-0.0775287\pi$
$978$	155.044	−	89.5145i	0.158531	−	0.0915282i
$979$		−	73.9698i		−	0.0755565i
$980$		0			0
$981$	107.823			0.109912
$982$	−174.993	−	303.097i	−0.178200	−	0.308652i
$983$	1139.26	+	657.754i	1.15897	+	0.669129i	0.951056	−	0.309019i	$-0.100001\pi$
$983$	1139.26	+	657.754i	1.15897	+	0.669129i	0.207910	+	0.978148i	$0.433334\pi$
$984$	101.397	−	175.625i	0.103046	−	0.178480i
$985$	−942.021	+	543.876i	−0.956367	+	0.552159i
$986$			996.184i			1.01033i
$987$		0			0
$988$	864.999			0.875505
$989$	−97.6325	−	169.104i	−0.0987184	−	0.170985i
$990$	38.1838	+	22.0454i	0.0385695	+	0.0222681i
$991$	−521.640	+	903.506i	−0.526377	+	0.911712i	0.473151	+	0.880982i	$0.343117\pi$
$991$	−521.640	+	903.506i	−0.526377	+	0.911712i	−0.999528	+	0.0307302i	$0.990217\pi$
$992$	42.1766	−	24.3507i	0.0425168	−	0.0245471i
$993$			575.677i			0.579736i
$994$		0			0
$995$	1005.48			1.01054
$996$	−11.1472	−	19.3075i	−0.0111920	−	0.0193850i
$997$	710.425	+	410.164i	0.712562	+	0.411398i	0.812009	−	0.583645i	$-0.198374\pi$
$997$	710.425	+	410.164i	0.712562	+	0.411398i	−0.0994467	+	0.995043i	$0.531707\pi$
$998$	−341.833	+	592.073i	−0.342519	+	0.593259i
$999$	319.103	−	184.234i	0.319422	−	0.184418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.3.g.b.31.2		4
3.2	odd	2		882.3.n.a.325.1		4
7.2	even	3		294.3.g.c.19.2		4
7.3	odd	6		42.3.c.a.13.1	✓	4
7.4	even	3		42.3.c.a.13.2	yes	4
7.5	odd	6	inner	294.3.g.b.19.2		4
7.6	odd	2		294.3.g.c.31.2		4
21.2	odd	6		882.3.n.d.19.1		4
21.5	even	6		882.3.n.a.19.1		4
21.11	odd	6		126.3.c.b.55.3		4
21.17	even	6		126.3.c.b.55.4		4
21.20	even	2		882.3.n.d.325.1		4
28.3	even	6		336.3.f.c.97.3		4
28.11	odd	6		336.3.f.c.97.2		4
35.3	even	12		1050.3.h.a.349.7		8
35.4	even	6		1050.3.f.a.601.3		4
35.17	even	12		1050.3.h.a.349.2		8
35.18	odd	12		1050.3.h.a.349.6		8
35.24	odd	6		1050.3.f.a.601.4		4
35.32	odd	12		1050.3.h.a.349.3		8
56.3	even	6		1344.3.f.e.769.2		4
56.11	odd	6		1344.3.f.e.769.3		4
56.45	odd	6		1344.3.f.f.769.4		4
56.53	even	6		1344.3.f.f.769.1		4
84.11	even	6		1008.3.f.g.433.1		4
84.59	odd	6		1008.3.f.g.433.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.c.a.13.1	✓	4	7.3	odd	6
42.3.c.a.13.2	yes	4	7.4	even	3
126.3.c.b.55.3		4	21.11	odd	6
126.3.c.b.55.4		4	21.17	even	6
294.3.g.b.19.2		4	7.5	odd	6	inner
294.3.g.b.31.2		4	1.1	even	1	trivial
294.3.g.c.19.2		4	7.2	even	3
294.3.g.c.31.2		4	7.6	odd	2
336.3.f.c.97.2		4	28.11	odd	6
336.3.f.c.97.3		4	28.3	even	6
882.3.n.a.19.1		4	21.5	even	6
882.3.n.a.325.1		4	3.2	odd	2
882.3.n.d.19.1		4	21.2	odd	6
882.3.n.d.325.1		4	21.20	even	2
1008.3.f.g.433.1		4	84.11	even	6
1008.3.f.g.433.4		4	84.59	odd	6
1050.3.f.a.601.3		4	35.4	even	6
1050.3.f.a.601.4		4	35.24	odd	6
1050.3.h.a.349.2		8	35.17	even	12
1050.3.h.a.349.3		8	35.32	odd	12
1050.3.h.a.349.6		8	35.18	odd	12
1050.3.h.a.349.7		8	35.3	even	12
1344.3.f.e.769.2		4	56.3	even	6
1344.3.f.e.769.3		4	56.11	odd	6
1344.3.f.f.769.1		4	56.53	even	6
1344.3.f.f.769.4		4	56.45	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	294.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(5.12132 - 2.95680i) q^{5} -2.44949i q^{6} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(5.12132 - 2.95680i) q^{5} -2.44949i q^{6} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(7.24264 + 4.18154i) q^{10} +(0.878680 - 1.52192i) q^{11} +(3.00000 - 1.73205i) q^{12} -18.7554i q^{13} -10.2426 q^{15} +(-2.00000 - 3.46410i) q^{16} +(20.3345 + 11.7401i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(19.9706 - 11.5300i) q^{19} +11.8272i q^{20} +2.48528 q^{22} +(-9.36396 - 16.2189i) q^{23} +(4.24264 + 2.44949i) q^{24} +(4.98528 - 8.63476i) q^{25} +(22.9706 - 13.2621i) q^{26} -5.19615i q^{27} +30.0000 q^{29} +(-7.24264 - 12.5446i) q^{30} +(7.45584 + 4.30463i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-2.63604 + 1.52192i) q^{33} +33.2061i q^{34} -6.00000 q^{36} +(35.4558 + 61.4113i) q^{37} +(28.2426 + 16.3059i) q^{38} +(-16.2426 + 28.1331i) q^{39} +(-14.4853 + 8.36308i) q^{40} -41.3951i q^{41} +10.4264 q^{43} +(1.75736 + 3.04384i) q^{44} +(15.3640 + 8.87039i) q^{45} +(13.2426 - 22.9369i) q^{46} +(-33.5147 + 19.3497i) q^{47} +6.92820i q^{48} +14.1005 q^{50} +(-20.3345 - 35.2204i) q^{51} +(32.4853 + 18.7554i) q^{52} +(18.5147 - 32.0684i) q^{53} +(6.36396 - 3.67423i) q^{54} -10.3923i q^{55} -39.9411 q^{57} +(21.2132 + 36.7423i) q^{58} +(-84.4264 - 48.7436i) q^{59} +(10.2426 - 17.7408i) q^{60} +(-14.4853 + 8.36308i) q^{61} +12.1753i q^{62} +8.00000 q^{64} +(-55.4558 - 96.0523i) q^{65} +(-3.72792 - 2.15232i) q^{66} +(-30.4853 + 52.8021i) q^{67} +(-40.6690 + 23.4803i) q^{68} +32.4377i q^{69} -110.610 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-49.1543 - 28.3793i) q^{73} +(-50.1421 + 86.8487i) q^{74} +(-14.9558 + 8.63476i) q^{75} +46.1200i q^{76} -45.9411 q^{78} +(34.9117 + 60.4688i) q^{79} +(-20.4853 - 11.8272i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(50.6985 - 29.2708i) q^{82} -6.43583i q^{83} +138.853 q^{85} +(7.37258 + 12.7697i) q^{86} +(-45.0000 - 25.9808i) q^{87} +(-2.48528 + 4.30463i) q^{88} +(36.4523 - 21.0457i) q^{89} +25.0892i q^{90} +37.4558 q^{92} +(-7.45584 - 12.9139i) q^{93} +(-47.3970 - 27.3647i) q^{94} +(68.1838 - 118.098i) q^{95} +(-8.48528 + 4.89898i) q^{96} -51.7153i q^{97} +5.27208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 4 q^{4} + 12 q^{5} + 6 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 - 4 * q^4 + 12 * q^5 + 6 * q^9	\( 4 q - 6 q^{3} - 4 q^{4} + 12 q^{5} + 6 q^{9} + 12 q^{10} + 12 q^{11} + 12 q^{12} - 24 q^{15} - 8 q^{16} - 12 q^{17} + 12 q^{19} - 24 q^{22} - 12 q^{23} - 14 q^{25} + 24 q^{26} + 120 q^{29} - 12 q^{30} - 72 q^{31} - 36 q^{33} - 24 q^{36} + 40 q^{37} + 96 q^{38} - 48 q^{39} - 24 q^{40} - 128 q^{43} + 24 q^{44} + 36 q^{45} + 36 q^{46} - 168 q^{47} + 96 q^{50} + 12 q^{51} + 96 q^{52} + 108 q^{53} - 24 q^{57} - 168 q^{59} + 24 q^{60} - 24 q^{61} + 32 q^{64} - 120 q^{65} + 36 q^{66} - 88 q^{67} + 24 q^{68} - 120 q^{71} + 24 q^{73} - 144 q^{74} + 42 q^{75} - 48 q^{78} - 64 q^{79} - 48 q^{80} - 18 q^{81} + 84 q^{82} + 216 q^{85} + 120 q^{86} - 180 q^{87} + 24 q^{88} + 324 q^{89} + 48 q^{92} + 72 q^{93} + 48 q^{94} + 120 q^{95} + 72 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 - 4 * q^4 + 12 * q^5 + 6 * q^9 + 12 * q^10 + 12 * q^11 + 12 * q^12 - 24 * q^15 - 8 * q^16 - 12 * q^17 + 12 * q^19 - 24 * q^22 - 12 * q^23 - 14 * q^25 + 24 * q^26 + 120 * q^29 - 12 * q^30 - 72 * q^31 - 36 * q^33 - 24 * q^36 + 40 * q^37 + 96 * q^38 - 48 * q^39 - 24 * q^40 - 128 * q^43 + 24 * q^44 + 36 * q^45 + 36 * q^46 - 168 * q^47 + 96 * q^50 + 12 * q^51 + 96 * q^52 + 108 * q^53 - 24 * q^57 - 168 * q^59 + 24 * q^60 - 24 * q^61 + 32 * q^64 - 120 * q^65 + 36 * q^66 - 88 * q^67 + 24 * q^68 - 120 * q^71 + 24 * q^73 - 144 * q^74 + 42 * q^75 - 48 * q^78 - 64 * q^79 - 48 * q^80 - 18 * q^81 + 84 * q^82 + 216 * q^85 + 120 * q^86 - 180 * q^87 + 24 * q^88 + 324 * q^89 + 48 * q^92 + 72 * q^93 + 48 * q^94 + 120 * q^95 + 72 * q^99

Introduction

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