LMFDB - Embedded newform 294.3.g.c.19.2

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			19.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.19
Dual form			294.3.g.c.31.2

$q$-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 $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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	$-0.534742\pi$
$5$	−5.12132	−	2.95680i	−1.02426	−	0.591359i	−0.915336	+	0.402691i	$0.868075\pi$
$6$		−	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	0.903198	−	0.429224i	$-0.141213\pi$
$11$	0.878680	+	1.52192i	0.0798800	+	0.138356i	−0.823318	+	0.567580i	$0.807880\pi$
$12$	−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	$-0.909319\pi$
$17$	−20.3345	+	11.7401i	−1.19615	+	0.690597i	−0.236454	+	0.971643i	$0.575985\pi$
$18$	−2.12132	−	3.67423i	−0.117851	−	0.204124i
$19$	−19.9706	−	11.5300i	−1.05108	−	0.606843i	−0.128130	−	0.991757i	$-0.540898\pi$
$19$	−19.9706	−	11.5300i	−1.05108	−	0.606843i	−0.922952	+	0.384915i	$0.874231\pi$
$20$			11.8272i			0.591359i
$21$		0			0
$22$	2.48528			0.112967
$23$	−9.36396	+	16.2189i	−0.407129	+	0.705168i	−0.994567	−	0.104102i	$-0.966803\pi$
$23$	−9.36396	+	16.2189i	−0.407129	+	0.705168i	0.587438	+	0.809269i	$0.300137\pi$
$24$	−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	$-0.711010\pi$
$31$	−7.45584	+	4.30463i	−0.240511	+	0.138859i	0.374901	+	0.927065i	$0.377677\pi$
$32$	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	0.231556	−	0.972822i	$-0.425619\pi$
$37$	35.4558	−	61.4113i	0.958266	−	1.65977i	0.726711	−	0.686944i	$-0.241048\pi$
$38$	−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	$-0.198270\pi$
$47$	33.5147	+	19.3497i	0.713079	+	0.411696i	−0.0991210	+	0.995075i	$0.531603\pi$
$48$			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	0.986131	−	0.165967i	$-0.0530744\pi$
$53$	18.5147	+	32.0684i	0.349334	+	0.605065i	−0.636797	+	0.771031i	$0.719741\pi$
$54$	−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	$-0.357186\pi$
$59$	84.4264	−	48.7436i	1.43096	−	0.826163i	0.997194	+	0.0748645i	$0.0238524\pi$
$60$	10.2426	+	17.7408i	0.170711	+	0.295680i
$61$	14.4853	+	8.36308i	0.237464	+	0.137100i	0.614010	−	0.789298i	$-0.289555\pi$
$61$	14.4853	+	8.36308i	0.237464	+	0.137100i	−0.376547	+	0.926398i	$0.622889\pi$
$62$			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	0.543684	−	0.839290i	$-0.317029\pi$
$67$	−30.4853	−	52.8021i	−0.455004	−	0.788090i	−0.998688	+	0.0511995i	$0.983696\pi$
$68$	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	$-0.539571\pi$
$73$	49.1543	−	28.3793i	0.673347	−	0.388757i	0.797344	+	0.603526i	$0.206238\pi$
$74$	−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	−0.555912	−	0.831241i	$-0.687631\pi$
$79$	34.9117	−	60.4688i	0.441920	−	0.765428i	0.997832	+	0.0658132i	$0.0209641\pi$
$80$	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	$-0.409323\pi$
$89$	−36.4523	−	21.0457i	−0.409576	−	0.236469i	−0.690608	+	0.723230i	$0.742657\pi$
$90$			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	$-0.677084\pi$
$101$	−5.72435	+	3.30496i	−0.0566767	+	0.0327223i	0.471394	+	0.881923i	$0.343751\pi$
$102$	28.7574	+	49.8092i	0.281935	+	0.488326i
$103$	152.309	+	87.9354i	1.47872	+	0.853742i	0.999710	−	0.0240648i	$-0.00766082\pi$
$103$	152.309	+	87.9354i	1.47872	+	0.853742i	0.479014	+	0.877807i	$0.340994\pi$
$104$			53.0482i			0.510079i
$105$		0			0
$106$	52.3675			0.494033
$107$	23.1213	−	40.0473i	0.216087	−	0.374274i	−0.737521	−	0.675324i	$-0.764004\pi$
$107$	23.1213	−	40.0473i	0.216087	−	0.374274i	0.953608	+	0.301050i	$0.0973371\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	17.9706	+	31.1259i	0.164868	+	0.285559i	0.936608	−	0.350378i	$-0.113947\pi$
$109$	17.9706	+	31.1259i	0.164868	+	0.285559i	−0.771741	+	0.635937i	$0.780614\pi$
$110$	−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	$-0.318536\pi$
$131$	10.5442	+	6.08767i	0.0804897	+	0.0464708i	−0.459215	+	0.888325i	$0.651869\pi$
$132$		−	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	−0.992055	−	0.125808i	$-0.959848\pi$
$137$	−82.8823	−	143.556i	−0.604980	−	1.04786i	0.387075	−	0.922048i	$-0.373486\pi$
$138$	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	0.258200	+	0.966091i	$0.416871\pi$
$149$	−105.426	+	182.604i	−0.707560	+	1.22553i	−0.965760	+	0.259438i	$0.916463\pi$
$150$	21.1508	−	12.2114i	0.141005	−	0.0814093i
$151$	36.1838	+	62.6721i	0.239628	+	0.415047i	0.960607	−	0.277909i	$-0.0896413\pi$
$151$	36.1838	+	62.6721i	0.239628	+	0.415047i	−0.720980	+	0.692956i	$0.756308\pi$
$152$	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	$-0.933828\pi$
$157$	−202.368	+	116.837i	−1.28897	+	0.744184i	−0.310495	+	0.950575i	$0.600495\pi$
$158$	−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	−0.731881	−	0.681432i	$-0.761357\pi$
$163$	36.5442	−	63.2963i	0.224197	−	0.388321i	0.956078	+	0.293111i	$0.0946907\pi$
$164$	−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	$-0.311394\pi$
$173$	20.6360	+	11.9142i	0.119283	+	0.0688683i	−0.439171	+	0.898403i	$0.644728\pi$
$174$		−	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	0.883486	−	0.468458i	$-0.155190\pi$
$179$	6.45227	+	11.1757i	0.0360462	+	0.0624339i	−0.847439	+	0.530892i	$0.821857\pi$
$180$	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	−0.704808	−	0.709398i	$-0.748967\pi$
$191$	50.0330	−	86.6597i	0.261953	−	0.453716i	0.966761	+	0.255682i	$0.0823001\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	−39.4558	−	68.3395i	−0.204434	−	0.354091i	0.745518	−	0.666486i	$-0.232202\pi$
$193$	−39.4558	−	68.3395i	−0.204434	−	0.354091i	−0.949952	+	0.312395i	$0.898869\pi$
$194$	−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	$-0.807170\pi$
$199$	−147.250	+	85.0147i	−0.739949	+	0.427210i	0.0821020	+	0.996624i	$0.473837\pi$
$200$	−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	$-0.544617\pi$
$227$	147.088	−	84.9215i	0.647966	−	0.374103i	0.787677	+	0.616089i	$0.211284\pi$
$228$	39.9411	+	69.1801i	0.175180	+	0.303421i
$229$	−95.2721	−	55.0054i	−0.416035	−	0.240198i	0.277344	−	0.960771i	$-0.410546\pi$
$229$	−95.2721	−	55.0054i	−0.416035	−	0.240198i	−0.693380	+	0.720573i	$0.743879\pi$
$230$		−	156.623i		−	0.680970i
$231$		0			0
$232$	−84.8528			−0.365745
$233$	−28.6325	+	49.5929i	−0.122886	+	0.212845i	−0.920905	−	0.389788i	$-0.872548\pi$
$233$	−28.6325	+	49.5929i	−0.122886	+	0.212845i	0.798019	+	0.602633i	$0.205882\pi$
$234$	−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	$-0.780207\pi$
$241$	−145.757	+	84.1531i	−0.604802	+	0.349183i	0.166126	+	0.986105i	$0.446874\pi$
$242$	−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	$-0.524496\pi$
$257$	−251.548	−	145.231i	−0.978785	−	0.565102i	−0.901903	+	0.431938i	$0.857830\pi$
$258$		−	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	0.938154	−	0.346218i	$-0.112534\pi$
$263$	44.5111	+	77.0956i	0.169244	+	0.293139i	−0.768910	+	0.639357i	$0.779201\pi$
$264$	−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	$-0.782507\pi$
$269$	−165.842	+	95.7490i	−0.616513	+	0.355944i	0.158997	+	0.987279i	$0.449174\pi$
$270$	21.7279	+	37.6339i	0.0804738	+	0.139385i
$271$	−188.309	−	108.720i	−0.694866	−	0.401181i	0.110566	−	0.993869i	$-0.464734\pi$
$271$	−188.309	−	108.720i	−0.694866	−	0.401181i	−0.805432	+	0.592688i	$0.798067\pi$
$272$		−	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	−0.999587	−	0.0287438i	$-0.990849\pi$
$277$	−145.338	−	251.733i	−0.524686	−	0.908783i	0.474901	−	0.880039i	$-0.342484\pi$
$278$	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	$-0.415462\pi$
$283$	347.912	−	200.867i	1.22937	−	0.709777i	0.966898	+	0.255163i	$0.0821290\pi$
$284$	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	$-0.516222\pi$
$311$	245.220	−	141.578i	0.788490	−	0.455235i	0.839431	+	0.543467i	$0.182889\pi$
$312$	45.9411	+	79.5724i	0.147247	+	0.255040i
$313$	42.0732	+	24.2910i	0.134419	+	0.0776069i	0.565702	−	0.824610i	$-0.308605\pi$
$313$	42.0732	+	24.2910i	0.134419	+	0.0776069i	−0.431282	+	0.902217i	$0.641939\pi$
$314$			330.465i			1.05244i
$315$		0			0
$316$	−139.647			−0.441920
$317$	289.014	−	500.587i	0.911717	−	1.57914i	0.100079	−	0.994980i	$-0.468090\pi$
$317$	289.014	−	500.587i	0.911717	−	1.57914i	0.811638	−	0.584161i	$-0.198576\pi$
$318$	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	0.497931	+	0.867216i	$0.334093\pi$
$331$	−166.184	+	287.839i	−0.502066	+	0.869603i	−0.999997	+	0.00238698i	$0.999240\pi$
$332$	−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	0.999022	−	0.0442250i	$-0.0140819\pi$
$347$	160.040	+	277.198i	0.461211	+	0.798841i	−0.537811	+	0.843066i	$0.680749\pi$
$348$	−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	0.619012	−	0.785381i	$-0.287533\pi$
$353$	567.864	−	327.856i	1.60868	−	0.928771i	0.989666	−	0.143390i	$-0.0458002\pi$
$354$	−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	−0.789885	−	0.613255i	$-0.789860\pi$
$359$	48.8787	−	84.6604i	0.136152	−	0.235823i	0.926037	+	0.377433i	$0.123193\pi$
$360$	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	$-0.522563\pi$
$367$	278.044	−	160.529i	0.757612	−	0.437408i	0.828438	+	0.560081i	$0.189230\pi$
$368$	−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	−0.963884	−	0.266322i	$-0.914192\pi$
$373$	−93.7351	+	162.354i	−0.251300	+	0.435265i	0.712584	+	0.701587i	$0.247525\pi$
$374$	−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	$-0.0315426\pi$
$383$	538.867	+	311.115i	1.40696	+	0.812311i	0.411870	+	0.911243i	$0.364876\pi$
$384$		−	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	0.681994	−	0.731358i	$-0.261113\pi$
$389$	−113.735	−	196.995i	−0.292378	−	0.506414i	−0.974372	+	0.224945i	$0.927780\pi$
$390$	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	0.996005	+	0.0893004i	$0.0284631\pi$
$397$	623.823	+	360.165i	1.57134	+	0.907216i	0.575339	+	0.817915i	$0.304870\pi$
$398$			240.458i			0.604166i
$399$		0			0
$400$	−39.8823			−0.0997056
$401$	−348.588	+	603.772i	−0.869296	+	1.50567i	−0.00657959	+	0.999978i	$0.502094\pi$
$401$	−348.588	+	603.772i	−0.869296	+	1.50567i	−0.862717	+	0.505687i	$0.831239\pi$
$402$	−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	$-0.706613\pi$
$409$	−88.6690	+	51.1931i	−0.216795	+	0.125166i	0.387671	+	0.921798i	$0.373280\pi$
$410$	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	−0.975286	−	0.220944i	$-0.929086\pi$
$431$	−292.643	−	506.873i	−0.678987	−	1.17604i	0.296300	−	0.955095i	$-0.404247\pi$
$432$	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	$-0.480860\pi$
$439$	−339.926	−	196.256i	−0.774319	−	0.447053i	−0.834413	+	0.551140i	$0.814193\pi$
$440$			29.3939i			0.0668043i
$441$		0			0
$442$	622.794			1.40904
$443$	407.371	−	705.587i	0.919574	−	1.59275i	0.119510	−	0.992833i	$-0.461868\pi$
$443$	407.371	−	705.587i	0.919574	−	1.59275i	0.800064	−	0.599915i	$-0.204799\pi$
$444$	−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	−0.977603	−	0.210459i	$-0.932504\pi$
$457$	−140.088	+	242.640i	−0.306539	+	0.530941i	0.671064	+	0.741400i	$0.265838\pi$
$458$	−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	$-0.575370\pi$
$467$	−557.470	−	321.856i	−1.19373	−	0.689198i	−0.959150	+	0.282899i	$0.908704\pi$
$468$			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	$-0.722958\pi$
$479$	−145.955	+	84.2674i	−0.304709	+	0.175924i	0.339848	+	0.940481i	$0.389624\pi$
$480$	−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	0.867449	−	0.497526i	$-0.165758\pi$
$487$	1.38983	+	2.40725i	0.00285385	+	0.00494302i	−0.864595	+	0.502469i	$0.832425\pi$
$488$	−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	−0.515445	−	0.856923i	$-0.672373\pi$
$499$	241.713	−	418.659i	0.484394	−	0.838996i	0.999839	+	0.0179271i	$0.00570668\pi$
$500$	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	$-0.311780\pi$
$509$	59.6512	+	34.4396i	0.117193	+	0.0676614i	−0.440258	+	0.897871i	$0.645113\pi$
$510$		−	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	$-0.757307\pi$
$521$	−253.503	+	146.360i	−0.486570	+	0.280922i	0.236580	+	0.971612i	$0.423973\pi$
$522$	−63.6396	−	110.227i	−0.121915	−	0.211163i
$523$	426.999	+	246.528i	0.816442	+	0.471373i	0.849188	−	0.528091i	$-0.177092\pi$
$523$	426.999	+	246.528i	0.816442	+	0.471373i	−0.0327460	+	0.999464i	$0.510425\pi$
$524$		−	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	0.234742	−	0.972058i	$-0.424575\pi$
$541$	518.926	−	898.806i	0.959198	−	1.66138i	0.724456	−	0.689322i	$-0.242091\pi$
$542$	−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	−0.993250	−	0.115996i	$-0.962994\pi$
$557$	−332.574	−	576.034i	−0.597080	−	1.03417i	0.396170	−	0.918177i	$-0.370339\pi$
$558$	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	$-0.930188\pi$
$563$	−718.191	+	414.648i	−1.27565	+	0.736497i	−0.299604	+	0.954064i	$0.596855\pi$
$564$	−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	0.368016	+	0.929820i	$0.380037\pi$
$569$	−353.485	+	612.254i	−0.621240	+	1.07602i	−0.989255	+	0.146199i	$0.953296\pi$
$570$	289.279	−	167.015i	0.507507	−	0.293010i
$571$	183.456	+	317.755i	0.321289	+	0.556488i	0.980754	−	0.195246i	$-0.0625507\pi$
$571$	183.456	+	317.755i	0.321289	+	0.556488i	−0.659466	+	0.751735i	$0.729217\pi$
$572$	−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	$-0.556827\pi$
$577$	338.059	−	195.178i	0.585891	−	0.338264i	0.763471	+	0.645842i	$0.223494\pi$
$578$	−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	$-0.0409594\pi$
$593$	816.245	+	471.259i	1.37647	+	0.794704i	0.384735	+	0.923027i	$0.374293\pi$
$594$		−	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	0.922999	+	0.384803i	$0.125731\pi$
$599$	476.054	+	824.550i	0.794749	+	1.37655i	−0.128250	+	0.991742i	$0.540936\pi$
$600$	−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	$-0.644391\pi$
$607$	−871.514	−	503.169i	−1.43577	−	0.828944i	−0.997552	+	0.0699241i	$0.977724\pi$
$608$		−	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	0.935870	−	0.352344i	$-0.114615\pi$
$613$	99.7939	+	172.848i	0.162796	+	0.281971i	−0.773074	+	0.634315i	$0.781282\pi$
$614$	−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	$-0.652210\pi$
$619$	48.6762	−	28.1032i	0.0786368	−	0.0454010i	0.538803	+	0.842432i	$0.318877\pi$
$620$	−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	−0.924236	−	0.381823i	$-0.875297\pi$
$641$	−508.176	−	880.186i	−0.792786	−	1.37315i	0.131450	−	0.991323i	$-0.458037\pi$
$642$	−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	$-0.407629\pi$
$647$	814.587	−	470.302i	1.25902	−	0.726896i	0.972884	+	0.231292i	$0.0742953\pi$
$648$	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	0.436989	+	0.899467i	$0.356045\pi$
$653$	−365.985	+	633.904i	−0.560467	+	0.970757i	−0.997456	+	0.0712901i	$0.977288\pi$
$654$	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	$-0.584897\pi$
$661$	290.881	−	167.940i	0.440063	−	0.254070i	0.703624	+	0.710572i	$0.251564\pi$
$662$	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	0.998202	+	0.0599456i	$0.0190927\pi$
$677$	1048.82	+	605.536i	1.54922	+	0.894441i	0.551015	+	0.834495i	$0.314241\pi$
$678$			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	0.823201	+	0.567750i	$0.192186\pi$
$683$	616.945	+	1068.58i	0.903287	+	1.56454i	0.0800856	+	0.996788i	$0.474481\pi$
$684$	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	$-0.353317\pi$
$691$	−75.0883	−	43.3523i	−0.108666	−	0.0627384i	−0.553348	+	0.832950i	$0.686650\pi$
$692$		−	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	−0.925116	−	0.379684i	$-0.876033\pi$
$709$	−94.8234	+	164.239i	−0.133742	+	0.231649i	0.791374	+	0.611332i	$0.209366\pi$
$710$	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	$-0.335991\pi$
$719$	−10.3978	−	6.00319i	−0.0144615	−	0.00834937i	−0.507213	+	0.861821i	$0.669324\pi$
$720$		−	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	0.999706	+	0.0242419i	$0.00771721\pi$
$733$	1114.57	+	643.495i	1.52055	+	0.877892i	0.520847	+	0.853650i	$0.325616\pi$
$734$		−	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	−0.824616	−	0.565693i	$-0.808609\pi$
$739$	−666.735	−	1154.82i	−0.902213	−	1.56268i	−0.0775967	−	0.996985i	$-0.524725\pi$
$740$	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	−0.881825	−	0.471576i	$-0.843685\pi$
$751$	−24.4193	+	42.2954i	−0.0325157	+	0.0563188i	0.849310	+	0.527895i	$0.177019\pi$
$752$	−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	$-0.665846\pi$
$761$	−1139.80	−	658.062i	−1.49776	−	0.864734i	−0.999997	+	0.00257751i	$0.999180\pi$
$762$		−	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	$-0.513013\pi$
$773$	621.489	−	358.817i	0.803996	−	0.464187i	0.844867	+	0.534977i	$0.179680\pi$
$774$	−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	$-0.595872\pi$
$787$	300.676	−	173.595i	0.382054	−	0.220579i	0.678711	+	0.734405i	$0.262539\pi$
$788$	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	0.898870	−	0.438215i	$-0.144389\pi$
$809$	56.5736	+	97.9883i	0.0699303	+	0.121123i	−0.828940	+	0.559337i	$0.811056\pi$
$810$	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	−0.976007	−	0.217737i	$-0.930132\pi$
$821$	−245.839	+	425.805i	−0.299438	+	0.518642i	0.676570	+	0.736379i	$0.263466\pi$
$822$	−351.640	+	203.019i	−0.427785	+	0.246982i
$823$	470.926	+	815.668i	0.572207	+	0.991091i	0.996339	+	0.0854906i	$0.0272458\pi$
$823$	470.926	+	815.668i	0.572207	+	0.991091i	−0.424132	+	0.905600i	$0.639421\pi$
$824$	−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	$-0.413077\pi$
$829$	1026.70	−	592.764i	1.23848	−	0.715035i	0.968783	+	0.247911i	$0.0797440\pi$
$830$	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	$-0.655197\pi$
$857$	53.4746	−	30.8736i	0.0623974	−	0.0360252i	0.530874	+	0.847451i	$0.321864\pi$
$858$	−40.3675	−	69.9186i	−0.0470484	−	0.0814902i
$859$	−165.676	−	95.6532i	−0.192871	−	0.111354i	0.400455	−	0.916316i	$-0.368852\pi$
$859$	−165.676	−	95.6532i	−0.192871	−	0.111354i	−0.593326	+	0.804962i	$0.702185\pi$
$860$			123.315i			0.143390i
$861$		0			0
$862$	−827.720			−0.960232
$863$	247.253	−	428.255i	0.286504	−	0.496240i	−0.686468	−	0.727160i	$-0.740840\pi$
$863$	247.253	−	428.255i	0.286504	−	0.496240i	0.972973	+	0.230919i	$0.0741733\pi$
$864$	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	−0.706946	−	0.707267i	$-0.749928\pi$
$877$	227.177	−	393.481i	0.259038	−	0.448668i	0.965985	+	0.258600i	$0.0832611\pi$
$878$	−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	$-0.151692\pi$
$887$	829.882	+	479.133i	0.935606	+	0.540172i	0.0470256	+	0.998894i	$0.485026\pi$
$888$			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	0.977194	−	0.212349i	$-0.0681114\pi$
$907$	276.360	+	478.670i	0.304697	+	0.527751i	−0.672497	+	0.740100i	$0.734778\pi$
$908$	−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	0.402976	+	0.915210i	$0.367976\pi$
$919$	−543.227	+	940.898i	−0.591107	+	1.02383i	−0.994084	+	0.108617i	$0.965358\pi$
$920$	−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	$-0.647654\pi$
$929$	−1342.99	−	775.374i	−1.44563	−	0.834633i	−0.998217	+	0.0596956i	$0.980987\pi$
$930$		−	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	$-0.672815\pi$
$941$	−31.4817	+	18.1760i	−0.0334556	+	0.0193156i	0.483179	+	0.875522i	$0.339482\pi$
$942$	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	−0.889420	−	0.457091i	$-0.848892\pi$
$947$	−46.2685	+	80.1394i	−0.0488580	+	0.0846245i	0.840562	+	0.541715i	$0.182225\pi$
$948$	−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	$-0.596145\pi$
$971$	−1236.12	−	713.672i	−1.27303	−	0.734987i	−0.975558	+	0.219743i	$0.929478\pi$
$972$			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	0.970485	+	0.241163i	$0.0775287\pi$
$977$	678.131	+	1174.56i	0.694095	+	1.20221i	−0.276389	+	0.961046i	$0.589138\pi$
$978$	−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	$-0.899999\pi$
$983$	−1139.26	+	657.754i	−1.15897	+	0.669129i	−0.207910	+	0.978148i	$0.566666\pi$
$984$	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	−0.999528	−	0.0307302i	$-0.990217\pi$
$991$	−521.640	−	903.506i	−0.526377	−	0.911712i	0.473151	−	0.880982i	$-0.343117\pi$
$992$	−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	$-0.801626\pi$
$997$	−710.425	+	410.164i	−0.712562	+	0.411398i	0.0994467	+	0.995043i	$0.468293\pi$
$998$	−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.c.19.2		4
3.2	odd	2		882.3.n.d.19.1		4
7.2	even	3		42.3.c.a.13.2	yes	4
7.3	odd	6	inner	294.3.g.c.31.2		4
7.4	even	3		294.3.g.b.31.2		4
7.5	odd	6		42.3.c.a.13.1	✓	4
7.6	odd	2		294.3.g.b.19.2		4
21.2	odd	6		126.3.c.b.55.3		4
21.5	even	6		126.3.c.b.55.4		4
21.11	odd	6		882.3.n.a.325.1		4
21.17	even	6		882.3.n.d.325.1		4
21.20	even	2		882.3.n.a.19.1		4
28.19	even	6		336.3.f.c.97.3		4
28.23	odd	6		336.3.f.c.97.2		4
35.2	odd	12		1050.3.h.a.349.3		8
35.9	even	6		1050.3.f.a.601.3		4
35.12	even	12		1050.3.h.a.349.2		8
35.19	odd	6		1050.3.f.a.601.4		4
35.23	odd	12		1050.3.h.a.349.6		8
35.33	even	12		1050.3.h.a.349.7		8
56.5	odd	6		1344.3.f.f.769.4		4
56.19	even	6		1344.3.f.e.769.2		4
56.37	even	6		1344.3.f.f.769.1		4
56.51	odd	6		1344.3.f.e.769.3		4
84.23	even	6		1008.3.f.g.433.1		4
84.47	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	7.5	odd	6
42.3.c.a.13.2	yes	4	7.2	even	3
126.3.c.b.55.3		4	21.2	odd	6
126.3.c.b.55.4		4	21.5	even	6
294.3.g.b.19.2		4	7.6	odd	2
294.3.g.b.31.2		4	7.4	even	3
294.3.g.c.19.2		4	1.1	even	1	trivial
294.3.g.c.31.2		4	7.3	odd	6	inner
336.3.f.c.97.2		4	28.23	odd	6
336.3.f.c.97.3		4	28.19	even	6
882.3.n.a.19.1		4	21.20	even	2
882.3.n.a.325.1		4	21.11	odd	6
882.3.n.d.19.1		4	3.2	odd	2
882.3.n.d.325.1		4	21.17	even	6
1008.3.f.g.433.1		4	84.23	even	6
1008.3.f.g.433.4		4	84.47	odd	6
1050.3.f.a.601.3		4	35.9	even	6
1050.3.f.a.601.4		4	35.19	odd	6
1050.3.h.a.349.2		8	35.12	even	12
1050.3.h.a.349.3		8	35.2	odd	12
1050.3.h.a.349.6		8	35.23	odd	12
1050.3.h.a.349.7		8	35.33	even	12
1344.3.f.e.769.2		4	56.19	even	6
1344.3.f.e.769.3		4	56.51	odd	6
1344.3.f.f.769.1		4	56.37	even	6
1344.3.f.f.769.4		4	56.5	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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