LMFDB - Embedded newform 294.3.g.c.19.1

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			19.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	294.19
Dual form			294.3.g.c.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.878680 - 0.507306i) q^{5} +2.44949i q^{6} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.878680 - 0.507306i) q^{5} +2.44949i q^{6} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.24264 - 0.717439i) q^{10} +(5.12132 + 8.87039i) q^{11} +(-3.00000 - 1.73205i) q^{12} -8.95743i q^{13} -1.75736 q^{15} +(-2.00000 + 3.46410i) q^{16} +(26.3345 - 15.2042i) q^{17} +(2.12132 + 3.67423i) q^{18} +(13.9706 + 8.06591i) q^{19} +2.02922i q^{20} -14.4853 q^{22} +(3.36396 - 5.82655i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-11.9853 - 20.7591i) q^{25} +(10.9706 + 6.33386i) q^{26} -5.19615i q^{27} +30.0000 q^{29} +(1.24264 - 2.15232i) q^{30} +(43.4558 - 25.0892i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(15.3640 + 8.87039i) q^{33} +43.0041i q^{34} -6.00000 q^{36} +(-15.4558 + 26.7703i) q^{37} +(-19.7574 + 11.4069i) q^{38} +(-7.75736 - 13.4361i) q^{39} +(-2.48528 - 1.43488i) q^{40} -7.10228i q^{41} -74.4264 q^{43} +(10.2426 - 17.7408i) q^{44} +(-2.63604 + 1.52192i) q^{45} +(4.75736 + 8.23999i) q^{46} +(50.4853 + 29.1477i) q^{47} +6.92820i q^{48} +33.8995 q^{50} +(26.3345 - 45.6127i) q^{51} +(-15.5147 + 8.95743i) q^{52} +(35.4853 + 61.4623i) q^{53} +(6.36396 + 3.67423i) q^{54} -10.3923i q^{55} +27.9411 q^{57} +(-21.2132 + 36.7423i) q^{58} +(-0.426407 + 0.246186i) q^{59} +(1.75736 + 3.04384i) q^{60} +(-2.48528 - 1.43488i) q^{61} +70.9631i q^{62} +8.00000 q^{64} +(-4.54416 + 7.87071i) q^{65} +(-21.7279 + 12.5446i) q^{66} +(-13.5147 - 23.4082i) q^{67} +(-52.6690 - 30.4085i) q^{68} -11.6531i q^{69} +50.6102 q^{71} +(4.24264 - 7.34847i) q^{72} +(-61.1543 + 35.3075i) q^{73} +(-21.8579 - 37.8589i) q^{74} +(-35.9558 - 20.7591i) q^{75} -32.2636i q^{76} +21.9411 q^{78} +(-66.9117 + 115.894i) q^{79} +(3.51472 - 2.02922i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(8.69848 + 5.02207i) q^{82} -104.415i q^{83} -30.8528 q^{85} +(52.6274 - 91.1534i) q^{86} +(45.0000 - 25.9808i) q^{87} +(14.4853 + 25.0892i) q^{88} +(-125.548 - 72.4850i) q^{89} -4.30463i q^{90} -13.4558 q^{92} +(43.4558 - 75.2677i) q^{93} +(-71.3970 + 41.2211i) q^{94} +(-8.18377 - 14.1747i) q^{95} +(-8.48528 - 4.89898i) q^{96} -100.705i q^{97} +30.7279 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
$5$	−0.878680	−	0.507306i	−0.175736	−	0.101461i	0.409552	−	0.912287i	$-0.365685\pi$
$5$	−0.878680	−	0.507306i	−0.175736	−	0.101461i	−0.585288	+	0.810826i	$0.699018\pi$
$6$			2.44949i			0.408248i
$7$		0			0
$7$		0			0
$8$	2.82843			0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	1.24264	−	0.717439i	0.124264	−	0.0717439i
$11$	5.12132	+	8.87039i	0.465575	+	0.806399i	0.999227	−	0.0393049i	$-0.0125144\pi$
$11$	5.12132	+	8.87039i	0.465575	+	0.806399i	−0.533653	+	0.845704i	$0.679181\pi$
$12$	−3.00000	−	1.73205i	−0.250000	−	0.144338i
$13$		−	8.95743i		−	0.689033i	−0.938780	−	0.344516i	$-0.888043\pi$
$13$		−	8.95743i		−	0.689033i	0.938780	−	0.344516i	$-0.111957\pi$
$14$		0			0
$15$	−1.75736			−0.117157
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	26.3345	−	15.2042i	1.54909	−	0.894367i	0.550878	−	0.834586i	$-0.314293\pi$
$17$	26.3345	−	15.2042i	1.54909	−	0.894367i	0.998211	−	0.0597816i	$-0.0190404\pi$
$18$	2.12132	+	3.67423i	0.117851	+	0.204124i
$19$	13.9706	+	8.06591i	0.735293	+	0.424521i	0.820355	−	0.571854i	$-0.193776\pi$
$19$	13.9706	+	8.06591i	0.735293	+	0.424521i	−0.0850625	+	0.996376i	$0.527109\pi$
$20$			2.02922i			0.101461i
$21$		0			0
$22$	−14.4853			−0.658422
$23$	3.36396	−	5.82655i	0.146259	−	0.253328i	−0.783583	−	0.621287i	$-0.786610\pi$
$23$	3.36396	−	5.82655i	0.146259	−	0.253328i	0.929842	+	0.367959i	$0.119943\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$	−11.9853	−	20.7591i	−0.479411	−	0.830365i
$26$	10.9706	+	6.33386i	0.421945	+	0.243610i
$27$		−	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	$0.326959\pi$
$30$	1.24264	−	2.15232i	0.0414214	−	0.0717439i
$31$	43.4558	−	25.0892i	1.40180	−	0.809330i	0.407224	−	0.913328i	$-0.366497\pi$
$31$	43.4558	−	25.0892i	1.40180	−	0.809330i	0.994578	+	0.103998i	$0.0331635\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$	15.3640	+	8.87039i	0.465575	+	0.268800i
$34$			43.0041i			1.26483i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−15.4558	+	26.7703i	−0.417726	+	0.723522i	−0.995710	−	0.0925257i	$-0.970506\pi$
$37$	−15.4558	+	26.7703i	−0.417726	+	0.723522i	0.577985	+	0.816048i	$0.303839\pi$
$38$	−19.7574	+	11.4069i	−0.519931	+	0.300182i
$39$	−7.75736	−	13.4361i	−0.198907	−	0.344516i
$40$	−2.48528	−	1.43488i	−0.0621320	−	0.0358719i
$41$		−	7.10228i		−	0.173226i	−0.996242	−	0.0866132i	$-0.972396\pi$
$41$		−	7.10228i		−	0.173226i	0.996242	−	0.0866132i	$-0.0276044\pi$
$42$		0			0
$43$	−74.4264			−1.73085			−0.865423	−	0.501041i	$-0.832950\pi$
$43$	−74.4264			−1.73085			−0.865423	+	0.501041i	$0.832950\pi$
$44$	10.2426	−	17.7408i	0.232787	−	0.403199i
$45$	−2.63604	+	1.52192i	−0.0585786	+	0.0338204i
$46$	4.75736	+	8.23999i	0.103421	+	0.179130i
$47$	50.4853	+	29.1477i	1.07415	+	0.620164i	0.929314	−	0.369291i	$-0.120400\pi$
$47$	50.4853	+	29.1477i	1.07415	+	0.620164i	0.144841	+	0.989455i	$0.453733\pi$
$48$			6.92820i			0.144338i
$49$		0			0
$50$	33.8995			0.677990
$51$	26.3345	−	45.6127i	0.516363	−	0.894367i
$52$	−15.5147	+	8.95743i	−0.298360	+	0.172258i
$53$	35.4853	+	61.4623i	0.669534	+	1.15967i	0.978035	+	0.208442i	$0.0668393\pi$
$53$	35.4853	+	61.4623i	0.669534	+	1.15967i	−0.308501	+	0.951224i	$0.599827\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		−	10.3923i		−	0.188951i
$56$		0			0
$57$	27.9411			0.490195
$58$	−21.2132	+	36.7423i	−0.365745	+	0.633489i
$59$	−0.426407	+	0.246186i	−0.00722724	+	0.00417265i	−0.503609	−	0.863932i	$-0.667995\pi$
$59$	−0.426407	+	0.246186i	−0.00722724	+	0.00417265i	0.496382	+	0.868104i	$0.334662\pi$
$60$	1.75736	+	3.04384i	0.0292893	+	0.0507306i
$61$	−2.48528	−	1.43488i	−0.0407423	−	0.0235226i	0.479490	−	0.877547i	$-0.340821\pi$
$61$	−2.48528	−	1.43488i	−0.0407423	−	0.0235226i	−0.520233	+	0.854024i	$0.674155\pi$
$62$			70.9631i			1.14457i
$63$		0			0
$64$	8.00000			0.125000
$65$	−4.54416	+	7.87071i	−0.0699101	+	0.121088i
$66$	−21.7279	+	12.5446i	−0.329211	+	0.190070i
$67$	−13.5147	−	23.4082i	−0.201712	−	0.349376i	0.747368	−	0.664410i	$-0.231317\pi$
$67$	−13.5147	−	23.4082i	−0.201712	−	0.349376i	−0.949080	+	0.315035i	$0.897984\pi$
$68$	−52.6690	−	30.4085i	−0.774545	−	0.447184i
$69$		−	11.6531i		−	0.168886i
$70$		0			0
$71$	50.6102			0.712819			0.356410	−	0.934330i	$-0.384001\pi$
$71$	50.6102			0.712819			0.356410	+	0.934330i	$0.384001\pi$
$72$	4.24264	−	7.34847i	0.0589256	−	0.102062i
$73$	−61.1543	+	35.3075i	−0.837731	+	0.483664i	−0.856492	−	0.516160i	$-0.827361\pi$
$73$	−61.1543	+	35.3075i	−0.837731	+	0.483664i	0.0187616	+	0.999824i	$0.494028\pi$
$74$	−21.8579	−	37.8589i	−0.295377	−	0.511607i
$75$	−35.9558	−	20.7591i	−0.479411	−	0.276788i
$76$		−	32.2636i		−	0.424521i
$77$		0			0
$78$	21.9411			0.281296
$79$	−66.9117	+	115.894i	−0.846983	+	1.46702i	0.0369042	+	0.999319i	$0.488250\pi$
$79$	−66.9117	+	115.894i	−0.846983	+	1.46702i	−0.883888	+	0.467699i	$0.845083\pi$
$80$	3.51472	−	2.02922i	0.0439340	−	0.0253653i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	8.69848	+	5.02207i	0.106079	+	0.0612448i
$83$		−	104.415i		−	1.25802i	−0.777398	−	0.629009i	$-0.783461\pi$
$83$		−	104.415i		−	1.25802i	0.777398	−	0.629009i	$-0.216539\pi$
$84$		0			0
$85$	−30.8528			−0.362974
$86$	52.6274	−	91.1534i	0.611947	−	1.05992i
$87$	45.0000	−	25.9808i	0.517241	−	0.298629i
$88$	14.4853	+	25.0892i	0.164605	+	0.285105i
$89$	−125.548	−	72.4850i	−1.41065	−	0.814438i	−0.415199	−	0.909730i	$-0.636288\pi$
$89$	−125.548	−	72.4850i	−1.41065	−	0.814438i	−0.995449	+	0.0952921i	$0.969621\pi$
$90$		−	4.30463i		−	0.0478293i
$91$		0			0
$92$	−13.4558			−0.146259
$93$	43.4558	−	75.2677i	0.467267	−	0.809330i
$94$	−71.3970	+	41.2211i	−0.759542	+	0.438522i
$95$	−8.18377	−	14.1747i	−0.0861449	−	0.149207i
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$		−	100.705i		−	1.03820i	−0.854714	−	0.519099i	$-0.826268\pi$
$97$		−	100.705i		−	1.03820i	0.854714	−	0.519099i	$-0.173732\pi$
$98$		0			0
$99$	30.7279			0.310383
$100$	−23.9706	+	41.5182i	−0.239706	+	0.415182i
$101$	−120.276	+	69.4412i	−1.19085	+	0.687536i	−0.958499	−	0.285096i	$-0.907975\pi$
$101$	−120.276	+	69.4412i	−1.19085	+	0.687536i	−0.232349	+	0.972632i	$0.574641\pi$
$102$	37.2426	+	64.5061i	0.365124	+	0.632413i
$103$	−68.3087	−	39.4380i	−0.663191	−	0.382893i	0.130301	−	0.991475i	$-0.458406\pi$
$103$	−68.3087	−	39.4380i	−0.663191	−	0.382893i	−0.793492	+	0.608581i	$0.791739\pi$
$104$		−	25.3354i		−	0.243610i
$105$		0			0
$106$	−100.368			−0.946864
$107$	18.8787	−	32.6988i	0.176436	−	0.305597i	−0.764221	−	0.644954i	$-0.776876\pi$
$107$	18.8787	−	32.6988i	0.176436	−	0.305597i	0.940657	+	0.339358i	$0.110210\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	−15.9706	−	27.6618i	−0.146519	−	0.253778i	0.783420	−	0.621493i	$-0.213474\pi$
$109$	−15.9706	−	27.6618i	−0.146519	−	0.253778i	−0.929939	+	0.367715i	$0.880140\pi$
$110$	12.7279	+	7.34847i	0.115708	+	0.0668043i
$111$			53.5406i			0.482348i
$112$		0			0
$113$	−106.971			−0.946642			−0.473321	−	0.880890i	$-0.656945\pi$
$113$	−106.971			−0.946642			−0.473321	+	0.880890i	$0.656945\pi$
$114$	−19.7574	+	34.2208i	−0.173310	+	0.300182i
$115$	−5.91169	+	3.41311i	−0.0514060	+	0.0296793i
$116$	−30.0000	−	51.9615i	−0.258621	−	0.447944i
$117$	−23.2721	−	13.4361i	−0.198907	−	0.114839i
$118$		−	0.696320i		−	0.00590101i
$119$		0			0
$120$	−4.97056			−0.0414214
$121$	8.04416	−	13.9329i	0.0664806	−	0.115148i
$122$	3.51472	−	2.02922i	0.0288092	−	0.0166330i
$123$	−6.15076	−	10.6534i	−0.0500062	−	0.0866132i
$124$	−86.9117	−	50.1785i	−0.700901	−	0.404665i
$125$			49.6861i			0.397489i
$126$		0			0
$127$	22.0589			0.173692			0.0868460	−	0.996222i	$-0.472321\pi$
$127$	22.0589			0.173692			0.0868460	+	0.996222i	$0.472321\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$	−111.640	+	64.4552i	−0.865423	+	0.499652i
$130$	−6.42641	−	11.1309i	−0.0494339	−	0.0856220i
$131$	61.4558	+	35.4815i	0.469129	+	0.270852i	0.715875	−	0.698229i	$-0.246028\pi$
$131$	61.4558	+	35.4815i	0.469129	+	0.270852i	−0.246746	+	0.969080i	$0.579361\pi$
$132$		−	35.4815i		−	0.268800i
$133$		0			0
$134$	38.2254			0.285264
$135$	−2.63604	+	4.56575i	−0.0195262	+	0.0338204i
$136$	74.4853	−	43.0041i	0.547686	−	0.316207i
$137$	52.8823	+	91.5947i	0.386002	+	0.668575i	0.991908	−	0.126962i	$-0.0405225\pi$
$137$	52.8823	+	91.5947i	0.386002	+	0.668575i	−0.605906	+	0.795536i	$0.707189\pi$
$138$	14.2721	+	8.23999i	0.103421	+	0.0597101i
$139$			181.322i			1.30447i	0.758015	+	0.652237i	$0.226169\pi$
$139$			181.322i			1.30447i	−0.758015	+	0.652237i	$0.773831\pi$
$140$		0			0
$141$	100.971			0.716103
$142$	−35.7868	+	61.9845i	−0.252020	+	0.436511i
$143$	79.4558	−	45.8739i	0.555635	−	0.320796i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$	−26.3604	−	15.2192i	−0.181796	−	0.104960i
$146$		−	99.8646i		−	0.684004i
$147$		0			0
$148$	61.8234			0.417726
$149$	−20.5736	+	35.6345i	−0.138078	+	0.239158i	−0.926769	−	0.375632i	$-0.877426\pi$
$149$	−20.5736	+	35.6345i	−0.138078	+	0.239158i	0.788691	+	0.614790i	$0.210759\pi$
$150$	50.8492	−	29.3578i	0.338995	−	0.195719i
$151$	−40.1838	−	69.6003i	−0.266118	−	0.460929i	0.701738	−	0.712435i	$-0.252408\pi$
$151$	−40.1838	−	69.6003i	−0.266118	−	0.460929i	−0.967856	+	0.251506i	$0.919074\pi$
$152$	39.5147	+	22.8138i	0.259965	+	0.150091i
$153$		−	91.2255i		−	0.596245i
$154$		0			0
$155$	−50.9117			−0.328463
$156$	−15.5147	+	26.8723i	−0.0994533	+	0.172258i
$157$	−49.6325	+	28.6553i	−0.316130	+	0.182518i	−0.649666	−	0.760219i	$-0.725091\pi$
$157$	−49.6325	+	28.6553i	−0.316130	+	0.182518i	0.333536	+	0.942737i	$0.391758\pi$
$158$	−94.6274	−	163.899i	−0.598908	−	1.03734i
$159$	106.456	+	61.4623i	0.669534	+	0.386555i
$160$			5.73951i			0.0358719i
$161$		0			0
$162$	12.7279			0.0785674
$163$	87.4558	−	151.478i	0.536539	−	0.929313i	−0.462548	−	0.886594i	$-0.653065\pi$
$163$	87.4558	−	151.478i	0.536539	−	0.929313i	0.999087	−	0.0427185i	$-0.0136019\pi$
$164$	−12.3015	+	7.10228i	−0.0750092	+	0.0433066i
$165$	−9.00000	−	15.5885i	−0.0545455	−	0.0944755i
$166$	127.882	+	73.8329i	0.770375	+	0.444776i
$167$			196.163i			1.17463i	0.809359	+	0.587315i	$0.199815\pi$
$167$			196.163i			1.17463i	−0.809359	+	0.587315i	$0.800185\pi$
$168$		0			0
$169$	88.7645			0.525234
$170$	21.8162	−	37.7868i	0.128331	−	0.222275i
$171$	41.9117	−	24.1977i	0.245098	−	0.141507i
$172$	74.4264	+	128.910i	0.432712	+	0.749479i
$173$	33.3640	+	19.2627i	0.192855	+	0.111345i	0.593319	−	0.804968i	$-0.297817\pi$
$173$	33.3640	+	19.2627i	0.192855	+	0.111345i	−0.400463	+	0.916313i	$0.631151\pi$
$174$			73.4847i			0.422326i
$175$		0			0
$176$	−40.9706			−0.232787
$177$	−0.426407	+	0.738558i	−0.00240908	+	0.00417265i
$178$	177.551	−	102.509i	0.997479	−	0.575895i
$179$	95.5477	+	165.494i	0.533786	+	0.924545i	0.999221	+	0.0394627i	$0.0125646\pi$
$179$	95.5477	+	165.494i	0.533786	+	0.924545i	−0.465435	+	0.885082i	$0.654102\pi$
$180$	5.27208	+	3.04384i	0.0292893	+	0.0169102i
$181$			120.793i			0.667367i	0.942685	+	0.333683i	$0.108292\pi$
$181$			120.793i			0.667367i	−0.942685	+	0.333683i	$0.891708\pi$
$182$		0			0
$183$	−4.97056			−0.0271615
$184$	9.51472	−	16.4800i	0.0517104	−	0.0895651i
$185$	27.1615	−	15.6817i	0.146819	−	0.0847659i
$186$	61.4558	+	106.445i	0.330408	+	0.572283i
$187$	269.735	+	155.732i	1.44243	+	0.832789i
$188$		−	116.591i		−	0.620164i
$189$		0			0
$190$	23.1472			0.121827
$191$	−56.0330	+	97.0520i	−0.293367	+	0.508126i	−0.974604	−	0.223937i	$-0.928109\pi$
$191$	−56.0330	+	97.0520i	−0.293367	+	0.508126i	0.681237	+	0.732063i	$0.261442\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	11.4558	+	19.8421i	0.0593567	+	0.102809i	0.894177	−	0.447714i	$-0.147762\pi$
$193$	11.4558	+	19.8421i	0.0593567	+	0.102809i	−0.834820	+	0.550523i	$0.814428\pi$
$194$	123.338	+	71.2093i	0.635763	+	0.367058i
$195$			15.7414i			0.0807252i
$196$		0			0
$197$	−116.059			−0.589131			−0.294566	−	0.955631i	$-0.595175\pi$
$197$	−116.059			−0.589131			−0.294566	+	0.955631i	$0.595175\pi$
$198$	−21.7279	+	37.6339i	−0.109737	+	0.190070i
$199$	141.250	−	81.5506i	0.709798	−	0.409802i	−0.101188	−	0.994867i	$-0.532264\pi$
$199$	141.250	−	81.5506i	0.709798	−	0.409802i	0.810986	+	0.585065i	$0.198931\pi$
$200$	−33.8995	−	58.7156i	−0.169497	−	0.293578i
$201$	−40.5442	−	23.4082i	−0.201712	−	0.116459i
$202$		−	196.409i		−	0.972323i
$203$		0			0
$204$	−105.338			−0.516363
$205$	−3.60303	+	6.24063i	−0.0175758	+	0.0304421i
$206$	96.6030	−	55.7738i	0.468947	−	0.270747i
$207$	−10.0919	−	17.4797i	−0.0487531	−	0.0844428i
$208$	31.0294	+	17.9149i	0.149180	+	0.0861291i
$209$			165.232i			0.790586i
$210$		0			0
$211$	106.426			0.504391			0.252195	−	0.967676i	$-0.418847\pi$
$211$	106.426			0.504391			0.252195	+	0.967676i	$0.418847\pi$
$212$	70.9706	−	122.925i	0.334767	−	0.579833i
$213$	75.9153	−	43.8297i	0.356410	−	0.205773i
$214$	26.6985	+	46.2431i	0.124759	+	0.216089i
$215$	65.3970	+	37.7570i	0.304172	+	0.175614i
$216$		−	14.6969i		−	0.0680414i
$217$		0			0
$218$	45.1716			0.207209
$219$	−61.1543	+	105.922i	−0.279244	+	0.483664i
$220$	−18.0000	+	10.3923i	−0.0818182	+	0.0472377i
$221$	−136.191	−	235.890i	−0.616248	−	1.06737i
$222$	−65.5736	−	37.8589i	−0.295377	−	0.170536i
$223$		−	57.0047i		−	0.255627i	−0.991798	−	0.127813i	$-0.959204\pi$
$223$		−	57.0047i		−	0.255627i	0.991798	−	0.127813i	$-0.0407958\pi$
$224$		0			0
$225$	−71.9117			−0.319608
$226$	75.6396	−	131.012i	0.334689	−	0.579698i
$227$	248.912	−	143.709i	1.09653	−	0.633080i	0.161221	−	0.986918i	$-0.448457\pi$
$227$	248.912	−	143.709i	1.09653	−	0.633080i	0.935307	+	0.353838i	$0.115124\pi$
$228$	−27.9411	−	48.3954i	−0.122549	−	0.212261i
$229$	−120.728	−	69.7023i	−0.527196	−	0.304377i	0.212678	−	0.977122i	$-0.431782\pi$
$229$	−120.728	−	69.7023i	−0.527196	−	0.304377i	−0.739874	+	0.672746i	$0.765115\pi$
$230$		−	9.65375i		−	0.0419728i
$231$		0			0
$232$	84.8528			0.365745
$233$	−181.368	+	314.138i	−0.778401	+	1.34823i	0.154461	+	0.987999i	$0.450636\pi$
$233$	−181.368	+	314.138i	−0.778401	+	1.34823i	−0.932863	+	0.360232i	$0.882698\pi$
$234$	32.9117	−	19.0016i	0.140648	−	0.0812033i
$235$	−29.5736	−	51.2230i	−0.125845	−	0.217970i
$236$	0.852814	+	0.492372i	0.00361362	+	0.00208632i
$237$			231.789i			0.978012i
$238$		0			0
$239$	18.4781			0.0773144			0.0386572	−	0.999253i	$-0.487692\pi$
$239$	18.4781			0.0773144			0.0386572	+	0.999253i	$0.487692\pi$
$240$	3.51472	−	6.08767i	0.0146447	−	0.0253653i
$241$	−154.243	+	89.0520i	−0.640011	+	0.369510i	−0.784619	−	0.619979i	$-0.787141\pi$
$241$	−154.243	+	89.0520i	−0.640011	+	0.369510i	0.144608	+	0.989489i	$0.453808\pi$
$242$	11.3762	+	19.7041i	0.0470089	+	0.0814218i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$			5.73951i			0.0235226i
$245$		0			0
$246$	17.3970			0.0707194
$247$	72.2498	−	125.140i	0.292509	−	0.506641i
$248$	122.912	−	70.9631i	0.495612	−	0.286142i
$249$	−90.4264	−	156.623i	−0.363158	−	0.629009i
$250$	−60.8528	−	35.1334i	−0.243411	−	0.140534i
$251$			50.6709i			0.201876i	0.994893	+	0.100938i	$0.0321844\pi$
$251$			50.6709i			0.201876i	−0.994893	+	0.100938i	$0.967816\pi$
$252$		0			0
$253$	68.9117			0.272378
$254$	−15.5980	+	27.0165i	−0.0614094	+	0.106364i
$255$	−46.2792	+	26.7193i	−0.181487	+	0.104782i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−162.452	−	93.7919i	−0.632110	−	0.364949i	0.149459	−	0.988768i	$-0.452247\pi$
$257$	−162.452	−	93.7919i	−0.632110	−	0.364949i	−0.781569	+	0.623819i	$0.785580\pi$
$258$		−	182.307i		−	0.706615i
$259$		0			0
$260$	18.1766			0.0699101
$261$	45.0000	−	77.9423i	0.172414	−	0.298629i
$262$	−86.9117	+	50.1785i	−0.331724	+	0.191521i
$263$	201.489	+	348.989i	0.766117	+	1.32695i	0.939654	+	0.342127i	$0.111147\pi$
$263$	201.489	+	348.989i	0.766117	+	1.32695i	−0.173537	+	0.984827i	$0.555519\pi$
$264$	43.4558	+	25.0892i	0.164605	+	0.0950350i
$265$		−	72.0076i		−	0.271727i
$266$		0			0
$267$	−251.095			−0.940432
$268$	−27.0294	+	46.8164i	−0.100856	+	0.174688i
$269$	−416.158	+	240.269i	−1.54706	+	0.893193i	−0.548691	+	0.836025i	$0.684874\pi$
$269$	−416.158	+	240.269i	−1.54706	+	0.893193i	−0.998365	+	0.0571675i	$0.981793\pi$
$270$	−3.72792	−	6.45695i	−0.0138071	−	0.0239146i
$271$	32.3087	+	18.6534i	0.119220	+	0.0688318i	0.558424	−	0.829556i	$-0.311406\pi$
$271$	32.3087	+	18.6534i	0.119220	+	0.0688318i	−0.439204	+	0.898387i	$0.644739\pi$
$272$			121.634i			0.447184i
$273$		0			0
$274$	−149.574			−0.545889
$275$	122.761	−	212.628i	0.446403	−	0.773193i
$276$	−20.1838	+	11.6531i	−0.0731296	+	0.0422214i
$277$	41.3381	+	71.5997i	0.149235	+	0.258483i	0.930945	−	0.365160i	$-0.118986\pi$
$277$	41.3381	+	71.5997i	0.149235	+	0.258483i	−0.781710	+	0.623642i	$0.785652\pi$
$278$	−222.073	−	128.214i	−0.798824	−	0.461201i
$279$		−	150.535i		−	0.539554i
$280$		0			0
$281$	−150.853			−0.536843			−0.268421	−	0.963302i	$-0.586502\pi$
$281$	−150.853			−0.536843			−0.268421	+	0.963302i	$0.586502\pi$
$282$	−71.3970	+	123.663i	−0.253181	+	0.438522i
$283$	246.088	−	142.079i	0.869570	−	0.502046i	0.00236468	−	0.999997i	$-0.499247\pi$
$283$	246.088	−	142.079i	0.869570	−	0.502046i	0.867205	+	0.497951i	$0.165914\pi$
$284$	−50.6102	−	87.6594i	−0.178205	−	0.308660i
$285$	−24.5513	−	14.1747i	−0.0861449	−	0.0497358i
$286$			129.751i			0.453674i
$287$		0			0
$288$	−16.9706			−0.0589256
$289$	317.838	−	550.512i	1.09979	−	1.90488i
$290$	37.2792	−	21.5232i	0.128549	−	0.0742178i
$291$	−87.2132	−	151.058i	−0.299702	−	0.519099i
$292$	122.309	+	70.6149i	0.418865	+	0.241832i
$293$		−	537.237i		−	1.83357i	−0.399379	−	0.916786i	$-0.630774\pi$
$293$		−	537.237i		−	1.83357i	0.399379	−	0.916786i	$-0.369226\pi$
$294$		0			0
$295$	0.499567			0.00169345
$296$	−43.7157	+	75.7179i	−0.147688	+	0.255804i
$297$	46.0919	−	26.6112i	0.155192	−	0.0895999i
$298$	−29.0955	−	50.3948i	−0.0976358	−	0.169110i
$299$	−52.1909	−	30.1324i	−0.174552	−	0.100777i
$300$			83.0365i			0.276788i
$301$		0			0
$302$	113.657			0.376347
$303$	−120.276	+	208.324i	−0.396949	+	0.687536i
$304$	−55.8823	+	32.2636i	−0.183823	+	0.106130i
$305$	1.45584	+	2.52160i	0.00477326	+	0.00826753i
$306$	111.728	+	64.5061i	0.365124	+	0.210804i
$307$		−	34.7430i		−	0.113169i	−0.998398	−	0.0565847i	$-0.981979\pi$
$307$		−	34.7430i		−	0.113169i	0.998398	−	0.0565847i	$-0.0180211\pi$
$308$		0			0
$309$	−136.617			−0.442127
$310$	36.0000	−	62.3538i	0.116129	−	0.201141i
$311$	−77.2203	+	44.5832i	−0.248297	+	0.143354i	−0.618984	−	0.785403i	$-0.712456\pi$
$311$	−77.2203	+	44.5832i	−0.248297	+	0.143354i	0.370687	+	0.928758i	$0.379122\pi$
$312$	−21.9411	−	38.0031i	−0.0703241	−	0.121805i
$313$	−450.073	−	259.850i	−1.43793	−	0.830191i	−0.440227	−	0.897886i	$-0.645102\pi$
$313$	−450.073	−	259.850i	−1.43793	−	0.830191i	−0.997706	+	0.0676951i	$0.978435\pi$
$314$		−	81.0495i		−	0.258119i
$315$		0			0
$316$	267.647			0.846983
$317$	−271.014	+	469.411i	−0.854935	+	1.48079i	0.0217710	+	0.999763i	$0.493070\pi$
$317$	−271.014	+	469.411i	−0.854935	+	1.48079i	−0.876706	+	0.481027i	$0.840264\pi$
$318$	−150.551	+	86.9208i	−0.473432	+	0.273336i
$319$	153.640	+	266.112i	0.481629	+	0.834206i
$320$	−7.02944	−	4.05845i	−0.0219670	−	0.0126826i
$321$		−	65.3977i		−	0.203731i
$322$		0			0
$323$	490.544			1.51871
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$	−185.948	+	107.357i	−0.572149	+	0.330330i
$326$	123.681	+	214.222i	0.379390	+	0.657123i
$327$	−47.9117	−	27.6618i	−0.146519	−	0.0845927i
$328$		−	20.0883i		−	0.0612448i
$329$		0			0
$330$	25.4558			0.0771389
$331$	−89.8162	+	155.566i	−0.271348	+	0.469989i	−0.969207	−	0.246246i	$-0.920803\pi$
$331$	−89.8162	+	155.566i	−0.271348	+	0.469989i	0.697859	+	0.716235i	$0.254136\pi$
$332$	−180.853	+	104.415i	−0.544737	+	0.314504i
$333$	46.3675	+	80.3109i	0.139242	+	0.241174i
$334$	−240.250	−	138.708i	−0.719311	−	0.415294i
$335$			27.4244i			0.0818638i
$336$		0			0
$337$	291.823			0.865945			0.432972	−	0.901407i	$-0.357465\pi$
$337$	291.823			0.865945			0.432972	+	0.901407i	$0.357465\pi$
$338$	−62.7660	+	108.714i	−0.185698	+	0.321639i
$339$	−160.456	+	92.6392i	−0.473321	+	0.273272i
$340$	30.8528	+	53.4386i	0.0907436	+	0.157172i
$341$	445.103	+	256.980i	1.30529	+	0.753607i
$342$			68.4415i			0.200121i
$343$		0			0
$344$	−210.510			−0.611947
$345$	−5.91169	+	10.2393i	−0.0171353	+	0.0296793i
$346$	−47.1838	+	27.2416i	−0.136369	+	0.0787328i
$347$	−226.040	−	391.513i	−0.651413	−	1.12828i	−0.982780	−	0.184778i	$-0.940843\pi$
$347$	−226.040	−	391.513i	−0.651413	−	1.12828i	0.331368	−	0.943502i	$-0.392490\pi$
$348$	−90.0000	−	51.9615i	−0.258621	−	0.149315i
$349$			235.067i			0.673543i	0.941586	+	0.336772i	$0.109335\pi$
$349$			235.067i			0.673543i	−0.941586	+	0.336772i	$0.890665\pi$
$350$		0			0
$351$	−46.5442			−0.132604
$352$	28.9706	−	50.1785i	0.0823027	−	0.142553i
$353$	−21.8635	+	12.6229i	−0.0619363	+	0.0357590i	−0.530648	−	0.847592i	$-0.678052\pi$
$353$	−21.8635	+	12.6229i	−0.0619363	+	0.0357590i	0.468712	+	0.883351i	$0.344718\pi$
$354$	−0.603030	−	1.04448i	−0.00170348	−	0.00295051i
$355$	−44.4701	−	25.6748i	−0.125268	−	0.0723235i
$356$			289.940i			0.814438i
$357$		0			0
$358$	−270.250			−0.754888
$359$	53.1213	−	92.0088i	0.147970	−	0.256292i	−0.782507	−	0.622642i	$-0.786059\pi$
$359$	53.1213	−	92.0088i	0.147970	−	0.256292i	0.930477	+	0.366350i	$0.119393\pi$
$360$	−7.45584	+	4.30463i	−0.0207107	+	0.0119573i
$361$	−50.3823	−	87.2646i	−0.139563	−	0.241730i
$362$	−147.941	−	85.4138i	−0.408677	−	0.235950i
$363$		−	27.8658i		−	0.0767652i
$364$		0			0
$365$	71.6468			0.196292
$366$	3.51472	−	6.08767i	0.00960306	−	0.0166330i
$367$	−248.044	+	143.208i	−0.675868	+	0.390213i	−0.798297	−	0.602265i	$-0.794265\pi$
$367$	−248.044	+	143.208i	−0.675868	+	0.390213i	0.122428	+	0.992477i	$0.460932\pi$
$368$	13.4558	+	23.3062i	0.0365648	+	0.0633321i
$369$	−18.4523	−	10.6534i	−0.0500062	−	0.0288711i
$370$			44.3545i			0.119877i
$371$		0			0
$372$	−173.823			−0.467267
$373$	211.735	−	366.736i	0.567654	−	0.983206i	−0.429143	−	0.903237i	$-0.641184\pi$
$373$	211.735	−	366.736i	0.567654	−	0.983206i	0.996797	−	0.0799696i	$-0.0254823\pi$
$374$	−381.463	+	220.238i	−1.01995	+	0.588871i
$375$	43.0294	+	74.5292i	0.114745	+	0.198744i
$376$	142.794	+	82.4421i	0.379771	+	0.219261i
$377$		−	268.723i		−	0.712793i
$378$		0			0
$379$	101.103			0.266761			0.133381	−	0.991065i	$-0.457417\pi$
$379$	101.103			0.266761			0.133381	+	0.991065i	$0.457417\pi$
$380$	−16.3675	+	28.3494i	−0.0430725	+	0.0746037i
$381$	33.0883	−	19.1035i	0.0868460	−	0.0501405i
$382$	−79.2426	−	137.252i	−0.207441	−	0.359299i
$383$	−190.867	−	110.197i	−0.498348	−	0.287721i	0.229683	−	0.973265i	$-0.426231\pi$
$383$	−190.867	−	110.197i	−0.498348	−	0.287721i	−0.728031	+	0.685544i	$0.759564\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−32.4020			−0.0839431
$387$	−111.640	+	193.365i	−0.288474	+	0.499652i
$388$	−174.426	+	100.705i	−0.449553	+	0.259549i
$389$	191.735	+	332.095i	0.492892	+	0.853714i	0.999966	−	0.00818803i	$-0.00260636\pi$
$389$	191.735	+	332.095i	0.492892	+	0.853714i	−0.507074	+	0.861902i	$0.669273\pi$
$390$	−19.2792	−	11.1309i	−0.0494339	−	0.0285407i
$391$		−	204.586i		−	0.523238i
$392$		0			0
$393$	122.912			0.312752
$394$	82.0660	−	142.143i	0.208289	−	0.360768i
$395$	117.588	−	67.8894i	0.297691	−	0.171872i
$396$	−30.7279	−	53.2223i	−0.0775958	−	0.134400i
$397$	420.177	+	242.589i	1.05838	+	0.611056i	0.924984	−	0.380007i	$-0.124078\pi$
$397$	420.177	+	242.589i	1.05838	+	0.611056i	0.133396	+	0.991063i	$0.457412\pi$
$398$			230.660i			0.579548i
$399$		0			0
$400$	95.8823			0.239706
$401$	126.588	−	219.257i	0.315680	−	0.546775i	−0.663901	−	0.747820i	$-0.731101\pi$
$401$	126.588	−	219.257i	0.315680	−	0.546775i	0.979582	+	0.201045i	$0.0644339\pi$
$402$	57.3381	−	33.1042i	0.142632	−	0.0823487i
$403$	−224.735	−	389.253i	−0.557655	−	0.965887i
$404$	240.551	+	138.882i	0.595424	+	0.343768i
$405$			9.13151i			0.0225469i
$406$		0			0
$407$	−316.617			−0.777930
$408$	74.4853	−	129.012i	0.182562	−	0.316207i
$409$	4.66905	−	2.69568i	0.0114158	−	0.00659089i	−0.494281	−	0.869302i	$-0.664569\pi$
$409$	4.66905	−	2.69568i	0.0114158	−	0.00659089i	0.505697	+	0.862711i	$0.331235\pi$
$410$	−5.09545	−	8.82559i	−0.0124279	−	0.0215258i
$411$	158.647	+	91.5947i	0.386002	+	0.222858i
$412$			157.752i			0.382893i
$413$		0			0
$414$	28.5442			0.0689472
$415$	−52.9706	+	91.7477i	−0.127640	+	0.221079i
$416$	−43.8823	+	25.3354i	−0.105486	+	0.0609025i
$417$	157.029	+	271.983i	0.376569	+	0.652237i
$418$	−202.368	−	116.837i	−0.484133	−	0.279514i
$419$			294.431i			0.702700i	0.936244	+	0.351350i	$0.114277\pi$
$419$			294.431i			0.702700i	−0.936244	+	0.351350i	$0.885723\pi$
$420$		0			0
$421$	−290.441			−0.689883			−0.344941	−	0.938624i	$-0.612101\pi$
$421$	−290.441			−0.689883			−0.344941	+	0.938624i	$0.612101\pi$
$422$	−75.2548	+	130.345i	−0.178329	+	0.308875i
$423$	151.456	−	87.4431i	0.358052	−	0.206721i
$424$	100.368	+	173.842i	0.236716	+	0.410004i
$425$	−631.253	−	364.454i	−1.48530	−	0.857540i
$426$			123.969i			0.291007i
$427$		0			0
$428$	−75.5147			−0.176436
$429$	79.4558	−	137.622i	0.185212	−	0.320796i
$430$	−92.4853	+	53.3964i	−0.215082	+	0.124178i
$431$	−25.3568	−	43.9193i	−0.0588325	−	0.101901i	0.835109	−	0.550084i	$-0.185404\pi$
$431$	−25.3568	−	43.9193i	−0.0588325	−	0.101901i	−0.893942	+	0.448183i	$0.852071\pi$
$432$	18.0000	+	10.3923i	0.0416667	+	0.0240563i
$433$		−	724.761i		−	1.67381i	−0.547347	−	0.836906i	$-0.684362\pi$
$433$		−	724.761i		−	1.67381i	0.547347	−	0.836906i	$-0.315638\pi$
$434$		0			0
$435$	−52.7208			−0.121197
$436$	−31.9411	+	55.3237i	−0.0732595	+	0.126889i
$437$	93.9929	−	54.2668i	0.215087	−	0.124180i
$438$	−86.4853	−	149.797i	−0.197455	−	0.342002i
$439$	321.926	+	185.864i	0.733317	+	0.423381i	0.819634	−	0.572887i	$-0.194177\pi$
$439$	321.926	+	185.864i	0.733317	+	0.423381i	−0.0863177	+	0.996268i	$0.527510\pi$
$440$		−	29.3939i		−	0.0668043i
$441$		0			0
$442$	385.206			0.871507
$443$	114.629	−	198.543i	0.258756	−	0.448178i	−0.707153	−	0.707061i	$-0.750021\pi$
$443$	114.629	−	198.543i	0.258756	−	0.448178i	0.965909	+	0.258882i	$0.0833541\pi$
$444$	92.7351	−	53.5406i	0.208863	−	0.120587i
$445$	73.5442	+	127.382i	0.165268	+	0.286252i
$446$	69.8162	+	40.3084i	0.156539	+	0.0903776i
$447$			71.2690i			0.159439i
$448$		0			0
$449$	−600.323			−1.33702			−0.668511	−	0.743702i	$-0.733068\pi$
$449$	−600.323			−1.33702			−0.668511	+	0.743702i	$0.733068\pi$
$450$	50.8492	−	88.0735i	0.112998	−	0.195719i
$451$	63.0000	−	36.3731i	0.139690	−	0.0806498i
$452$	106.971	+	185.278i	0.236661	+	0.409908i
$453$	−120.551	−	69.6003i	−0.266118	−	0.153643i
$454$			406.471i			0.895311i
$455$		0			0
$456$	79.0294			0.173310
$457$	−241.912	+	419.003i	−0.529347	+	0.916856i	0.470067	+	0.882631i	$0.344230\pi$
$457$	−241.912	+	419.003i	−0.529347	+	0.916856i	−0.999414	+	0.0342255i	$0.989104\pi$
$458$	170.735	−	98.5739i	0.372784	−	0.215227i
$459$	−79.0036	−	136.838i	−0.172121	−	0.298122i
$460$	11.8234	+	6.82623i	0.0257030	+	0.0148396i
$461$			274.661i			0.595794i	0.954598	+	0.297897i	$0.0962852\pi$
$461$			274.661i			0.595794i	−0.954598	+	0.297897i	$0.903715\pi$
$462$		0			0
$463$	−153.470			−0.331469			−0.165734	−	0.986170i	$-0.552999\pi$
$463$	−153.470			−0.331469			−0.165734	+	0.986170i	$0.552999\pi$
$464$	−60.0000	+	103.923i	−0.129310	+	0.223972i
$465$	−76.3675	+	44.0908i	−0.164231	+	0.0948190i
$466$	−256.492	−	444.258i	−0.550413	−	0.953343i
$467$	53.4701	+	30.8710i	0.114497	+	0.0661049i	0.556155	−	0.831079i	$-0.312276\pi$
$467$	53.4701	+	30.8710i	0.114497	+	0.0661049i	−0.441658	+	0.897184i	$0.645609\pi$
$468$			53.7446i			0.114839i
$469$		0			0
$470$	83.6468			0.177972
$471$	−49.6325	+	85.9660i	−0.105377	+	0.182518i
$472$	−1.20606	+	0.696320i	−0.00255521	+	0.00147525i
$473$	−381.161	−	660.191i	−0.805838	−	1.39575i
$474$	−283.882	−	163.899i	−0.598908	−	0.345780i
$475$		−	386.689i		−	0.814082i
$476$		0			0
$477$	212.912			0.446356
$478$	−13.0660	+	22.6310i	−0.0273348	+	0.0473452i
$479$	481.955	−	278.257i	1.00617	−	0.580912i	0.0961020	−	0.995371i	$-0.469363\pi$
$479$	481.955	−	278.257i	1.00617	−	0.580912i	0.910068	+	0.414459i	$0.136029\pi$
$480$	4.97056	+	8.60927i	0.0103553	+	0.0179360i
$481$	239.793	+	138.445i	0.498530	+	0.287827i
$482$		−	251.877i		−	0.522567i
$483$		0			0
$484$	−32.1766			−0.0664806
$485$	−51.0883	+	88.4876i	−0.105337	+	0.182449i
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	162.610	+	281.649i	0.333902	+	0.578335i	0.983273	−	0.182136i	$-0.0583013\pi$
$487$	162.610	+	281.649i	0.333902	+	0.578335i	−0.649371	+	0.760471i	$0.724968\pi$
$488$	−7.02944	−	4.05845i	−0.0144046	−	0.00831649i
$489$		−	302.956i		−	0.619542i
$490$		0			0
$491$	643.477			1.31054			0.655272	−	0.755393i	$-0.272554\pi$
$491$	643.477			1.31054			0.655272	+	0.755393i	$0.272554\pi$
$492$	−12.3015	+	21.3068i	−0.0250031	+	0.0433066i
$493$	790.036	−	456.127i	1.60251	−	0.925208i
$494$	102.177	+	176.975i	0.206835	+	0.358249i
$495$	−27.0000	−	15.5885i	−0.0545455	−	0.0314918i
$496$			200.714i			0.404665i
$497$		0			0
$498$	255.765			0.513583
$499$	−377.713	+	654.218i	−0.756939	+	1.31106i	0.187465	+	0.982271i	$0.439973\pi$
$499$	−377.713	+	654.218i	−0.756939	+	1.31106i	−0.944404	+	0.328786i	$0.893360\pi$
$500$	86.0589	−	49.6861i	0.172118	−	0.0993722i
$501$	169.882	+	294.245i	0.339086	+	0.587315i
$502$	−62.0589	−	35.8297i	−0.123623	−	0.0713739i
$503$		−	509.409i		−	1.01274i	−0.862316	−	0.506371i	$-0.830987\pi$
$503$		−	509.409i		−	1.01274i	0.862316	−	0.506371i	$-0.169013\pi$
$504$		0			0
$505$	140.912			0.279033
$506$	−48.7279	+	84.3992i	−0.0963002	+	0.166797i
$507$	133.147	−	76.8723i	0.262617	−	0.151622i
$508$	−22.0589	−	38.2071i	−0.0434230	−	0.0752108i
$509$	666.349	+	384.717i	1.30913	+	0.755828i	0.981951	−	0.189133i	$-0.0605677\pi$
$509$	666.349	+	384.717i	1.30913	+	0.755828i	0.327182	+	0.944961i	$0.393901\pi$
$510$		−	75.5737i		−	0.148184i
$511$		0			0
$512$	22.6274			0.0441942
$513$	41.9117	−	72.5932i	0.0816992	−	0.141507i
$514$	229.742	−	132.642i	0.446969	−	0.258058i
$515$	40.0143	+	69.3068i	0.0776976	+	0.134576i
$516$	223.279	+	128.910i	0.432712	+	0.249826i
$517$			597.099i			1.15493i
$518$		0			0
$519$	66.7279			0.128570
$520$	−12.8528	+	22.2617i	−0.0247169	+	0.0428110i
$521$	463.503	−	267.604i	0.889641	−	0.513635i	0.0158162	−	0.999875i	$-0.494965\pi$
$521$	463.503	−	267.604i	0.889641	−	0.513635i	0.873825	+	0.486240i	$0.161632\pi$
$522$	63.6396	+	110.227i	0.121915	+	0.211163i
$523$	−726.999	−	419.733i	−1.39006	−	0.802549i	−0.396735	−	0.917933i	$-0.629857\pi$
$523$	−726.999	−	419.733i	−1.39006	−	0.802549i	−0.993321	+	0.115384i	$0.963190\pi$
$524$		−	141.926i		−	0.270852i
$525$		0			0
$526$	−569.897			−1.08345
$527$	762.926	−	1321.43i	1.44768	−	2.50745i
$528$	−61.4558	+	35.4815i	−0.116394	+	0.0671999i
$529$	241.868	+	418.927i	0.457217	+	0.791922i
$530$	88.1909	+	50.9170i	0.166398	+	0.0960699i
$531$			1.47712i			0.00278176i
$532$		0			0
$533$	−63.6182			−0.119359
$534$	177.551	−	307.528i	0.332493	−	0.575895i
$535$	−33.1766	+	19.1545i	−0.0620124	+	0.0358029i
$536$	−38.2254	−	66.2083i	−0.0713160	−	0.123523i
$537$	286.643	+	165.494i	0.533786	+	0.308182i
$538$		−	679.583i		−	1.26317i
$539$		0			0
$540$	10.5442			0.0195262
$541$	−142.926	+	247.555i	−0.264188	+	0.457588i	−0.967351	−	0.253442i	$-0.918437\pi$
$541$	−142.926	+	247.555i	−0.264188	+	0.457588i	0.703162	+	0.711029i	$0.251771\pi$
$542$	−45.6913	+	26.3799i	−0.0843014	+	0.0486714i
$543$	104.610	+	181.190i	0.192652	+	0.333683i
$544$	−148.971	−	86.0082i	−0.273843	−	0.158103i
$545$			32.4078i			0.0594639i
$546$		0			0
$547$	−741.470			−1.35552			−0.677761	−	0.735283i	$-0.737049\pi$
$547$	−741.470			−1.35552			−0.677761	+	0.735283i	$0.737049\pi$
$548$	105.765	−	183.189i	0.193001	−	0.334287i
$549$	−7.45584	+	4.30463i	−0.0135808	+	0.00784086i
$550$	173.610	+	300.702i	0.315655	+	0.546730i
$551$	419.117	+	241.977i	0.760648	+	0.439160i
$552$		−	32.9600i		−	0.0597101i
$553$		0			0
$554$	−116.922			−0.211050
$555$	27.1615	−	47.0450i	0.0489396	−	0.0847659i
$556$	314.059	−	181.322i	0.564854	−	0.326119i
$557$	−417.426	−	723.004i	−0.749419	−	1.29803i	−0.948101	−	0.317968i	$-0.897000\pi$
$557$	−417.426	−	723.004i	−0.749419	−	1.29803i	0.198682	−	0.980064i	$-0.436334\pi$
$558$	184.368	+	106.445i	0.330408	+	0.190761i
$559$			666.669i			1.19261i
$560$		0			0
$561$	539.470			0.961622
$562$	106.669	−	184.756i	0.189803	−	0.328748i
$563$	−361.809	+	208.891i	−0.642645	+	0.371031i	−0.785633	−	0.618693i	$-0.787662\pi$
$563$	−361.809	+	208.891i	−0.642645	+	0.371031i	0.142988	+	0.989724i	$0.454329\pi$
$564$	−100.971	−	174.886i	−0.179026	−	0.310082i
$565$	93.9929	+	54.2668i	0.166359	+	0.0960474i
$566$			401.861i			0.710001i
$567$		0			0
$568$	143.147			0.252020
$569$	−336.515	+	582.861i	−0.591414	+	1.02436i	0.402628	+	0.915364i	$0.368097\pi$
$569$	−336.515	+	582.861i	−0.591414	+	1.02436i	−0.994042	+	0.108996i	$0.965236\pi$
$570$	34.7208	−	20.0461i	0.0609136	−	0.0351685i
$571$	132.544	+	229.573i	0.232126	+	0.402055i	0.958434	−	0.285315i	$-0.0920984\pi$
$571$	132.544	+	229.573i	0.232126	+	0.402055i	−0.726307	+	0.687370i	$0.758765\pi$
$572$	−158.912	−	91.7477i	−0.277818	−	0.160398i
$573$			194.104i			0.338750i
$574$		0			0
$575$	−161.272			−0.280473
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	405.941	−	234.370i	0.703537	−	0.406188i	−0.105126	−	0.994459i	$-0.533525\pi$
$577$	405.941	−	234.370i	0.703537	−	0.406188i	0.808664	+	0.588271i	$0.200191\pi$
$578$	449.491	+	778.541i	0.777666	+	1.34696i
$579$	34.3675	+	19.8421i	0.0593567	+	0.0342696i
$580$			60.8767i			0.104960i
$581$		0			0
$582$	246.676			0.423842
$583$	−363.463	+	629.536i	−0.623436	+	1.07982i
$584$	−172.971	+	99.8646i	−0.296182	+	0.171001i
$585$	13.6325	+	23.6121i	0.0233034	+	0.0403626i
$586$	657.978	+	379.884i	1.12283	+	0.648266i
$587$		−	120.530i		−	0.205332i	−0.994716	−	0.102666i	$-0.967263\pi$
$587$		−	120.530i		−	0.205332i	0.994716	−	0.102666i	$-0.0327372\pi$
$588$		0			0
$589$	809.470			1.37431
$590$	−0.353247	+	0.611842i	−0.000598724	+	0.00103702i
$591$	−174.088	+	100.510i	−0.294566	+	0.170068i
$592$	−61.8234	−	107.081i	−0.104431	−	0.180880i
$593$	−486.245	−	280.734i	−0.819975	−	0.473413i	0.0304327	−	0.999537i	$-0.490311\pi$
$593$	−486.245	−	280.734i	−0.819975	−	0.473413i	−0.850408	+	0.526124i	$0.823645\pi$
$594$			75.2677i			0.126713i
$595$		0			0
$596$	82.2944			0.138078
$597$	141.250	−	244.652i	0.236599	−	0.409802i
$598$	73.8091	−	42.6137i	0.123427	−	0.0712604i
$599$	−470.054	−	814.158i	−0.784732	−	1.35920i	−0.929159	−	0.369680i	$-0.879467\pi$
$599$	−470.054	−	814.158i	−0.784732	−	1.35920i	0.144427	−	0.989515i	$-0.453866\pi$
$600$	−101.698	−	58.7156i	−0.169497	−	0.0978594i
$601$			563.527i			0.937649i	0.883291	+	0.468824i	$0.155322\pi$
$601$			563.527i			0.937649i	−0.883291	+	0.468824i	$0.844678\pi$
$602$		0			0
$603$	−81.0883			−0.134475
$604$	−80.3675	+	139.201i	−0.133059	+	0.230465i
$605$	−14.1365	+	8.16170i	−0.0233661	+	0.0134904i
$606$	−170.095	−	294.614i	−0.280686	−	0.486162i
$607$	265.514	+	153.294i	0.437420	+	0.252544i	0.702503	−	0.711681i	$-0.252066\pi$
$607$	265.514	+	153.294i	0.437420	+	0.252544i	−0.265083	+	0.964226i	$0.585399\pi$
$608$		−	91.2553i		−	0.150091i
$609$		0			0
$610$	−4.11775			−0.00675041
$611$	261.088	−	452.218i	0.427313	−	0.740128i
$612$	−158.007	+	91.2255i	−0.258182	+	0.149061i
$613$	−137.794	−	238.666i	−0.224786	−	0.389341i	0.731469	−	0.681875i	$-0.238835\pi$
$613$	−137.794	−	238.666i	−0.224786	−	0.389341i	−0.956255	+	0.292533i	$0.905502\pi$
$614$	42.5513	+	24.5670i	0.0693018	+	0.0400114i
$615$			12.4813i			0.0202947i
$616$		0			0
$617$	461.294			0.747639			0.373820	−	0.927501i	$-0.378048\pi$
$617$	461.294			0.747639			0.373820	+	0.927501i	$0.378048\pi$
$618$	96.6030	−	167.321i	0.156316	−	0.270747i
$619$	−324.676	+	187.452i	−0.524517	+	0.302830i	−0.738781	−	0.673946i	$-0.764598\pi$
$619$	−324.676	+	187.452i	−0.524517	+	0.302830i	0.214264	+	0.976776i	$0.431265\pi$
$620$	50.9117	+	88.1816i	0.0821156	+	0.142228i
$621$	−30.2756	−	17.4797i	−0.0487531	−	0.0281476i
$622$		−	126.100i		−	0.202734i
$623$		0			0
$624$	62.0589			0.0994533
$625$	−274.426	+	475.320i	−0.439082	+	0.760512i
$626$	636.500	−	367.483i	1.01677	−	0.587034i
$627$	143.095	+	247.849i	0.228222	+	0.395293i
$628$	99.2649	+	57.3106i	0.158065	+	0.0912590i
$629$			939.978i			1.49440i
$630$		0			0
$631$	−1127.32			−1.78656			−0.893282	−	0.449496i	$-0.851603\pi$
$631$	−1127.32			−1.78656			−0.893282	+	0.449496i	$0.851603\pi$
$632$	−189.255	+	327.799i	−0.299454	+	0.518669i
$633$	159.640	−	92.1680i	0.252195	−	0.145605i
$634$	−383.272	−	663.847i	−0.604530	−	1.04708i
$635$	−19.3827	−	11.1906i	−0.0305239	−	0.0176230i
$636$		−	245.849i		−	0.386555i
$637$		0			0
$638$	−434.558			−0.681126
$639$	75.9153	−	131.489i	0.118803	−	0.205773i
$640$	9.94113	−	5.73951i	0.0155330	−	0.00896799i
$641$	442.176	+	765.871i	0.689822	+	1.19481i	0.971895	+	0.235414i	$0.0756445\pi$
$641$	442.176	+	765.871i	0.689822	+	1.19481i	−0.282074	+	0.959393i	$0.591022\pi$
$642$	80.0955	+	46.2431i	0.124759	+	0.0720298i
$643$		−	300.765i		−	0.467753i	−0.972266	−	0.233876i	$-0.924859\pi$
$643$		−	300.765i		−	0.467753i	0.972266	−	0.233876i	$-0.0751411\pi$
$644$		0			0
$645$	130.794			0.202781
$646$	−346.867	+	600.791i	−0.536946	+	0.930018i
$647$	−814.587	+	470.302i	−1.25902	+	0.726896i	−0.972884	−	0.231292i	$-0.925705\pi$
$647$	−814.587	+	470.302i	−1.25902	+	0.726896i	−0.286137	+	0.958189i	$0.592371\pi$
$648$	−12.7279	−	22.0454i	−0.0196419	−	0.0340207i
$649$	−4.36753	−	2.52160i	−0.00672963	−	0.00388536i
$650$		−	303.652i		−	0.467157i
$651$		0			0
$652$	−349.823			−0.536539
$653$	227.985	−	394.881i	0.349135	−	0.604719i	−0.636961	−	0.770896i	$-0.719809\pi$
$653$	227.985	−	394.881i	0.349135	−	0.604719i	0.986096	+	0.166177i	$0.0531423\pi$
$654$	67.7574	−	39.1197i	0.103605	−	0.0598161i
$655$	−36.0000	−	62.3538i	−0.0549618	−	0.0951967i
$656$	24.6030	+	14.2046i	0.0375046	+	0.0216533i
$657$			211.845i			0.322443i
$658$		0			0
$659$	403.684			0.612571			0.306285	−	0.951940i	$-0.400914\pi$
$659$	403.684			0.612571			0.306285	+	0.951940i	$0.400914\pi$
$660$	−18.0000	+	31.1769i	−0.0272727	+	0.0472377i
$661$	−998.881	+	576.704i	−1.51117	+	0.872473i	−0.511252	+	0.859431i	$0.670818\pi$
$661$	−998.881	+	576.704i	−1.51117	+	0.872473i	−0.999915	+	0.0130418i	$0.995849\pi$
$662$	−127.019	−	220.004i	−0.191872	−	0.332332i
$663$	−408.573	−	235.890i	−0.616248	−	0.355791i
$664$		−	295.331i		−	0.444776i
$665$		0			0
$666$	−131.147			−0.196918
$667$	100.919	−	174.797i	0.151303	−	0.262064i
$668$	339.765	−	196.163i	0.508629	−	0.293657i
$669$	−49.3675	−	85.5071i	−0.0737930	−	0.127813i
$670$	−33.5879	−	19.3920i	−0.0501312	−	0.0289432i
$671$		−	29.3939i		−	0.0438061i
$672$		0			0
$673$	−607.440			−0.902585			−0.451293	−	0.892376i	$-0.649037\pi$
$673$	−607.440			−0.902585			−0.451293	+	0.892376i	$0.649037\pi$
$674$	−206.350	+	357.409i	−0.306158	+	0.530281i
$675$	−107.868	+	62.2773i	−0.159804	+	0.0922627i
$676$	−88.7645	−	153.745i	−0.131308	−	0.227433i
$677$	985.180	+	568.794i	1.45521	+	0.840168i	0.998770	−	0.0495834i	$-0.0157894\pi$
$677$	985.180	+	568.794i	1.45521	+	0.840168i	0.456444	+	0.889752i	$0.349123\pi$
$678$		−	262.023i		−	0.386465i
$679$		0			0
$680$	−87.2649			−0.128331
$681$	248.912	−	431.128i	0.365509	−	0.633080i
$682$	−629.470	+	363.425i	−0.922977	+	0.532881i
$683$	409.055	+	708.505i	0.598910	+	1.03734i	0.992982	+	0.118263i	$0.0377325\pi$
$683$	409.055	+	708.505i	0.598910	+	1.03734i	−0.394073	+	0.919079i	$0.628934\pi$
$684$	−83.8234	−	48.3954i	−0.122549	−	0.0707536i
$685$		−	107.310i		−	0.156657i
$686$		0			0
$687$	−241.456			−0.351464
$688$	148.853	−	257.821i	0.216356	−	0.374739i
$689$	550.544	−	317.857i	0.799048	−	0.461331i
$690$	−8.36039	−	14.4806i	−0.0121165	−	0.0209864i
$691$	−176.912	−	102.140i	−0.256023	−	0.147815i	0.366496	−	0.930420i	$-0.380557\pi$
$691$	−176.912	−	102.140i	−0.256023	−	0.147815i	−0.622519	+	0.782605i	$0.713891\pi$
$692$		−	77.0508i		−	0.111345i
$693$		0			0
$694$	639.338			0.921236
$695$	91.9857	−	159.324i	0.132354	−	0.229243i
$696$	127.279	−	73.4847i	0.182872	−	0.105581i
$697$	−107.985	−	187.035i	−0.154928	−	0.268343i
$698$	−287.897	−	166.217i	−0.412459	−	0.238133i
$699$			628.276i			0.898821i
$700$		0			0
$701$	−318.853			−0.454854			−0.227427	−	0.973795i	$-0.573031\pi$
$701$	−318.853			−0.454854			−0.227427	+	0.973795i	$0.573031\pi$
$702$	32.9117	−	57.0047i	0.0468827	−	0.0812033i
$703$	−431.854	+	249.331i	−0.614301	+	0.354667i
$704$	40.9706	+	70.9631i	0.0581968	+	0.100800i
$705$	−88.7208	−	51.2230i	−0.125845	−	0.0726567i
$706$		−	35.7030i		−	0.0505708i
$707$		0			0
$708$	1.70563			0.00240908
$709$	108.823	−	188.488i	0.153489	−	0.265850i	−0.779019	−	0.627000i	$-0.784283\pi$
$709$	108.823	−	188.488i	0.153489	−	0.265850i	0.932508	+	0.361150i	$0.117616\pi$
$710$	62.8903	−	36.3097i	0.0885778	−	0.0511404i
$711$	200.735	+	347.683i	0.282328	+	0.489006i
$712$	−355.103	−	205.019i	−0.498740	−	0.287947i
$713$		−	337.597i		−	0.473488i
$714$		0			0
$715$	−93.0883			−0.130193
$716$	191.095	−	330.987i	0.266893	−	0.462272i
$717$	27.7172	−	16.0025i	0.0386572	−	0.0223187i
$718$	75.1249	+	130.120i	0.104631	+	0.181226i
$719$	−1045.60	−	603.679i	−1.45425	−	0.839609i	−0.455527	−	0.890222i	$-0.650549\pi$
$719$	−1045.60	−	603.679i	−1.45425	−	0.839609i	−0.998718	+	0.0506134i	$0.983882\pi$
$720$		−	12.1753i		−	0.0169102i
$721$		0			0
$722$	142.503			0.197372
$723$	−154.243	+	267.156i	−0.213337	+	0.369510i
$724$	209.220	−	120.793i	0.288978	−	0.166842i
$725$	−359.558	−	622.773i	−0.495943	−	0.858998i
$726$	34.1285	+	19.7041i	0.0470089	+	0.0271406i
$727$			123.231i			0.169506i	0.996402	+	0.0847528i	$0.0270100\pi$
$727$			123.231i			0.169506i	−0.996402	+	0.0847528i	$0.972990\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$	−50.6619	+	87.7490i	−0.0693999	+	0.120204i
$731$	−1959.98	+	1131.60i	−2.68124	+	1.54801i
$732$	4.97056	+	8.60927i	0.00679039	+	0.0117613i
$733$	325.434	+	187.890i	0.443976	+	0.256330i	0.705283	−	0.708926i	$-0.250820\pi$
$733$	325.434	+	187.890i	0.443976	+	0.256330i	−0.261307	+	0.965256i	$0.584153\pi$
$734$		−	405.054i		−	0.551844i
$735$		0			0
$736$	−38.0589			−0.0517104
$737$	138.426	−	239.762i	0.187824	−	0.325321i
$738$	26.0955	−	15.0662i	0.0353597	−	0.0204149i
$739$	−361.265	−	625.729i	−0.488856	−	0.846724i	0.511061	−	0.859544i	$-0.329252\pi$
$739$	−361.265	−	625.729i	−0.488856	−	0.846724i	−0.999918	+	0.0128200i	$0.995919\pi$
$740$	−54.3229	−	31.3634i	−0.0734094	−	0.0423829i
$741$		−	250.281i		−	0.337761i
$742$		0			0
$743$	1268.48			1.70724			0.853618	−	0.520899i	$-0.174403\pi$
$743$	1268.48			1.70724			0.853618	+	0.520899i	$0.174403\pi$
$744$	122.912	−	212.889i	0.165204	−	0.286142i
$745$	36.1552	−	20.8742i	0.0485305	−	0.0280191i
$746$	299.439	+	518.643i	0.401392	+	0.695232i
$747$	−271.279	−	156.623i	−0.363158	−	0.209670i
$748$		−	622.926i		−	0.832789i
$749$		0			0
$750$	−121.706			−0.162274
$751$	−219.581	+	380.325i	−0.292384	+	0.506425i	−0.974373	−	0.224938i	$-0.927782\pi$
$751$	−219.581	+	380.325i	−0.292384	+	0.506425i	0.681989	+	0.731363i	$0.261115\pi$
$752$	−201.941	+	116.591i	−0.268539	+	0.155041i
$753$	43.8823	+	76.0063i	0.0582766	+	0.100938i
$754$	329.117	+	190.016i	0.436495	+	0.252010i
$755$			81.5419i			0.108002i
$756$		0			0
$757$	−668.530			−0.883131			−0.441565	−	0.897229i	$-0.645577\pi$
$757$	−668.530			−0.883131			−0.441565	+	0.897229i	$0.645577\pi$
$758$	−71.4903	+	123.825i	−0.0943144	+	0.163357i
$759$	103.368	−	59.6793i	0.136189	−	0.0786288i
$760$	−23.1472	−	40.0921i	−0.0304568	−	0.0527528i
$761$	−762.202	−	440.058i	−1.00158	−	0.578263i	−0.0928647	−	0.995679i	$-0.529602\pi$
$761$	−762.202	−	440.058i	−1.00158	−	0.578263i	−0.908715	+	0.417416i	$0.862936\pi$
$762$			54.0330i			0.0709094i
$763$		0			0
$764$	224.132			0.293367
$765$	−46.2792	+	80.1580i	−0.0604957	+	0.104782i
$766$	269.927	−	155.842i	0.352385	−	0.203450i
$767$	2.20519	+	3.81951i	0.00287509	+	0.00497980i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$		−	1163.41i		−	1.51289i	−0.654059	−	0.756444i	$-0.726935\pi$
$769$		−	1163.41i		−	1.51289i	0.654059	−	0.756444i	$-0.273065\pi$
$770$		0			0
$771$	−324.905			−0.421407
$772$	22.9117	−	39.6842i	0.0296784	−	0.0514044i
$773$	464.511	−	268.186i	0.600920	−	0.346941i	−0.168483	−	0.985704i	$-0.553887\pi$
$773$	464.511	−	268.186i	0.600920	−	0.346941i	0.769403	+	0.638763i	$0.220554\pi$
$774$	−157.882	−	273.460i	−0.203982	−	0.353308i
$775$	−1041.66	−	601.403i	−1.34408	−	0.776004i
$776$		−	284.837i		−	0.367058i
$777$		0			0
$778$	−542.309			−0.697055
$779$	57.2864	−	99.2229i	0.0735383	−	0.127372i
$780$	27.2649	−	15.7414i	0.0349550	−	0.0201813i
$781$	259.191	+	448.932i	0.331871	+	0.574817i
$782$	250.566	+	144.664i	0.320416	+	0.184992i
$783$		−	155.885i		−	0.199086i
$784$		0			0
$785$	58.1481			0.0740740
$786$	−86.9117	+	150.535i	−0.110575	+	0.191521i
$787$	−72.6762	+	41.9596i	−0.0923459	+	0.0533159i	−0.545462	−	0.838136i	$-0.683646\pi$
$787$	−72.6762	+	41.9596i	−0.0923459	+	0.0533159i	0.453116	+	0.891452i	$0.350312\pi$
$788$	116.059	+	201.020i	0.147283	+	0.255101i
$789$	604.467	+	348.989i	0.766117	+	0.442318i
$790$			192.020i			0.243064i
$791$		0			0
$792$	86.9117			0.109737
$793$	−12.8528	+	22.2617i	−0.0162078	+	0.0280728i
$794$	−594.219	+	343.073i	−0.748387	+	0.432082i
$795$	−62.3604	−	108.011i	−0.0784407	−	0.135863i
$796$	−282.500	−	163.101i	−0.354899	−	0.204901i
$797$			1005.57i			1.26169i	0.775908	+	0.630846i	$0.217292\pi$
$797$			1005.57i			1.26169i	−0.775908	+	0.630846i	$0.782708\pi$
$798$		0			0
$799$	1772.67			2.21862
$800$	−67.7990	+	117.431i	−0.0847487	+	0.146789i
$801$	−376.643	+	217.455i	−0.470216	+	0.271479i
$802$	179.022	+	310.076i	0.223220	+	0.386628i
$803$	−626.382	−	361.642i	−0.780052	−	0.450363i
$804$			93.6327i			0.116459i
$805$		0			0
$806$	635.647			0.788644
$807$	−416.158	+	720.807i	−0.515685	+	0.893193i
$808$	−340.191	+	196.409i	−0.421028	+	0.243081i
$809$	141.426	+	244.958i	0.174816	+	0.302791i	0.940098	−	0.340905i	$-0.110734\pi$
$809$	141.426	+	244.958i	0.174816	+	0.302791i	−0.765281	+	0.643696i	$0.777400\pi$
$810$	−11.1838	−	6.45695i	−0.0138071	−	0.00797154i
$811$			923.997i			1.13933i	0.821877	+	0.569665i	$0.192927\pi$
$811$			923.997i			1.13933i	−0.821877	+	0.569665i	$0.807073\pi$
$812$		0			0
$813$	64.6173			0.0794801
$814$	223.882	−	387.775i	0.275040	−	0.476383i
$815$	−153.691	+	88.7337i	−0.188578	+	0.108876i
$816$	105.338	+	182.451i	0.129091	+	0.223592i
$817$	−1039.78	−	600.317i	−1.27268	−	0.734782i
$818$			7.62452i			0.00932093i
$819$		0			0
$820$	14.4121			0.0175758
$821$	−636.161	+	1101.86i	−0.774862	+	1.34210i	0.160010	+	0.987115i	$0.448847\pi$
$821$	−636.161	+	1101.86i	−0.774862	+	1.34210i	−0.934872	+	0.354985i	$0.884486\pi$
$822$	−224.360	+	129.535i	−0.272945	+	0.157585i
$823$	−190.926	−	330.693i	−0.231988	−	0.401815i	0.726405	−	0.687267i	$-0.241190\pi$
$823$	−190.926	−	330.693i	−0.231988	−	0.401815i	−0.958393	+	0.285452i	$0.907856\pi$
$824$	−193.206	−	111.548i	−0.234473	−	0.135373i
$825$		−	425.256i		−	0.515462i
$826$		0			0
$827$	653.022			0.789628			0.394814	−	0.918761i	$-0.370809\pi$
$827$	653.022			0.789628			0.394814	+	0.918761i	$0.370809\pi$
$828$	−20.1838	+	34.9593i	−0.0243765	+	0.0422214i
$829$	−186.698	+	107.790i	−0.225208	+	0.130024i	−0.608360	−	0.793662i	$-0.708172\pi$
$829$	−186.698	+	107.790i	−0.225208	+	0.130024i	0.383151	+	0.923686i	$0.374839\pi$
$830$	−74.9117	−	129.751i	−0.0902550	−	0.156326i
$831$	124.014	+	71.5997i	0.149235	+	0.0861609i
$832$		−	71.6594i		−	0.0861291i
$833$		0			0
$834$	−444.146			−0.532550
$835$	99.5147	−	172.365i	0.119179	−	0.206425i
$836$	286.191	−	165.232i	0.342334	−	0.197646i
$837$	−130.368	−	225.803i	−0.155756	−	0.269777i
$838$	−360.603	−	208.194i	−0.430314	−	0.248442i
$839$		−	632.267i		−	0.753596i	−0.926295	−	0.376798i	$-0.877025\pi$
$839$		−	632.267i		−	0.753596i	0.926295	−	0.376798i	$-0.122975\pi$
$840$		0			0
$841$	59.0000			0.0701546
$842$	205.373	−	355.716i	0.243910	−	0.422465i
$843$	−226.279	+	130.642i	−0.268421	+	0.154973i
$844$	−106.426	−	184.336i	−0.126098	−	0.218408i
$845$	−77.9956	−	45.0308i	−0.0923024	−	0.0532908i
$846$			247.326i			0.292348i
$847$		0			0
$848$	−283.882			−0.334767
$849$	246.088	−	426.237i	0.289857	−	0.502046i
$850$	892.727	−	515.416i	1.05027	−	0.606372i
$851$	103.986	+	180.109i	0.122192	+	0.211643i
$852$	−151.831	−	87.6594i	−0.178205	−	0.102887i
$853$			919.650i			1.07814i	0.842262	+	0.539068i	$0.181224\pi$
$853$			919.650i			1.07814i	−0.842262	+	0.539068i	$0.818776\pi$
$854$		0			0
$855$	−49.1026			−0.0574299
$856$	53.3970	−	92.4863i	0.0623796	−	0.108045i
$857$	456.525	−	263.575i	0.532702	−	0.307556i	−0.209414	−	0.977827i	$-0.567156\pi$
$857$	456.525	−	263.575i	0.532702	−	0.307556i	0.742116	+	0.670272i	$0.233822\pi$
$858$	112.368	+	194.626i	0.130964	+	0.226837i
$859$	207.676	+	119.902i	0.241765	+	0.139583i	0.615988	−	0.787756i	$-0.288757\pi$
$859$	207.676	+	119.902i	0.241765	+	0.139583i	−0.374223	+	0.927339i	$0.622090\pi$
$860$		−	151.028i		−	0.175614i
$861$		0			0
$862$	71.7199			0.0832018
$863$	−181.253	+	313.940i	−0.210027	+	0.363778i	−0.951723	−	0.306959i	$-0.900689\pi$
$863$	−181.253	+	313.940i	−0.210027	+	0.363778i	0.741696	+	0.670737i	$0.234022\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$	−19.5442	−	33.8515i	−0.0225944	−	0.0391346i
$866$	887.647	+	512.483i	1.02500	+	0.591782i
$867$		−	1101.02i		−	1.26992i
$868$		0			0
$869$	−1370.70			−1.57734
$870$	37.2792	−	64.5695i	0.0428497	−	0.0742178i
$871$	−209.677	+	121.057i	−0.240731	+	0.138986i
$872$	−45.1716	−	78.2395i	−0.0518023	−	0.0897242i
$873$	−261.640	−	151.058i	−0.299702	−	0.173033i
$874$			153.490i			0.175617i
$875$		0			0
$876$	244.617			0.279244
$877$	430.823	−	746.208i	0.491247	−	0.850864i	−0.508702	−	0.860942i	$-0.669875\pi$
$877$	430.823	−	746.208i	0.491247	−	0.850864i	0.999949	+	0.0100781i	$0.00320801\pi$
$878$	−455.272	+	262.851i	−0.518533	+	0.299375i
$879$	−465.260	−	805.855i	−0.529307	−	0.916786i
$880$	36.0000	+	20.7846i	0.0409091	+	0.0236189i
$881$		−	334.553i		−	0.379742i	−0.981809	−	0.189871i	$-0.939193\pi$
$881$		−	334.553i		−	0.379742i	0.981809	−	0.189871i	$-0.0608071\pi$
$882$		0			0
$883$	−1488.01			−1.68518			−0.842590	−	0.538555i	$-0.818970\pi$
$883$	−1488.01			−1.68518			−0.842590	+	0.538555i	$0.818970\pi$
$884$	−272.382	+	471.779i	−0.308124	+	0.533687i
$885$	0.749350	−	0.432637i	0.000846723	−	0.000488856i
$886$	162.110	+	280.782i	0.182968	+	0.316910i
$887$	694.118	+	400.749i	0.782545	+	0.451803i	0.837332	−	0.546695i	$-0.184114\pi$
$887$	694.118	+	400.749i	0.782545	+	0.451803i	−0.0547862	+	0.998498i	$0.517448\pi$
$888$			151.436i			0.170536i
$889$		0			0
$890$	−208.014			−0.233724
$891$	46.0919	−	79.8335i	0.0517305	−	0.0895999i
$892$	−98.7351	+	57.0047i	−0.110690	+	0.0639066i
$893$	470.205	+	814.419i	0.526546	+	0.912004i
$894$	−87.2864	−	50.3948i	−0.0976358	−	0.0563700i
$895$		−	193.888i		−	0.216634i
$896$		0			0
$897$	−104.382			−0.116368
$898$	424.492	−	735.242i	0.472709	−	0.818756i
$899$	1303.68	−	752.677i	1.45014	−	0.837238i
$900$	71.9117	+	124.555i	0.0799019	+	0.138394i
$901$	1868.98	+	1079.05i	2.07434	+	1.19762i
$902$			102.879i			0.114056i
$903$		0			0
$904$	−302.558			−0.334689
$905$	61.2792	−	106.139i	0.0677118	−	0.117280i
$906$	170.485	−	98.4297i	0.188174	−	0.108642i
$907$	403.640	+	699.124i	0.445027	+	0.770810i	0.998054	−	0.0623537i	$-0.0198607\pi$
$907$	403.640	+	699.124i	0.445027	+	0.770810i	−0.553027	+	0.833163i	$0.686527\pi$
$908$	−497.823	−	287.418i	−0.548264	−	0.316540i
$909$			416.647i			0.458358i
$910$		0			0
$911$	−442.742			−0.485996			−0.242998	−	0.970027i	$-0.578131\pi$
$911$	−442.742			−0.485996			−0.242998	+	0.970027i	$0.578131\pi$
$912$	−55.8823	+	96.7909i	−0.0612744	+	0.106130i
$913$	926.205	−	534.745i	1.01446	−	0.585701i
$914$	−342.115	−	592.560i	−0.374305	−	0.648315i
$915$	4.36753	+	2.52160i	0.00477326	+	0.00275584i
$916$			278.809i			0.304377i
$917$		0			0
$918$	223.456			0.243416
$919$	59.2275	−	102.585i	0.0644478	−	0.111627i	−0.832001	−	0.554774i	$-0.812805\pi$
$919$	59.2275	−	102.585i	0.0644478	−	0.111627i	0.896449	+	0.443147i	$0.146138\pi$
$920$	−16.7208	+	9.65375i	−0.0181748	+	0.0104932i
$921$	−30.0883	−	52.1145i	−0.0326692	−	0.0565847i
$922$	−336.390	−	194.215i	−0.364848	−	0.210645i
$923$		−	453.337i		−	0.491156i
$924$		0			0
$925$	740.971			0.801049
$926$	108.520	−	187.962i	0.117192	−	0.202982i
$927$	−204.926	+	118.314i	−0.221064	+	0.127631i
$928$	−84.8528	−	146.969i	−0.0914362	−	0.158372i
$929$	544.988	+	314.649i	0.586639	+	0.338696i	0.763767	−	0.645492i	$-0.223347\pi$
$929$	544.988	+	314.649i	0.586639	+	0.338696i	−0.177128	+	0.984188i	$0.556681\pi$
$930$		−	124.708i		−	0.134094i
$931$		0			0
$932$	725.470			0.778401
$933$	−77.2203	+	133.750i	−0.0827656	+	0.143354i
$934$	−75.6182	+	43.6582i	−0.0809617	+	0.0467432i
$935$	−158.007	−	273.676i	−0.168992	−	0.292702i
$936$	−65.8234	−	38.0031i	−0.0703241	−	0.0406016i
$937$		−	210.631i		−	0.224793i	−0.993663	−	0.112397i	$-0.964147\pi$
$937$		−	210.631i		−	0.224793i	0.993663	−	0.112397i	$-0.0358527\pi$
$938$		0			0
$939$	−900.146			−0.958622
$940$	−59.1472	+	102.446i	−0.0629225	+	0.108985i
$941$	−154.518	+	89.2112i	−0.164206	+	0.0948047i	−0.579851	−	0.814722i	$-0.696889\pi$
$941$	−154.518	+	89.2112i	−0.164206	+	0.0948047i	0.415645	+	0.909527i	$0.363556\pi$
$942$	−70.1909	−	121.574i	−0.0745126	−	0.129060i
$943$	−41.3818	−	23.8918i	−0.0438832	−	0.0253360i
$944$		−	1.96949i		−	0.00208632i
$945$		0			0
$946$	1078.09			1.13963
$947$	−211.731	+	366.730i	−0.223581	+	0.387254i	−0.955893	−	0.293716i	$-0.905108\pi$
$947$	−211.731	+	366.730i	−0.223581	+	0.387254i	0.732312	+	0.680970i	$0.238441\pi$
$948$	401.470	−	231.789i	0.423492	−	0.244503i
$949$	316.264	+	547.785i	0.333260	+	0.577224i
$950$	473.595	+	273.430i	0.498521	+	0.287821i
$951$			938.821i			0.987194i
$952$		0			0
$953$	−546.706			−0.573669			−0.286834	−	0.957980i	$-0.592603\pi$
$953$	−546.706			−0.573669			−0.286834	+	0.957980i	$0.592603\pi$
$954$	−150.551	+	260.762i	−0.157811	+	0.273336i
$955$	98.4701	−	56.8518i	0.103110	−	0.0595306i
$956$	−18.4781	−	32.0051i	−0.0193286	−	0.0334781i
$957$	460.919	+	266.112i	0.481629	+	0.278069i
$958$			787.030i			0.821534i
$959$		0			0
$960$	−14.0589			−0.0146447
$961$	778.440	−	1348.30i	0.810031	−	1.40302i
$962$	−339.119	+	195.790i	−0.352514	+	0.203524i
$963$	−56.6360	−	98.0965i	−0.0588121	−	0.101866i
$964$	308.485	+	178.104i	0.320005	+	0.184755i
$965$		−	23.2465i		−	0.0240896i
$966$		0			0
$967$	1262.32			1.30540			0.652701	−	0.757616i	$-0.273636\pi$
$967$	1262.32			1.30540			0.652701	+	0.757616i	$0.273636\pi$
$968$	22.7523	−	39.4082i	0.0235045	−	0.0407109i
$969$	735.816	−	424.824i	0.759356	−	0.438415i
$970$	−72.2498	−	125.140i	−0.0744843	−	0.129011i
$971$	936.116	+	540.467i	0.964074	+	0.556608i	0.897425	−	0.441168i	$-0.145436\pi$
$971$	936.116	+	540.467i	0.964074	+	0.556608i	0.0666496	+	0.997776i	$0.478769\pi$
$972$			31.1769i			0.0320750i
$973$		0			0
$974$	−459.931			−0.472208
$975$	−185.948	+	322.072i	−0.190716	+	0.330330i
$976$	9.94113	−	5.73951i	0.0101856	−	0.00588065i
$977$	−900.131	−	1559.07i	−0.921322	−	1.59578i	−0.797373	−	0.603487i	$-0.793777\pi$
$977$	−900.131	−	1559.07i	−0.921322	−	1.59578i	−0.123949	−	0.992289i	$-0.539556\pi$
$978$	371.044	+	214.222i	0.379390	+	0.219041i
$979$		−	1484.88i		−	1.51673i
$980$		0			0
$981$	−95.8234			−0.0976793
$982$	−455.007	+	788.095i	−0.463347	+	0.802541i
$983$	863.263	−	498.405i	0.878192	−	0.507025i	0.00813046	−	0.999967i	$-0.497412\pi$
$983$	863.263	−	498.405i	0.878192	−	0.507025i	0.870062	+	0.492942i	$0.164079\pi$
$984$	−17.3970	−	30.1324i	−0.0176798	−	0.0306224i
$985$	101.979	+	58.8774i	0.103532	+	0.0597740i
$986$			1290.12i			1.30844i
$987$		0			0
$988$	−288.999			−0.292509
$989$	−250.368	+	433.649i	−0.253152	+	0.438472i
$990$	38.1838	−	22.0454i	0.0385695	−	0.0222681i
$991$	−394.360	−	683.052i	−0.397942	−	0.689256i	0.595530	−	0.803333i	$-0.296942\pi$
$991$	−394.360	−	683.052i	−0.397942	−	0.689256i	−0.993472	+	0.114078i	$0.963609\pi$
$992$	−245.823	−	141.926i	−0.247806	−	0.143071i
$993$			311.133i			0.313326i
$994$		0			0
$995$	−165.484			−0.166316
$996$	−180.853	+	313.246i	−0.181579	+	0.314504i
$997$	1682.42	−	971.348i	1.68749	−	0.974271i	0.731054	−	0.682320i	$-0.239029\pi$
$997$	1682.42	−	971.348i	1.68749	−	0.974271i	0.956433	−	0.291952i	$-0.0943046\pi$
$998$	−534.167	−	925.204i	−0.535237	−	0.927058i
$999$	139.103	+	80.3109i	0.139242	+	0.0803913i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.3.g.c.19.1		4
3.2	odd	2		882.3.n.d.19.2		4
7.2	even	3		42.3.c.a.13.4	yes	4
7.3	odd	6	inner	294.3.g.c.31.1		4
7.4	even	3		294.3.g.b.31.1		4
7.5	odd	6		42.3.c.a.13.3	✓	4
7.6	odd	2		294.3.g.b.19.1		4
21.2	odd	6		126.3.c.b.55.1		4
21.5	even	6		126.3.c.b.55.2		4
21.11	odd	6		882.3.n.a.325.2		4
21.17	even	6		882.3.n.d.325.2		4
21.20	even	2		882.3.n.a.19.2		4
28.19	even	6		336.3.f.c.97.4		4
28.23	odd	6		336.3.f.c.97.1		4
35.2	odd	12		1050.3.h.a.349.8		8
35.9	even	6		1050.3.f.a.601.1		4
35.12	even	12		1050.3.h.a.349.5		8
35.19	odd	6		1050.3.f.a.601.2		4
35.23	odd	12		1050.3.h.a.349.1		8
35.33	even	12		1050.3.h.a.349.4		8
56.5	odd	6		1344.3.f.f.769.3		4
56.19	even	6		1344.3.f.e.769.1		4
56.37	even	6		1344.3.f.f.769.2		4
56.51	odd	6		1344.3.f.e.769.4		4
84.23	even	6		1008.3.f.g.433.2		4
84.47	odd	6		1008.3.f.g.433.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.c.a.13.3	✓	4	7.5	odd	6
42.3.c.a.13.4	yes	4	7.2	even	3
126.3.c.b.55.1		4	21.2	odd	6
126.3.c.b.55.2		4	21.5	even	6
294.3.g.b.19.1		4	7.6	odd	2
294.3.g.b.31.1		4	7.4	even	3
294.3.g.c.19.1		4	1.1	even	1	trivial
294.3.g.c.31.1		4	7.3	odd	6	inner
336.3.f.c.97.1		4	28.23	odd	6
336.3.f.c.97.4		4	28.19	even	6
882.3.n.a.19.2		4	21.20	even	2
882.3.n.a.325.2		4	21.11	odd	6
882.3.n.d.19.2		4	3.2	odd	2
882.3.n.d.325.2		4	21.17	even	6
1008.3.f.g.433.2		4	84.23	even	6
1008.3.f.g.433.3		4	84.47	odd	6
1050.3.f.a.601.1		4	35.9	even	6
1050.3.f.a.601.2		4	35.19	odd	6
1050.3.h.a.349.1		8	35.23	odd	12
1050.3.h.a.349.4		8	35.33	even	12
1050.3.h.a.349.5		8	35.12	even	12
1050.3.h.a.349.8		8	35.2	odd	12
1344.3.f.e.769.1		4	56.19	even	6
1344.3.f.e.769.4		4	56.51	odd	6
1344.3.f.f.769.2		4	56.37	even	6
1344.3.f.f.769.3		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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.878680 - 0.507306i) q^{5} +2.44949i q^{6} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.878680 - 0.507306i) q^{5} +2.44949i q^{6} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.24264 - 0.717439i) q^{10} +(5.12132 + 8.87039i) q^{11} +(-3.00000 - 1.73205i) q^{12} -8.95743i q^{13} -1.75736 q^{15} +(-2.00000 + 3.46410i) q^{16} +(26.3345 - 15.2042i) q^{17} +(2.12132 + 3.67423i) q^{18} +(13.9706 + 8.06591i) q^{19} +2.02922i q^{20} -14.4853 q^{22} +(3.36396 - 5.82655i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-11.9853 - 20.7591i) q^{25} +(10.9706 + 6.33386i) q^{26} -5.19615i q^{27} +30.0000 q^{29} +(1.24264 - 2.15232i) q^{30} +(43.4558 - 25.0892i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(15.3640 + 8.87039i) q^{33} +43.0041i q^{34} -6.00000 q^{36} +(-15.4558 + 26.7703i) q^{37} +(-19.7574 + 11.4069i) q^{38} +(-7.75736 - 13.4361i) q^{39} +(-2.48528 - 1.43488i) q^{40} -7.10228i q^{41} -74.4264 q^{43} +(10.2426 - 17.7408i) q^{44} +(-2.63604 + 1.52192i) q^{45} +(4.75736 + 8.23999i) q^{46} +(50.4853 + 29.1477i) q^{47} +6.92820i q^{48} +33.8995 q^{50} +(26.3345 - 45.6127i) q^{51} +(-15.5147 + 8.95743i) q^{52} +(35.4853 + 61.4623i) q^{53} +(6.36396 + 3.67423i) q^{54} -10.3923i q^{55} +27.9411 q^{57} +(-21.2132 + 36.7423i) q^{58} +(-0.426407 + 0.246186i) q^{59} +(1.75736 + 3.04384i) q^{60} +(-2.48528 - 1.43488i) q^{61} +70.9631i q^{62} +8.00000 q^{64} +(-4.54416 + 7.87071i) q^{65} +(-21.7279 + 12.5446i) q^{66} +(-13.5147 - 23.4082i) q^{67} +(-52.6690 - 30.4085i) q^{68} -11.6531i q^{69} +50.6102 q^{71} +(4.24264 - 7.34847i) q^{72} +(-61.1543 + 35.3075i) q^{73} +(-21.8579 - 37.8589i) q^{74} +(-35.9558 - 20.7591i) q^{75} -32.2636i q^{76} +21.9411 q^{78} +(-66.9117 + 115.894i) q^{79} +(3.51472 - 2.02922i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(8.69848 + 5.02207i) q^{82} -104.415i q^{83} -30.8528 q^{85} +(52.6274 - 91.1534i) q^{86} +(45.0000 - 25.9808i) q^{87} +(14.4853 + 25.0892i) q^{88} +(-125.548 - 72.4850i) q^{89} -4.30463i q^{90} -13.4558 q^{92} +(43.4558 - 75.2677i) q^{93} +(-71.3970 + 41.2211i) q^{94} +(-8.18377 - 14.1747i) q^{95} +(-8.48528 - 4.89898i) q^{96} -100.705i q^{97} +30.7279 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

L-functions

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