LMFDB - Embedded newform 294.4.e.a.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,4,Mod(67,294)]

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, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("294.67");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	294.e (of order $3$, 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:	$17.3465615417$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.79
Dual form			294.4.e.a.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.00000 + 1.73205i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.00000 + 1.73205i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-2.00000 - 3.46410i) q^{10} +(4.00000 + 6.92820i) q^{11} +(-6.00000 + 10.3923i) q^{12} -42.0000 q^{13} +6.00000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(62.0000 - 107.387i) q^{19} +8.00000 q^{20} -16.0000 q^{22} +(-38.0000 + 65.8179i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(60.5000 + 104.789i) q^{25} +(42.0000 - 72.7461i) q^{26} +27.0000 q^{27} +254.000 q^{29} +(-6.00000 + 10.3923i) q^{30} +(36.0000 + 62.3538i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(12.0000 - 20.7846i) q^{33} -4.00000 q^{34} +36.0000 q^{36} +(-199.000 + 344.678i) q^{37} +(124.000 + 214.774i) q^{38} +(63.0000 + 109.119i) q^{39} +(-8.00000 + 13.8564i) q^{40} +462.000 q^{41} +212.000 q^{43} +(16.0000 - 27.7128i) q^{44} +(-9.00000 - 15.5885i) q^{45} +(-76.0000 - 131.636i) q^{46} +(132.000 - 228.631i) q^{47} +48.0000 q^{48} -242.000 q^{50} +(3.00000 - 5.19615i) q^{51} +(84.0000 + 145.492i) q^{52} +(81.0000 + 140.296i) q^{53} +(-27.0000 + 46.7654i) q^{54} -16.0000 q^{55} -372.000 q^{57} +(-254.000 + 439.941i) q^{58} +(386.000 + 668.572i) q^{59} +(-12.0000 - 20.7846i) q^{60} +(-15.0000 + 25.9808i) q^{61} -144.000 q^{62} +64.0000 q^{64} +(42.0000 - 72.7461i) q^{65} +(24.0000 + 41.5692i) q^{66} +(382.000 + 661.643i) q^{67} +(4.00000 - 6.92820i) q^{68} +228.000 q^{69} -236.000 q^{71} +(-36.0000 + 62.3538i) q^{72} +(-209.000 - 361.999i) q^{73} +(-398.000 - 689.356i) q^{74} +(181.500 - 314.367i) q^{75} -496.000 q^{76} -252.000 q^{78} +(-276.000 + 478.046i) q^{79} +(-16.0000 - 27.7128i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-462.000 + 800.207i) q^{82} +1036.00 q^{83} -4.00000 q^{85} +(-212.000 + 367.195i) q^{86} +(-381.000 - 659.911i) q^{87} +(32.0000 + 55.4256i) q^{88} +(-15.0000 + 25.9808i) q^{89} +36.0000 q^{90} +304.000 q^{92} +(108.000 - 187.061i) q^{93} +(264.000 + 457.261i) q^{94} +(124.000 + 214.774i) q^{95} +(-48.0000 + 83.1384i) q^{96} -1190.00 q^{97} -72.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 3 q^{3} - 4 q^{4} - 2 q^{5} + 12 q^{6} + 16 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 - 2 * q^5 + 12 * q^6 + 16 * q^8 - 9 * q^9	\( 2 q - 2 q^{2} - 3 q^{3} - 4 q^{4} - 2 q^{5} + 12 q^{6} + 16 q^{8} - 9 q^{9} - 4 q^{10} + 8 q^{11} - 12 q^{12} - 84 q^{13} + 12 q^{15} - 16 q^{16} + 2 q^{17} - 18 q^{18} + 124 q^{19} + 16 q^{20} - 32 q^{22} - 76 q^{23} - 24 q^{24} + 121 q^{25} + 84 q^{26} + 54 q^{27} + 508 q^{29} - 12 q^{30} + 72 q^{31} - 32 q^{32} + 24 q^{33} - 8 q^{34} + 72 q^{36} - 398 q^{37} + 248 q^{38} + 126 q^{39} - 16 q^{40} + 924 q^{41} + 424 q^{43} + 32 q^{44} - 18 q^{45} - 152 q^{46} + 264 q^{47} + 96 q^{48} - 484 q^{50} + 6 q^{51} + 168 q^{52} + 162 q^{53} - 54 q^{54} - 32 q^{55} - 744 q^{57} - 508 q^{58} + 772 q^{59} - 24 q^{60} - 30 q^{61} - 288 q^{62} + 128 q^{64} + 84 q^{65} + 48 q^{66} + 764 q^{67} + 8 q^{68} + 456 q^{69} - 472 q^{71} - 72 q^{72} - 418 q^{73} - 796 q^{74} + 363 q^{75} - 992 q^{76} - 504 q^{78} - 552 q^{79} - 32 q^{80} - 81 q^{81} - 924 q^{82} + 2072 q^{83} - 8 q^{85} - 424 q^{86} - 762 q^{87} + 64 q^{88} - 30 q^{89} + 72 q^{90} + 608 q^{92} + 216 q^{93} + 528 q^{94} + 248 q^{95} - 96 q^{96} - 2380 q^{97} - 144 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 - 2 * q^5 + 12 * q^6 + 16 * q^8 - 9 * q^9 - 4 * q^10 + 8 * q^11 - 12 * q^12 - 84 * q^13 + 12 * q^15 - 16 * q^16 + 2 * q^17 - 18 * q^18 + 124 * q^19 + 16 * q^20 - 32 * q^22 - 76 * q^23 - 24 * q^24 + 121 * q^25 + 84 * q^26 + 54 * q^27 + 508 * q^29 - 12 * q^30 + 72 * q^31 - 32 * q^32 + 24 * q^33 - 8 * q^34 + 72 * q^36 - 398 * q^37 + 248 * q^38 + 126 * q^39 - 16 * q^40 + 924 * q^41 + 424 * q^43 + 32 * q^44 - 18 * q^45 - 152 * q^46 + 264 * q^47 + 96 * q^48 - 484 * q^50 + 6 * q^51 + 168 * q^52 + 162 * q^53 - 54 * q^54 - 32 * q^55 - 744 * q^57 - 508 * q^58 + 772 * q^59 - 24 * q^60 - 30 * q^61 - 288 * q^62 + 128 * q^64 + 84 * q^65 + 48 * q^66 + 764 * q^67 + 8 * q^68 + 456 * q^69 - 472 * q^71 - 72 * q^72 - 418 * q^73 - 796 * q^74 + 363 * q^75 - 992 * q^76 - 504 * q^78 - 552 * q^79 - 32 * q^80 - 81 * q^81 - 924 * q^82 + 2072 * q^83 - 8 * q^85 - 424 * q^86 - 762 * q^87 + 64 * q^88 - 30 * q^89 + 72 * q^90 + 608 * q^92 + 216 * q^93 + 528 * q^94 + 248 * q^95 - 96 * q^96 - 2380 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−1.00000	+	1.73205i	−0.0894427	+	0.154919i	−0.907276	−	0.420536i	$-0.861842\pi$
$5$	−1.00000	+	1.73205i	−0.0894427	+	0.154919i	0.817833	+	0.575456i	$0.195175\pi$
$6$	6.00000			0.408248
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−2.00000	−	3.46410i	−0.0632456	−	0.109545i
$11$	4.00000	+	6.92820i	0.109640	+	0.189903i	0.915625	−	0.402034i	$-0.131697\pi$
$11$	4.00000	+	6.92820i	0.109640	+	0.189903i	−0.805984	+	0.591937i	$0.798363\pi$
$12$	−6.00000	+	10.3923i	−0.144338	+	0.250000i
$13$	−42.0000			−0.896054			−0.448027	−	0.894020i	$-0.647873\pi$
$13$	−42.0000			−0.896054			−0.448027	+	0.894020i	$0.647873\pi$
$14$		0			0
$15$	6.00000			0.103280
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.0142668	+	0.0247108i	0.873071	−	0.487594i	$-0.162125\pi$
$17$	1.00000	+	1.73205i	0.0142668	+	0.0247108i	−0.858804	+	0.512305i	$0.828792\pi$
$18$	−9.00000	−	15.5885i	−0.117851	−	0.204124i
$19$	62.0000	−	107.387i	0.748620	−	1.29665i	−0.199865	−	0.979824i	$-0.564050\pi$
$19$	62.0000	−	107.387i	0.748620	−	1.29665i	0.948484	−	0.316824i	$-0.102616\pi$
$20$	8.00000			0.0894427
$21$		0			0
$22$	−16.0000			−0.155055
$23$	−38.0000	+	65.8179i	−0.344502	+	0.596695i	−0.985263	−	0.171045i	$-0.945286\pi$
$23$	−38.0000	+	65.8179i	−0.344502	+	0.596695i	0.640761	+	0.767740i	$0.278619\pi$
$24$	−12.0000	−	20.7846i	−0.102062	−	0.176777i
$25$	60.5000	+	104.789i	0.484000	+	0.838313i
$26$	42.0000	−	72.7461i	0.316803	−	0.548719i
$27$	27.0000			0.192450
$28$		0			0
$29$	254.000			1.62644			0.813218	−	0.581960i	$-0.197714\pi$
$29$	254.000			1.62644			0.813218	+	0.581960i	$0.197714\pi$
$30$	−6.00000	+	10.3923i	−0.0365148	+	0.0632456i
$31$	36.0000	+	62.3538i	0.208574	+	0.361261i	0.951266	−	0.308373i	$-0.0997845\pi$
$31$	36.0000	+	62.3538i	0.208574	+	0.361261i	−0.742692	+	0.669634i	$0.766451\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	12.0000	−	20.7846i	0.0633010	−	0.109640i
$34$	−4.00000			−0.0201763
$35$		0			0
$36$	36.0000			0.166667
$37$	−199.000	+	344.678i	−0.884200	+	1.53148i	−0.0375721	+	0.999294i	$0.511962\pi$
$37$	−199.000	+	344.678i	−0.884200	+	1.53148i	−0.846628	+	0.532185i	$0.821371\pi$
$38$	124.000	+	214.774i	0.529354	+	0.916868i
$39$	63.0000	+	109.119i	0.258669	+	0.448027i
$40$	−8.00000	+	13.8564i	−0.0316228	+	0.0547723i
$41$	462.000			1.75981			0.879906	−	0.475148i	$-0.157606\pi$
$41$	462.000			1.75981			0.879906	+	0.475148i	$0.157606\pi$
$42$		0			0
$43$	212.000			0.751853			0.375927	−	0.926649i	$-0.377324\pi$
$43$	212.000			0.751853			0.375927	+	0.926649i	$0.377324\pi$
$44$	16.0000	−	27.7128i	0.0548202	−	0.0949514i
$45$	−9.00000	−	15.5885i	−0.0298142	−	0.0516398i
$46$	−76.0000	−	131.636i	−0.243600	−	0.421927i
$47$	132.000	−	228.631i	0.409663	−	0.709558i	−0.585189	−	0.810897i	$-0.698979\pi$
$47$	132.000	−	228.631i	0.409663	−	0.709558i	0.994852	+	0.101339i	$0.0323128\pi$
$48$	48.0000			0.144338
$49$		0			0
$50$	−242.000			−0.684479
$51$	3.00000	−	5.19615i	0.00823694	−	0.0142668i
$52$	84.0000	+	145.492i	0.224014	+	0.388003i
$53$	81.0000	+	140.296i	0.209928	+	0.363607i	0.951692	−	0.307055i	$-0.0993436\pi$
$53$	81.0000	+	140.296i	0.209928	+	0.363607i	−0.741763	+	0.670662i	$0.766010\pi$
$54$	−27.0000	+	46.7654i	−0.0680414	+	0.117851i
$55$	−16.0000			−0.0392262
$56$		0			0
$57$	−372.000			−0.864432
$58$	−254.000	+	439.941i	−0.575032	+	0.995984i
$59$	386.000	+	668.572i	0.851744	+	1.47526i	0.879633	+	0.475654i	$0.157788\pi$
$59$	386.000	+	668.572i	0.851744	+	1.47526i	−0.0278883	+	0.999611i	$0.508878\pi$
$60$	−12.0000	−	20.7846i	−0.0258199	−	0.0447214i
$61$	−15.0000	+	25.9808i	−0.0314845	+	0.0545327i	−0.881338	−	0.472486i	$-0.843357\pi$
$61$	−15.0000	+	25.9808i	−0.0314845	+	0.0545327i	0.849854	+	0.527018i	$0.176690\pi$
$62$	−144.000			−0.294968
$63$		0			0
$64$	64.0000			0.125000
$65$	42.0000	−	72.7461i	0.0801455	−	0.138816i
$66$	24.0000	+	41.5692i	0.0447605	+	0.0775275i
$67$	382.000	+	661.643i	0.696548	+	1.20646i	0.969656	+	0.244473i	$0.0786151\pi$
$67$	382.000	+	661.643i	0.696548	+	1.20646i	−0.273108	+	0.961983i	$0.588052\pi$
$68$	4.00000	−	6.92820i	0.00713340	−	0.0123554i
$69$	228.000			0.397797
$70$		0			0
$71$	−236.000			−0.394480			−0.197240	−	0.980355i	$-0.563198\pi$
$71$	−236.000			−0.394480			−0.197240	+	0.980355i	$0.563198\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	−209.000	−	361.999i	−0.335090	−	0.580394i	0.648412	−	0.761290i	$-0.275434\pi$
$73$	−209.000	−	361.999i	−0.335090	−	0.580394i	−0.983502	+	0.180896i	$0.942100\pi$
$74$	−398.000	−	689.356i	−0.625224	−	1.08292i
$75$	181.500	−	314.367i	0.279438	−	0.484000i
$76$	−496.000			−0.748620
$77$		0			0
$78$	−252.000			−0.365813
$79$	−276.000	+	478.046i	−0.393069	+	0.680815i	−0.992853	−	0.119347i	$-0.961920\pi$
$79$	−276.000	+	478.046i	−0.393069	+	0.680815i	0.599784	+	0.800162i	$0.295253\pi$
$80$	−16.0000	−	27.7128i	−0.0223607	−	0.0387298i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	−462.000	+	800.207i	−0.622187	+	1.07766i
$83$	1036.00			1.37007			0.685035	−	0.728510i	$-0.259787\pi$
$83$	1036.00			1.37007			0.685035	+	0.728510i	$0.259787\pi$
$84$		0			0
$85$	−4.00000			−0.00510425
$86$	−212.000	+	367.195i	−0.265820	+	0.460414i
$87$	−381.000	−	659.911i	−0.469511	−	0.813218i
$88$	32.0000	+	55.4256i	0.0387638	+	0.0671408i
$89$	−15.0000	+	25.9808i	−0.0178651	+	0.0309433i	−0.874820	−	0.484449i	$-0.839020\pi$
$89$	−15.0000	+	25.9808i	−0.0178651	+	0.0309433i	0.856955	+	0.515392i	$0.172354\pi$
$90$	36.0000			0.0421637
$91$		0			0
$92$	304.000			0.344502
$93$	108.000	−	187.061i	0.120420	−	0.208574i
$94$	264.000	+	457.261i	0.289676	+	0.501733i
$95$	124.000	+	214.774i	0.133917	+	0.231951i
$96$	−48.0000	+	83.1384i	−0.0510310	+	0.0883883i
$97$	−1190.00			−1.24563			−0.622815	−	0.782369i	$-0.714011\pi$
$97$	−1190.00			−1.24563			−0.622815	+	0.782369i	$0.714011\pi$
$98$		0			0
$99$	−72.0000			−0.0730937
$100$	242.000	−	419.156i	0.242000	−	0.419156i
$101$	−685.000	−	1186.45i	−0.674852	−	1.16888i	−0.976512	−	0.215462i	$-0.930874\pi$
$101$	−685.000	−	1186.45i	−0.674852	−	1.16888i	0.301660	−	0.953416i	$-0.402459\pi$
$102$	6.00000	+	10.3923i	0.00582440	+	0.0100882i
$103$	−232.000	+	401.836i	−0.221938	+	0.384408i	−0.955396	−	0.295326i	$-0.904572\pi$
$103$	−232.000	+	401.836i	−0.221938	+	0.384408i	0.733458	+	0.679735i	$0.237905\pi$
$104$	−336.000			−0.316803
$105$		0			0
$106$	−324.000			−0.296884
$107$	1068.00	−	1849.83i	0.964930	−	1.67131i	0.255125	−	0.966908i	$-0.417883\pi$
$107$	1068.00	−	1849.83i	0.964930	−	1.67131i	0.709804	−	0.704399i	$-0.248783\pi$
$108$	−54.0000	−	93.5307i	−0.0481125	−	0.0833333i
$109$	613.000	+	1061.75i	0.538667	+	0.932999i	0.998976	+	0.0452405i	$0.0144054\pi$
$109$	613.000	+	1061.75i	0.538667	+	0.932999i	−0.460309	+	0.887759i	$0.652261\pi$
$110$	16.0000	−	27.7128i	0.0138685	−	0.0240210i
$111$	1194.00			1.02099
$112$		0			0
$113$	338.000			0.281384			0.140692	−	0.990053i	$-0.455067\pi$
$113$	338.000			0.281384			0.140692	+	0.990053i	$0.455067\pi$
$114$	372.000	−	644.323i	0.305623	−	0.529354i
$115$	−76.0000	−	131.636i	−0.0616264	−	0.106740i
$116$	−508.000	−	879.882i	−0.406609	−	0.704267i
$117$	189.000	−	327.358i	0.149342	−	0.258669i
$118$	−1544.00			−1.20455
$119$		0			0
$120$	48.0000			0.0365148
$121$	633.500	−	1097.25i	0.475958	−	0.824383i
$122$	−30.0000	−	51.9615i	−0.0222629	−	0.0385605i
$123$	−693.000	−	1200.31i	−0.508014	−	0.879906i
$124$	144.000	−	249.415i	0.104287	−	0.180630i
$125$	−492.000			−0.352047
$126$		0			0
$127$	2088.00			1.45890			0.729449	−	0.684035i	$-0.239777\pi$
$127$	2088.00			1.45890			0.729449	+	0.684035i	$0.239777\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	−318.000	−	550.792i	−0.217041	−	0.375927i
$130$	84.0000	+	145.492i	0.0566714	+	0.0981578i
$131$	146.000	−	252.879i	0.0973747	−	0.168658i	−0.813223	−	0.581953i	$-0.802289\pi$
$131$	146.000	−	252.879i	0.0973747	−	0.168658i	0.910597	+	0.413295i	$0.135622\pi$
$132$	−96.0000			−0.0633010
$133$		0			0
$134$	−1528.00			−0.985068
$135$	−27.0000	+	46.7654i	−0.0172133	+	0.0298142i
$136$	8.00000	+	13.8564i	0.00504408	+	0.00873660i
$137$	−409.000	−	708.409i	−0.255060	−	0.441777i	0.709852	−	0.704351i	$-0.248762\pi$
$137$	−409.000	−	708.409i	−0.255060	−	0.441777i	−0.964912	+	0.262574i	$0.915429\pi$
$138$	−228.000	+	394.908i	−0.140642	+	0.243600i
$139$	−2156.00			−1.31561			−0.657804	−	0.753189i	$-0.728515\pi$
$139$	−2156.00			−1.31561			−0.657804	+	0.753189i	$0.728515\pi$
$140$		0			0
$141$	−792.000			−0.473039
$142$	236.000	−	408.764i	0.139470	−	0.241568i
$143$	−168.000	−	290.985i	−0.0982438	−	0.170163i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	−254.000	+	439.941i	−0.145473	+	0.251966i
$146$	836.000			0.473889
$147$		0			0
$148$	1592.00			0.884200
$149$	1425.00	−	2468.17i	0.783494	−	1.35705i	−0.146401	−	0.989225i	$-0.546769\pi$
$149$	1425.00	−	2468.17i	0.783494	−	1.35705i	0.929895	−	0.367825i	$-0.119898\pi$
$150$	363.000	+	628.734i	0.197592	+	0.342240i
$151$	−836.000	−	1447.99i	−0.450548	−	0.780372i	0.547872	−	0.836562i	$-0.315438\pi$
$151$	−836.000	−	1447.99i	−0.450548	−	0.780372i	−0.998420	+	0.0561903i	$0.982105\pi$
$152$	496.000	−	859.097i	0.264677	−	0.458434i
$153$	−18.0000			−0.00951120
$154$		0			0
$155$	−144.000			−0.0746217
$156$	252.000	−	436.477i	0.129334	−	0.224014i
$157$	−223.000	−	386.247i	−0.113359	−	0.196343i	0.803764	−	0.594949i	$-0.202828\pi$
$157$	−223.000	−	386.247i	−0.113359	−	0.196343i	−0.917123	+	0.398605i	$0.869494\pi$
$158$	−552.000	−	956.092i	−0.277942	−	0.481409i
$159$	243.000	−	420.888i	0.121202	−	0.209928i
$160$	64.0000			0.0316228
$161$		0			0
$162$	162.000			0.0785674
$163$	−1354.00	+	2345.20i	−0.650635	+	1.12693i	0.332334	+	0.943162i	$0.392164\pi$
$163$	−1354.00	+	2345.20i	−0.650635	+	1.12693i	−0.982969	+	0.183771i	$0.941170\pi$
$164$	−924.000	−	1600.41i	−0.439953	−	0.762021i
$165$	24.0000	+	41.5692i	0.0113236	+	0.0196131i
$166$	−1036.00	+	1794.40i	−0.484393	+	0.838993i
$167$	896.000			0.415177			0.207589	−	0.978216i	$-0.433439\pi$
$167$	896.000			0.415177			0.207589	+	0.978216i	$0.433439\pi$
$168$		0			0
$169$	−433.000			−0.197087
$170$	4.00000	−	6.92820i	0.00180462	−	0.00312570i
$171$	558.000	+	966.484i	0.249540	+	0.432216i
$172$	−424.000	−	734.390i	−0.187963	−	0.325562i
$173$	−2017.00	+	3493.55i	−0.886414	+	1.53531i	−0.0423302	+	0.999104i	$0.513478\pi$
$173$	−2017.00	+	3493.55i	−0.886414	+	1.53531i	−0.844084	+	0.536211i	$0.819855\pi$
$174$	1524.00			0.663989
$175$		0			0
$176$	−128.000			−0.0548202
$177$	1158.00	−	2005.71i	0.491755	−	0.851744i
$178$	−30.0000	−	51.9615i	−0.0126326	−	0.0218802i
$179$	1740.00	+	3013.77i	0.726557	+	1.25843i	0.958330	+	0.285664i	$0.0922140\pi$
$179$	1740.00	+	3013.77i	0.726557	+	1.25843i	−0.231773	+	0.972770i	$0.574453\pi$
$180$	−36.0000	+	62.3538i	−0.0149071	+	0.0258199i
$181$	−2898.00			−1.19009			−0.595046	−	0.803692i	$-0.702866\pi$
$181$	−2898.00			−1.19009			−0.595046	+	0.803692i	$0.702866\pi$
$182$		0			0
$183$	90.0000			0.0363551
$184$	−304.000	+	526.543i	−0.121800	+	0.210964i
$185$	−398.000	−	689.356i	−0.158170	−	0.273959i
$186$	216.000	+	374.123i	0.0851499	+	0.147484i
$187$	−8.00000	+	13.8564i	−0.00312844	+	0.00541861i
$188$	−1056.00			−0.409663
$189$		0			0
$190$	−496.000			−0.189387
$191$	−1326.00	+	2296.70i	−0.502335	+	0.870070i	0.497661	+	0.867371i	$0.334192\pi$
$191$	−1326.00	+	2296.70i	−0.502335	+	0.870070i	−0.999996	+	0.00269837i	$0.999141\pi$
$192$	−96.0000	−	166.277i	−0.0360844	−	0.0625000i
$193$	−73.0000	−	126.440i	−0.0272262	−	0.0471571i	0.852091	−	0.523393i	$-0.175334\pi$
$193$	−73.0000	−	126.440i	−0.0272262	−	0.0471571i	−0.879317	+	0.476236i	$0.842001\pi$
$194$	1190.00	−	2061.14i	0.440397	−	0.762790i
$195$	−252.000			−0.0925441
$196$		0			0
$197$	−2546.00			−0.920787			−0.460393	−	0.887715i	$-0.652292\pi$
$197$	−2546.00			−0.920787			−0.460393	+	0.887715i	$0.652292\pi$
$198$	72.0000	−	124.708i	0.0258425	−	0.0447605i
$199$	1268.00	+	2196.24i	0.451689	+	0.782349i	0.998491	−	0.0549134i	$-0.0174883\pi$
$199$	1268.00	+	2196.24i	0.451689	+	0.782349i	−0.546802	+	0.837262i	$0.684155\pi$
$200$	484.000	+	838.313i	0.171120	+	0.296388i
$201$	1146.00	−	1984.93i	0.402152	−	0.696548i
$202$	2740.00			0.954385
$203$		0			0
$204$	−24.0000			−0.00823694
$205$	−462.000	+	800.207i	−0.157402	+	0.272629i
$206$	−464.000	−	803.672i	−0.156934	−	0.271818i
$207$	−342.000	−	592.361i	−0.114834	−	0.198898i
$208$	336.000	−	581.969i	0.112007	−	0.194001i
$209$	992.000			0.328316
$210$		0			0
$211$	−1300.00			−0.424150			−0.212075	−	0.977253i	$-0.568022\pi$
$211$	−1300.00			−0.424150			−0.212075	+	0.977253i	$0.568022\pi$
$212$	324.000	−	561.184i	0.104964	−	0.181803i
$213$	354.000	+	613.146i	0.113876	+	0.197240i
$214$	2136.00	+	3699.66i	0.682308	+	1.18179i
$215$	−212.000	+	367.195i	−0.0672478	+	0.116477i
$216$	216.000			0.0680414
$217$		0			0
$218$	−2452.00			−0.761791
$219$	−627.000	+	1086.00i	−0.193465	+	0.335090i
$220$	32.0000	+	55.4256i	0.00980654	+	0.0169854i
$221$	−42.0000	−	72.7461i	−0.0127838	−	0.0221422i
$222$	−1194.00	+	2068.07i	−0.360973	+	0.625224i
$223$	2576.00			0.773550			0.386775	−	0.922174i	$-0.373589\pi$
$223$	2576.00			0.773550			0.386775	+	0.922174i	$0.373589\pi$
$224$		0			0
$225$	−1089.00			−0.322667
$226$	−338.000	+	585.433i	−0.0994842	+	0.172312i
$227$	918.000	+	1590.02i	0.268413	+	0.464905i	0.968452	−	0.249199i	$-0.0801674\pi$
$227$	918.000	+	1590.02i	0.268413	+	0.464905i	−0.700039	+	0.714105i	$0.746834\pi$
$228$	744.000	+	1288.65i	0.216108	+	0.374310i
$229$	937.000	−	1622.93i	0.270387	−	0.468325i	−0.698574	−	0.715538i	$-0.746182\pi$
$229$	937.000	−	1622.93i	0.270387	−	0.468325i	0.968961	+	0.247213i	$0.0795149\pi$
$230$	304.000			0.0871529
$231$		0			0
$232$	2032.00			0.575032
$233$	−1865.00	+	3230.27i	−0.524379	+	0.908250i	0.475219	+	0.879868i	$0.342369\pi$
$233$	−1865.00	+	3230.27i	−0.524379	+	0.908250i	−0.999597	+	0.0283826i	$0.990964\pi$
$234$	378.000	+	654.715i	0.105601	+	0.182906i
$235$	264.000	+	457.261i	0.0732828	+	0.126930i
$236$	1544.00	−	2674.29i	0.425872	−	0.737632i
$237$	1656.00			0.453877
$238$		0			0
$239$	2004.00			0.542377			0.271188	−	0.962526i	$-0.412583\pi$
$239$	2004.00			0.542377			0.271188	+	0.962526i	$0.412583\pi$
$240$	−48.0000	+	83.1384i	−0.0129099	+	0.0223607i
$241$	323.000	+	559.452i	0.0863330	+	0.149533i	0.905958	−	0.423367i	$-0.139152\pi$
$241$	323.000	+	559.452i	0.0863330	+	0.149533i	−0.819625	+	0.572900i	$0.805818\pi$
$242$	1267.00	+	2194.51i	0.336553	+	0.582927i
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$	120.000			0.0314845
$245$		0			0
$246$	2772.00			0.718440
$247$	−2604.00	+	4510.26i	−0.670804	+	1.16187i
$248$	288.000	+	498.831i	0.0737420	+	0.127725i
$249$	−1554.00	−	2691.61i	−0.395505	−	0.685035i
$250$	492.000	−	852.169i	0.124467	−	0.215584i
$251$	1260.00			0.316855			0.158427	−	0.987371i	$-0.449358\pi$
$251$	1260.00			0.316855			0.158427	+	0.987371i	$0.449358\pi$
$252$		0			0
$253$	−608.000			−0.151086
$254$	−2088.00	+	3616.52i	−0.515798	+	0.893389i
$255$	6.00000	+	10.3923i	0.00147347	+	0.00255212i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2955.00	+	5118.21i	−0.717229	+	1.24228i	0.244865	+	0.969557i	$0.421256\pi$
$257$	−2955.00	+	5118.21i	−0.717229	+	1.24228i	−0.962094	+	0.272720i	$0.912077\pi$
$258$	1272.00			0.306943
$259$		0			0
$260$	−336.000			−0.0801455
$261$	−1143.00	+	1979.73i	−0.271073	+	0.469511i
$262$	292.000	+	505.759i	0.0688543	+	0.119259i
$263$	−1494.00	−	2587.68i	−0.350281	−	0.606705i	0.636017	−	0.771675i	$-0.280581\pi$
$263$	−1494.00	−	2587.68i	−0.350281	−	0.606705i	−0.986299	+	0.164970i	$0.947247\pi$
$264$	96.0000	−	166.277i	0.0223803	−	0.0387638i
$265$	−324.000			−0.0751063
$266$		0			0
$267$	90.0000			0.0206289
$268$	1528.00	−	2646.57i	0.348274	−	0.603228i
$269$	659.000	+	1141.42i	0.149368	+	0.258713i	0.930994	−	0.365035i	$-0.118943\pi$
$269$	659.000	+	1141.42i	0.149368	+	0.258713i	−0.781626	+	0.623747i	$0.785609\pi$
$270$	−54.0000	−	93.5307i	−0.0121716	−	0.0210819i
$271$	2820.00	−	4884.38i	0.632114	−	1.09485i	−0.355005	−	0.934864i	$-0.615521\pi$
$271$	2820.00	−	4884.38i	0.632114	−	1.09485i	0.987119	−	0.159989i	$-0.0511458\pi$
$272$	−32.0000			−0.00713340
$273$		0			0
$274$	1636.00			0.360709
$275$	−484.000	+	838.313i	−0.106132	+	0.183826i
$276$	−456.000	−	789.815i	−0.0994492	−	0.172251i
$277$	−3223.00	−	5582.40i	−0.699102	−	1.21088i	−0.968778	−	0.247929i	$-0.920250\pi$
$277$	−3223.00	−	5582.40i	−0.699102	−	1.21088i	0.269676	−	0.962951i	$-0.413083\pi$
$278$	2156.00	−	3734.30i	0.465138	−	0.805642i
$279$	−648.000			−0.139049
$280$		0			0
$281$	4930.00			1.04662			0.523308	−	0.852144i	$-0.324698\pi$
$281$	4930.00			1.04662			0.523308	+	0.852144i	$0.324698\pi$
$282$	792.000	−	1371.78i	0.167244	−	0.289676i
$283$	3130.00	+	5421.32i	0.657453	+	1.13874i	0.981273	+	0.192623i	$0.0616995\pi$
$283$	3130.00	+	5421.32i	0.657453	+	1.13874i	−0.323820	+	0.946119i	$0.604967\pi$
$284$	472.000	+	817.528i	0.0986199	+	0.170815i
$285$	372.000	−	644.323i	0.0773171	−	0.133917i
$286$	672.000			0.138938
$287$		0			0
$288$	288.000			0.0589256
$289$	2454.50	−	4251.32i	0.499593	−	0.865320i
$290$	−508.000	−	879.882i	−0.102865	−	0.178167i
$291$	1785.00	+	3091.71i	0.359583	+	0.622815i
$292$	−836.000	+	1447.99i	−0.167545	+	0.290197i
$293$	−2310.00			−0.460586			−0.230293	−	0.973121i	$-0.573968\pi$
$293$	−2310.00			−0.460586			−0.230293	+	0.973121i	$0.573968\pi$
$294$		0			0
$295$	−1544.00			−0.304729
$296$	−1592.00	+	2757.42i	−0.312612	+	0.541460i
$297$	108.000	+	187.061i	0.0211003	+	0.0365468i
$298$	2850.00	+	4936.34i	0.554014	+	0.959580i
$299$	1596.00	−	2764.35i	0.308693	−	0.534671i
$300$	−1452.00			−0.279438
$301$		0			0
$302$	3344.00			0.637171
$303$	−2055.00	+	3559.36i	−0.389626	+	0.674852i
$304$	992.000	+	1718.19i	0.187155	+	0.324162i
$305$	−30.0000	−	51.9615i	−0.00563211	−	0.00975511i
$306$	18.0000	−	31.1769i	0.00336272	−	0.00582440i
$307$	196.000			0.0364375			0.0182187	−	0.999834i	$-0.494200\pi$
$307$	196.000			0.0364375			0.0182187	+	0.999834i	$0.494200\pi$
$308$		0			0
$309$	1392.00			0.256272
$310$	144.000	−	249.415i	0.0263827	−	0.0456963i
$311$	3368.00	+	5833.55i	0.614089	+	1.06363i	0.990544	+	0.137199i	$0.0438099\pi$
$311$	3368.00	+	5833.55i	0.614089	+	1.06363i	−0.376454	+	0.926435i	$0.622857\pi$
$312$	504.000	+	872.954i	0.0914531	+	0.158401i
$313$	−197.000	+	341.214i	−0.0355754	+	0.0616184i	−0.883265	−	0.468874i	$-0.844660\pi$
$313$	−197.000	+	341.214i	−0.0355754	+	0.0616184i	0.847690	+	0.530493i	$0.177993\pi$
$314$	892.000			0.160314
$315$		0			0
$316$	2208.00			0.393069
$317$	3357.00	−	5814.49i	0.594788	−	1.03020i	−0.398788	−	0.917043i	$-0.630569\pi$
$317$	3357.00	−	5814.49i	0.594788	−	1.03020i	0.993577	−	0.113161i	$-0.0360975\pi$
$318$	486.000	+	841.777i	0.0857029	+	0.148442i
$319$	1016.00	+	1759.76i	0.178323	+	0.308865i
$320$	−64.0000	+	110.851i	−0.0111803	+	0.0193649i
$321$	−6408.00			−1.11420
$322$		0			0
$323$	248.000			0.0427216
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	−2541.00	−	4401.14i	−0.433690	−	0.751173i
$326$	−2708.00	−	4690.39i	−0.460068	−	0.796862i
$327$	1839.00	−	3185.24i	0.311000	−	0.538667i
$328$	3696.00			0.622187
$329$		0			0
$330$	−96.0000			−0.0160140
$331$	−346.000	+	599.290i	−0.0574558	+	0.0995164i	−0.893323	−	0.449416i	$-0.851632\pi$
$331$	−346.000	+	599.290i	−0.0574558	+	0.0995164i	0.835867	+	0.548932i	$0.184966\pi$
$332$	−2072.00	−	3588.81i	−0.342517	−	0.593258i
$333$	−1791.00	−	3102.10i	−0.294733	−	0.510493i
$334$	−896.000	+	1551.92i	−0.146787	+	0.254243i
$335$	−1528.00			−0.249205
$336$		0			0
$337$	−1566.00			−0.253132			−0.126566	−	0.991958i	$-0.540396\pi$
$337$	−1566.00			−0.253132			−0.126566	+	0.991958i	$0.540396\pi$
$338$	433.000	−	749.978i	0.0696808	−	0.120691i
$339$	−507.000	−	878.150i	−0.0812285	−	0.140692i
$340$	8.00000	+	13.8564i	0.00127606	+	0.00221020i
$341$	−288.000	+	498.831i	−0.0457363	+	0.0792176i
$342$	−2232.00			−0.352903
$343$		0			0
$344$	1696.00			0.265820
$345$	−228.000	+	394.908i	−0.0355800	+	0.0616264i
$346$	−4034.00	−	6987.09i	−0.626790	−	1.08563i
$347$	2664.00	+	4614.18i	0.412135	+	0.713840i	0.995123	−	0.0986415i	$-0.0314497\pi$
$347$	2664.00	+	4614.18i	0.412135	+	0.713840i	−0.582988	+	0.812481i	$0.698116\pi$
$348$	−1524.00	+	2639.65i	−0.234756	+	0.406609i
$349$	11326.0			1.73715			0.868577	−	0.495554i	$-0.165035\pi$
$349$	11326.0			1.73715			0.868577	+	0.495554i	$0.165035\pi$
$350$		0			0
$351$	−1134.00			−0.172446
$352$	128.000	−	221.703i	0.0193819	−	0.0335704i
$353$	1065.00	+	1844.63i	0.160579	+	0.278130i	0.935076	−	0.354446i	$-0.115331\pi$
$353$	1065.00	+	1844.63i	0.160579	+	0.278130i	−0.774498	+	0.632577i	$0.781997\pi$
$354$	2316.00	+	4011.43i	0.347723	+	0.602274i
$355$	236.000	−	408.764i	0.0352833	−	0.0611125i
$356$	120.000			0.0178651
$357$		0			0
$358$	−6960.00			−1.02751
$359$	−1522.00	+	2636.18i	−0.223755	+	0.387555i	−0.955945	−	0.293545i	$-0.905165\pi$
$359$	−1522.00	+	2636.18i	−0.223755	+	0.387555i	0.732190	+	0.681100i	$0.238498\pi$
$360$	−72.0000	−	124.708i	−0.0105409	−	0.0182574i
$361$	−4258.50	−	7375.94i	−0.620863	−	1.07537i
$362$	2898.00	−	5019.48i	0.420761	−	0.728780i
$363$	−3801.00			−0.549589
$364$		0			0
$365$	836.000			0.119886
$366$	−90.0000	+	155.885i	−0.0128535	+	0.0222629i
$367$	−6208.00	−	10752.6i	−0.882984	−	1.52937i	−0.848008	−	0.529984i	$-0.822198\pi$
$367$	−6208.00	−	10752.6i	−0.882984	−	1.52937i	−0.0349760	−	0.999388i	$-0.511135\pi$
$368$	−608.000	−	1053.09i	−0.0861255	−	0.149174i
$369$	−2079.00	+	3600.93i	−0.293302	+	0.508014i
$370$	1592.00			0.223687
$371$		0			0
$372$	−864.000			−0.120420
$373$	3721.00	−	6444.96i	0.516531	−	0.894658i	−0.483285	−	0.875463i	$-0.660556\pi$
$373$	3721.00	−	6444.96i	0.516531	−	0.894658i	0.999816	−	0.0191948i	$-0.00611026\pi$
$374$	−16.0000	−	27.7128i	−0.00221214	−	0.00383154i
$375$	738.000	+	1278.25i	0.101627	+	0.176023i
$376$	1056.00	−	1829.05i	0.144838	−	0.250867i
$377$	−10668.0			−1.45737
$378$		0			0
$379$	100.000			0.0135532			0.00677659	−	0.999977i	$-0.497843\pi$
$379$	100.000			0.0135532			0.00677659	+	0.999977i	$0.497843\pi$
$380$	496.000	−	859.097i	0.0669586	−	0.115976i
$381$	−3132.00	−	5424.78i	−0.421148	−	0.729449i
$382$	−2652.00	−	4593.40i	−0.355205	−	0.615232i
$383$	−4040.00	+	6997.49i	−0.538993	+	0.933563i	0.459965	+	0.887937i	$0.347862\pi$
$383$	−4040.00	+	6997.49i	−0.538993	+	0.933563i	−0.998959	+	0.0456266i	$0.985472\pi$
$384$	384.000			0.0510310
$385$		0			0
$386$	292.000			0.0385036
$387$	−954.000	+	1652.38i	−0.125309	+	0.217041i
$388$	2380.00	+	4122.28i	0.311408	+	0.539374i
$389$	2741.00	+	4747.55i	0.357260	+	0.618793i	0.987502	−	0.157606i	$-0.0503776\pi$
$389$	2741.00	+	4747.55i	0.357260	+	0.618793i	−0.630242	+	0.776399i	$0.717044\pi$
$390$	252.000	−	436.477i	0.0327193	−	0.0566714i
$391$	−152.000			−0.0196598
$392$		0			0
$393$	−876.000			−0.112439
$394$	2546.00	−	4409.80i	0.325547	−	0.563864i
$395$	−552.000	−	956.092i	−0.0703143	−	0.121788i
$396$	144.000	+	249.415i	0.0182734	+	0.0316505i
$397$	−5223.00	+	9046.50i	−0.660289	+	1.14365i	0.320250	+	0.947333i	$0.396233\pi$
$397$	−5223.00	+	9046.50i	−0.660289	+	1.14365i	−0.980540	+	0.196322i	$0.937100\pi$
$398$	−5072.00			−0.638785
$399$		0			0
$400$	−1936.00			−0.242000
$401$	5667.00	−	9815.53i	0.705727	−	1.22235i	−0.260702	−	0.965419i	$-0.583954\pi$
$401$	5667.00	−	9815.53i	0.705727	−	1.22235i	0.966429	−	0.256935i	$-0.0827128\pi$
$402$	2292.00	+	3969.86i	0.284365	+	0.492534i
$403$	−1512.00	−	2618.86i	−0.186894	−	0.323709i
$404$	−2740.00	+	4745.82i	−0.337426	+	0.584439i
$405$	162.000			0.0198762
$406$		0			0
$407$	−3184.00			−0.387776
$408$	24.0000	−	41.5692i	0.00291220	−	0.00504408i
$409$	−4297.00	−	7442.62i	−0.519494	−	0.899790i	−0.999743	−	0.0226578i	$-0.992787\pi$
$409$	−4297.00	−	7442.62i	−0.519494	−	0.899790i	0.480249	−	0.877132i	$-0.340546\pi$
$410$	−924.000	−	1600.41i	−0.111300	−	0.192778i
$411$	−1227.00	+	2125.23i	−0.147259	+	0.255060i
$412$	1856.00			0.221938
$413$		0			0
$414$	1368.00			0.162400
$415$	−1036.00	+	1794.40i	−0.122543	+	0.212250i
$416$	672.000	+	1163.94i	0.0792007	+	0.137180i
$417$	3234.00	+	5601.45i	0.379783	+	0.657804i
$418$	−992.000	+	1718.19i	−0.116077	+	0.201052i
$419$	10500.0			1.22424			0.612122	−	0.790763i	$-0.290316\pi$
$419$	10500.0			1.22424			0.612122	+	0.790763i	$0.290316\pi$
$420$		0			0
$421$	−12066.0			−1.39682			−0.698410	−	0.715698i	$-0.746109\pi$
$421$	−12066.0			−1.39682			−0.698410	+	0.715698i	$0.746109\pi$
$422$	1300.00	−	2251.67i	0.149960	−	0.259738i
$423$	1188.00	+	2057.68i	0.136554	+	0.236519i
$424$	648.000	+	1122.37i	0.0742209	+	0.128554i
$425$	−121.000	+	209.578i	−0.0138103	+	0.0239201i
$426$	−1416.00			−0.161046
$427$		0			0
$428$	−8544.00			−0.964930
$429$	−504.000	+	872.954i	−0.0567211	+	0.0982438i
$430$	−424.000	−	734.390i	−0.0475514	−	0.0823614i
$431$	−2166.00	−	3751.62i	−0.242071	−	0.419279i	0.719233	−	0.694769i	$-0.244493\pi$
$431$	−2166.00	−	3751.62i	−0.242071	−	0.419279i	−0.961304	+	0.275490i	$0.911160\pi$
$432$	−216.000	+	374.123i	−0.0240563	+	0.0416667i
$433$	−1918.00			−0.212871			−0.106436	−	0.994320i	$-0.533944\pi$
$433$	−1918.00			−0.212871			−0.106436	+	0.994320i	$0.533944\pi$
$434$		0			0
$435$	1524.00			0.167977
$436$	2452.00	−	4246.99i	0.269334	−	0.466500i
$437$	4712.00	+	8161.42i	0.515802	+	0.893395i
$438$	−1254.00	−	2171.99i	−0.136800	−	0.236945i
$439$	3996.00	−	6921.28i	0.434439	−	0.752470i	−0.562811	−	0.826586i	$-0.690280\pi$
$439$	3996.00	−	6921.28i	0.434439	−	0.752470i	0.997250	+	0.0741155i	$0.0236134\pi$
$440$	−128.000			−0.0138685
$441$		0			0
$442$	168.000			0.0180791
$443$	−1592.00	+	2757.42i	−0.170741	+	0.295732i	−0.938679	−	0.344792i	$-0.887949\pi$
$443$	−1592.00	+	2757.42i	−0.170741	+	0.295732i	0.767938	+	0.640524i	$0.221283\pi$
$444$	−2388.00	−	4136.14i	−0.255247	−	0.442100i
$445$	−30.0000	−	51.9615i	−0.00319581	−	0.00553531i
$446$	−2576.00	+	4461.76i	−0.273491	+	0.473701i
$447$	−8550.00			−0.904700
$448$		0			0
$449$	11426.0			1.20095			0.600475	−	0.799644i	$-0.294978\pi$
$449$	11426.0			1.20095			0.600475	+	0.799644i	$0.294978\pi$
$450$	1089.00	−	1886.20i	0.114080	−	0.197592i
$451$	1848.00	+	3200.83i	0.192947	+	0.334193i
$452$	−676.000	−	1170.87i	−0.0703459	−	0.121843i
$453$	−2508.00	+	4343.98i	−0.260124	+	0.450548i
$454$	−3672.00			−0.379594
$455$		0			0
$456$	−2976.00			−0.305623
$457$	8467.00	−	14665.3i	0.866673	−	1.50112i	0.00129662	−	0.999999i	$-0.499587\pi$
$457$	8467.00	−	14665.3i	0.866673	−	1.50112i	0.865376	−	0.501122i	$-0.167079\pi$
$458$	1874.00	+	3245.86i	0.191193	+	0.331156i
$459$	27.0000	+	46.7654i	0.00274565	+	0.00475560i
$460$	−304.000	+	526.543i	−0.0308132	+	0.0533700i
$461$	−17038.0			−1.72134			−0.860671	−	0.509161i	$-0.829956\pi$
$461$	−17038.0			−1.72134			−0.860671	+	0.509161i	$0.829956\pi$
$462$		0			0
$463$	−13592.0			−1.36431			−0.682153	−	0.731209i	$-0.738956\pi$
$463$	−13592.0			−1.36431			−0.682153	+	0.731209i	$0.738956\pi$
$464$	−2032.00	+	3519.53i	−0.203304	+	0.352134i
$465$	216.000	+	374.123i	0.0215414	+	0.0373108i
$466$	−3730.00	−	6460.55i	−0.370792	−	0.642230i
$467$	−4306.00	+	7458.21i	−0.426676	+	0.739025i	−0.996575	−	0.0826895i	$-0.973649\pi$
$467$	−4306.00	+	7458.21i	−0.426676	+	0.739025i	0.569899	+	0.821715i	$0.306982\pi$
$468$	−1512.00			−0.149342
$469$		0			0
$470$	−1056.00			−0.103638
$471$	−669.000	+	1158.74i	−0.0654478	+	0.113359i
$472$	3088.00	+	5348.57i	0.301137	+	0.521585i
$473$	848.000	+	1468.78i	0.0824336	+	0.142779i
$474$	−1656.00	+	2868.28i	−0.160470	+	0.277942i
$475$	15004.0			1.44933
$476$		0			0
$477$	−1458.00			−0.139952
$478$	−2004.00	+	3471.03i	−0.191759	+	0.332136i
$479$	−3716.00	−	6436.30i	−0.354464	−	0.613950i	0.632562	−	0.774510i	$-0.282003\pi$
$479$	−3716.00	−	6436.30i	−0.354464	−	0.613950i	−0.987026	+	0.160560i	$0.948670\pi$
$480$	−96.0000	−	166.277i	−0.00912871	−	0.0158114i
$481$	8358.00	−	14476.5i	0.792291	−	1.37229i
$482$	−1292.00			−0.122093
$483$		0			0
$484$	−5068.00			−0.475958
$485$	1190.00	−	2061.14i	0.111413	−	0.192972i
$486$	−243.000	−	420.888i	−0.0226805	−	0.0392837i
$487$	3308.00	+	5729.62i	0.307802	+	0.533129i	0.977881	−	0.209160i	$-0.0670731\pi$
$487$	3308.00	+	5729.62i	0.307802	+	0.533129i	−0.670079	+	0.742290i	$0.733740\pi$
$488$	−120.000	+	207.846i	−0.0111314	+	0.0192802i
$489$	8124.00			0.751288
$490$		0			0
$491$	17040.0			1.56620			0.783100	−	0.621896i	$-0.213637\pi$
$491$	17040.0			1.56620			0.783100	+	0.621896i	$0.213637\pi$
$492$	−2772.00	+	4801.24i	−0.254007	+	0.439953i
$493$	254.000	+	439.941i	0.0232040	+	0.0401906i
$494$	−5208.00	−	9020.52i	−0.474330	−	0.821564i
$495$	72.0000	−	124.708i	0.00653770	−	0.0113236i
$496$	−1152.00			−0.104287
$497$		0			0
$498$	6216.00			0.559329
$499$	1474.00	−	2553.04i	0.132235	−	0.229038i	−0.792303	−	0.610128i	$-0.791118\pi$
$499$	1474.00	−	2553.04i	0.132235	−	0.229038i	0.924538	+	0.381090i	$0.124451\pi$
$500$	984.000	+	1704.34i	0.0880116	+	0.152441i
$501$	−1344.00	−	2327.88i	−0.119851	−	0.207589i
$502$	−1260.00	+	2182.38i	−0.112025	+	0.194033i
$503$	17304.0			1.53389			0.766946	−	0.641712i	$-0.221776\pi$
$503$	17304.0			1.53389			0.766946	+	0.641712i	$0.221776\pi$
$504$		0			0
$505$	2740.00			0.241442
$506$	608.000	−	1053.09i	0.0534168	−	0.0925206i
$507$	649.500	+	1124.97i	0.0568941	+	0.0985435i
$508$	−4176.00	−	7233.04i	−0.364724	−	0.631721i
$509$	−2325.00	+	4027.02i	−0.202463	+	0.350677i	−0.949322	−	0.314307i	$-0.898228\pi$
$509$	−2325.00	+	4027.02i	−0.202463	+	0.350677i	0.746858	+	0.664983i	$0.231561\pi$
$510$	−24.0000			−0.00208380
$511$		0			0
$512$	512.000			0.0441942
$513$	1674.00	−	2899.45i	0.144072	−	0.249540i
$514$	−5910.00	−	10236.4i	−0.507157	−	0.878422i
$515$	−464.000	−	803.672i	−0.0397015	−	0.0687651i
$516$	−1272.00	+	2203.17i	−0.108521	+	0.187963i
$517$	2112.00			0.179663
$518$		0			0
$519$	12102.0			1.02354
$520$	336.000	−	581.969i	0.0283357	−	0.0490789i
$521$	−8427.00	−	14596.0i	−0.708625	−	1.22737i	−0.965367	−	0.260894i	$-0.915983\pi$
$521$	−8427.00	−	14596.0i	−0.708625	−	1.22737i	0.256742	−	0.966480i	$-0.417351\pi$
$522$	−2286.00	−	3959.47i	−0.191677	−	0.331995i
$523$	62.0000	−	107.387i	0.00518369	−	0.00897842i	−0.863422	−	0.504482i	$-0.831683\pi$
$523$	62.0000	−	107.387i	0.00518369	−	0.00897842i	0.868606	+	0.495504i	$0.165017\pi$
$524$	−1168.00			−0.0973747
$525$		0			0
$526$	5976.00			0.495373
$527$	−72.0000	+	124.708i	−0.00595136	+	0.0103081i
$528$	192.000	+	332.554i	0.0158252	+	0.0274101i
$529$	3195.50	+	5534.77i	0.262637	+	0.454900i
$530$	324.000	−	561.184i	0.0265541	−	0.0459930i
$531$	−6948.00			−0.567830
$532$		0			0
$533$	−19404.0			−1.57689
$534$	−90.0000	+	155.885i	−0.00729341	+	0.0126326i
$535$	2136.00	+	3699.66i	0.172612	+	0.298972i
$536$	3056.00	+	5293.15i	0.246267	+	0.426547i
$537$	5220.00	−	9041.31i	0.419478	−	0.726557i
$538$	−2636.00			−0.211238
$539$		0			0
$540$	216.000			0.0172133
$541$	−2691.00	+	4660.95i	−0.213854	+	0.370406i	−0.952918	−	0.303230i	$-0.901935\pi$
$541$	−2691.00	+	4660.95i	−0.213854	+	0.370406i	0.739063	+	0.673636i	$0.235268\pi$
$542$	5640.00	+	9768.77i	0.446972	+	0.774178i
$543$	4347.00	+	7529.22i	0.343550	+	0.595046i
$544$	32.0000	−	55.4256i	0.00252204	−	0.00436830i
$545$	−2452.00			−0.192720
$546$		0			0
$547$	17460.0			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$547$	17460.0			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$548$	−1636.00	+	2833.64i	−0.127530	+	0.220888i
$549$	−135.000	−	233.827i	−0.0104948	−	0.0181776i
$550$	−968.000	−	1676.63i	−0.0750467	−	0.129985i
$551$	15748.0	−	27276.3i	1.21758	−	2.10891i
$552$	1824.00			0.140642
$553$		0			0
$554$	12892.0			0.988680
$555$	−1194.00	+	2068.07i	−0.0913198	+	0.158170i
$556$	4312.00	+	7468.60i	0.328902	+	0.569675i
$557$	4757.00	+	8239.37i	0.361868	+	0.626774i	0.988268	−	0.152728i	$-0.0488057\pi$
$557$	4757.00	+	8239.37i	0.361868	+	0.626774i	−0.626400	+	0.779502i	$0.715472\pi$
$558$	648.000	−	1122.37i	0.0491613	−	0.0851499i
$559$	−8904.00			−0.673701
$560$		0			0
$561$	48.0000			0.00361241
$562$	−4930.00	+	8539.01i	−0.370035	+	0.640919i
$563$	−1994.00	−	3453.71i	−0.149267	−	0.258537i	0.781690	−	0.623667i	$-0.214358\pi$
$563$	−1994.00	−	3453.71i	−0.149267	−	0.258537i	−0.930957	+	0.365130i	$0.881025\pi$
$564$	1584.00	+	2743.57i	0.118260	+	0.204832i
$565$	−338.000	+	585.433i	−0.0251677	+	0.0435918i
$566$	−12520.0			−0.929779
$567$		0			0
$568$	−1888.00			−0.139470
$569$	−5673.00	+	9825.92i	−0.417969	+	0.723944i	−0.995735	−	0.0922585i	$-0.970591\pi$
$569$	−5673.00	+	9825.92i	−0.417969	+	0.723944i	0.577766	+	0.816203i	$0.303925\pi$
$570$	744.000	+	1288.65i	0.0546715	+	0.0946937i
$571$	4218.00	+	7305.79i	0.309138	+	0.535443i	0.978174	−	0.207787i	$-0.0666262\pi$
$571$	4218.00	+	7305.79i	0.309138	+	0.535443i	−0.669036	+	0.743230i	$0.733293\pi$
$572$	−672.000	+	1163.94i	−0.0491219	+	0.0850816i
$573$	7956.00			0.580047
$574$		0			0
$575$	−9196.00			−0.666956
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	−1049.00	−	1816.92i	−0.0756853	−	0.131091i	0.825699	−	0.564111i	$-0.190781\pi$
$577$	−1049.00	−	1816.92i	−0.0756853	−	0.131091i	−0.901384	+	0.433020i	$0.857448\pi$
$578$	4909.00	+	8502.64i	0.353266	+	0.611874i
$579$	−219.000	+	379.319i	−0.0157190	+	0.0272262i
$580$	2032.00			0.145473
$581$		0			0
$582$	−7140.00			−0.508527
$583$	−648.000	+	1122.37i	−0.0460333	+	0.0797320i
$584$	−1672.00	−	2895.99i	−0.118472	−	0.205200i
$585$	378.000	+	654.715i	0.0267152	+	0.0462720i
$586$	2310.00	−	4001.04i	0.162842	−	0.282050i
$587$	9436.00			0.663484			0.331742	−	0.943370i	$-0.392364\pi$
$587$	9436.00			0.663484			0.331742	+	0.943370i	$0.392364\pi$
$588$		0			0
$589$	8928.00			0.624570
$590$	1544.00	−	2674.29i	0.107738	−	0.186608i
$591$	3819.00	+	6614.70i	0.265808	+	0.460393i
$592$	−3184.00	−	5514.85i	−0.221050	−	0.382870i
$593$	657.000	−	1137.96i	0.0454971	−	0.0788032i	−0.842380	−	0.538884i	$-0.818846\pi$
$593$	657.000	−	1137.96i	0.0454971	−	0.0788032i	0.887877	+	0.460081i	$0.152180\pi$
$594$	−432.000			−0.0298404
$595$		0			0
$596$	−11400.0			−0.783494
$597$	3804.00	−	6588.72i	0.260783	−	0.451689i
$598$	3192.00	+	5528.71i	0.218279	+	0.378070i
$599$	4470.00	+	7742.27i	0.304907	+	0.528114i	0.977241	−	0.212134i	$-0.0680413\pi$
$599$	4470.00	+	7742.27i	0.304907	+	0.528114i	−0.672334	+	0.740248i	$0.734708\pi$
$600$	1452.00	−	2514.94i	0.0987961	−	0.171120i
$601$	16058.0			1.08988			0.544941	−	0.838474i	$-0.316552\pi$
$601$	16058.0			1.08988			0.544941	+	0.838474i	$0.316552\pi$
$602$		0			0
$603$	−6876.00			−0.464365
$604$	−3344.00	+	5791.98i	−0.225274	+	0.390186i
$605$	1267.00	+	2194.51i	0.0851419	+	0.147470i
$606$	−4110.00	−	7118.73i	−0.275507	−	0.477192i
$607$	−1968.00	+	3408.68i	−0.131596	+	0.227931i	−0.924292	−	0.381686i	$-0.875343\pi$
$607$	−1968.00	+	3408.68i	−0.131596	+	0.227931i	0.792696	+	0.609617i	$0.208677\pi$
$608$	−3968.00			−0.264677
$609$		0			0
$610$	120.000			0.00796501
$611$	−5544.00	+	9602.49i	−0.367081	+	0.635802i
$612$	36.0000	+	62.3538i	0.00237780	+	0.00411847i
$613$	−87.0000	−	150.688i	−0.00573230	−	0.00992863i	0.863145	−	0.504956i	$-0.168491\pi$
$613$	−87.0000	−	150.688i	−0.00573230	−	0.00992863i	−0.868877	+	0.495027i	$0.835158\pi$
$614$	−196.000	+	339.482i	−0.0128826	+	0.0223133i
$615$	2772.00			0.181753
$616$		0			0
$617$	16018.0			1.04515			0.522577	−	0.852592i	$-0.324971\pi$
$617$	16018.0			1.04515			0.522577	+	0.852592i	$0.324971\pi$
$618$	−1392.00	+	2411.01i	−0.0906059	+	0.156934i
$619$	1534.00	+	2656.97i	0.0996069	+	0.172524i	0.911522	−	0.411251i	$-0.134908\pi$
$619$	1534.00	+	2656.97i	0.0996069	+	0.172524i	−0.811915	+	0.583776i	$0.801575\pi$
$620$	288.000	+	498.831i	0.0186554	+	0.0323121i
$621$	−1026.00	+	1777.08i	−0.0662995	+	0.114834i
$622$	−13472.0			−0.868453
$623$		0			0
$624$	−2016.00			−0.129334
$625$	−7070.50	+	12246.5i	−0.452512	+	0.783774i
$626$	−394.000	−	682.428i	−0.0251556	−	0.0435708i
$627$	−1488.00	−	2577.29i	−0.0947767	−	0.164158i
$628$	−892.000	+	1544.99i	−0.0566794	+	0.0981716i
$629$	−796.000			−0.0504588
$630$		0			0
$631$	24656.0			1.55553			0.777765	−	0.628555i	$-0.216353\pi$
$631$	24656.0			1.55553			0.777765	+	0.628555i	$0.216353\pi$
$632$	−2208.00	+	3824.37i	−0.138971	+	0.240704i
$633$	1950.00	+	3377.50i	0.122442	+	0.212075i
$634$	6714.00	+	11629.0i	0.420579	+	0.728464i
$635$	−2088.00	+	3616.52i	−0.130488	+	0.226011i
$636$	−1944.00			−0.121202
$637$		0			0
$638$	−4064.00			−0.252187
$639$	1062.00	−	1839.44i	0.0657466	−	0.113876i
$640$	−128.000	−	221.703i	−0.00790569	−	0.0136931i
$641$	−3797.00	−	6576.60i	−0.233966	−	0.405242i	0.725005	−	0.688743i	$-0.241837\pi$
$641$	−3797.00	−	6576.60i	−0.233966	−	0.405242i	−0.958972	+	0.283501i	$0.908504\pi$
$642$	6408.00	−	11099.0i	0.393931	−	0.682308i
$643$	−3724.00			−0.228398			−0.114199	−	0.993458i	$-0.536430\pi$
$643$	−3724.00			−0.228398			−0.114199	+	0.993458i	$0.536430\pi$
$644$		0			0
$645$	1272.00			0.0776511
$646$	−248.000	+	429.549i	−0.0151044	+	0.0261616i
$647$	−1896.00	−	3283.97i	−0.115208	−	0.199546i	0.802655	−	0.596444i	$-0.203420\pi$
$647$	−1896.00	−	3283.97i	−0.115208	−	0.199546i	−0.917863	+	0.396898i	$0.870087\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	−3088.00	+	5348.57i	−0.186771	+	0.323497i
$650$	10164.0			0.613331
$651$		0			0
$652$	10832.0			0.650635
$653$	−12351.0	+	21392.6i	−0.740171	+	1.28201i	0.212245	+	0.977216i	$0.431922\pi$
$653$	−12351.0	+	21392.6i	−0.740171	+	1.28201i	−0.952417	+	0.304798i	$0.901411\pi$
$654$	3678.00	+	6370.48i	0.219910	+	0.380895i
$655$	292.000	+	505.759i	0.0174189	+	0.0301704i
$656$	−3696.00	+	6401.66i	−0.219976	+	0.381010i
$657$	3762.00			0.223394
$658$		0			0
$659$	−20144.0			−1.19074			−0.595371	−	0.803451i	$-0.702995\pi$
$659$	−20144.0			−1.19074			−0.595371	+	0.803451i	$0.702995\pi$
$660$	96.0000	−	166.277i	0.00566181	−	0.00980654i
$661$	1261.00	+	2184.12i	0.0742015	+	0.128521i	0.900739	−	0.434361i	$-0.143026\pi$
$661$	1261.00	+	2184.12i	0.0742015	+	0.128521i	−0.826537	+	0.562882i	$0.809693\pi$
$662$	−692.000	−	1198.58i	−0.0406274	−	0.0703687i
$663$	−126.000	+	218.238i	−0.00738075	+	0.0127838i
$664$	8288.00			0.484393
$665$		0			0
$666$	7164.00			0.416816
$667$	−9652.00	+	16717.8i	−0.560310	+	0.970486i
$668$	−1792.00	−	3103.84i	−0.103794	−	0.179777i
$669$	−3864.00	−	6692.64i	−0.223305	−	0.386775i
$670$	1528.00	−	2646.57i	0.0881071	−	0.152606i
$671$	−240.000			−0.0138079
$672$		0			0
$673$	−10414.0			−0.596479			−0.298239	−	0.954491i	$-0.596399\pi$
$673$	−10414.0			−0.596479			−0.298239	+	0.954491i	$0.596399\pi$
$674$	1566.00	−	2712.39i	0.0894956	−	0.155011i
$675$	1633.50	+	2829.30i	0.0931458	+	0.161333i
$676$	866.000	+	1499.96i	0.0492717	+	0.0853411i
$677$	11115.0	−	19251.7i	0.630996	−	1.09292i	−0.356353	−	0.934352i	$-0.615980\pi$
$677$	11115.0	−	19251.7i	0.630996	−	1.09292i	0.987348	−	0.158565i	$-0.0506868\pi$
$678$	2028.00			0.114874
$679$		0			0
$680$	−32.0000			−0.00180462
$681$	2754.00	−	4770.07i	0.154968	−	0.268413i
$682$	−576.000	−	997.661i	−0.0323404	−	0.0560153i
$683$	−9096.00	−	15754.7i	−0.509588	−	0.882633i	−0.999938	−	0.0111072i	$-0.996464\pi$
$683$	−9096.00	−	15754.7i	−0.509588	−	0.882633i	0.490350	−	0.871526i	$-0.336869\pi$
$684$	2232.00	−	3865.94i	0.124770	−	0.216108i
$685$	1636.00			0.0912531
$686$		0			0
$687$	−5622.00			−0.312216
$688$	−1696.00	+	2937.56i	−0.0939817	+	0.162781i
$689$	−3402.00	−	5892.44i	−0.188107	−	0.325811i
$690$	−456.000	−	789.815i	−0.0251589	−	0.0435764i
$691$	−4054.00	+	7021.73i	−0.223186	+	0.386569i	−0.955774	−	0.294103i	$-0.904979\pi$
$691$	−4054.00	+	7021.73i	−0.223186	+	0.386569i	0.732588	+	0.680673i	$0.238312\pi$
$692$	16136.0			0.886414
$693$		0			0
$694$	−10656.0			−0.582848
$695$	2156.00	−	3734.30i	0.117672	−	0.203813i
$696$	−3048.00	−	5279.29i	−0.165997	−	0.287516i
$697$	462.000	+	800.207i	0.0251069	+	0.0434864i
$698$	−11326.0	+	19617.2i	−0.614177	+	1.06379i
$699$	11190.0			0.605500
$700$		0			0
$701$	−5794.00			−0.312177			−0.156089	−	0.987743i	$-0.549889\pi$
$701$	−5794.00			−0.312177			−0.156089	+	0.987743i	$0.549889\pi$
$702$	1134.00	−	1964.15i	0.0609688	−	0.105601i
$703$	24676.0	+	42740.1i	1.32386	+	2.29299i
$704$	256.000	+	443.405i	0.0137051	+	0.0237379i
$705$	792.000	−	1371.78i	0.0423099	−	0.0732828i
$706$	−4260.00			−0.227092
$707$		0			0
$708$	−9264.00			−0.491755
$709$	977.000	−	1692.21i	0.0517518	−	0.0896367i	−0.838989	−	0.544148i	$-0.816853\pi$
$709$	977.000	−	1692.21i	0.0517518	−	0.0896367i	0.890741	+	0.454512i	$0.150186\pi$
$710$	472.000	+	817.528i	0.0249491	+	0.0432131i
$711$	−2484.00	−	4302.41i	−0.131023	−	0.226938i
$712$	−120.000	+	207.846i	−0.00631628	+	0.0109401i
$713$	−5472.00			−0.287417
$714$		0			0
$715$	672.000			0.0351488
$716$	6960.00	−	12055.1i	0.363279	−	0.629217i
$717$	−3006.00	−	5206.54i	−0.156571	−	0.271188i
$718$	−3044.00	−	5272.36i	−0.158219	−	0.274043i
$719$	16008.0	−	27726.7i	0.830317	−	1.43815i	−0.0674706	−	0.997721i	$-0.521493\pi$
$719$	16008.0	−	27726.7i	0.830317	−	1.43815i	0.897787	−	0.440429i	$-0.145174\pi$
$720$	288.000			0.0149071
$721$		0			0
$722$	17034.0			0.878033
$723$	969.000	−	1678.36i	0.0498444	−	0.0863330i
$724$	5796.00	+	10039.0i	0.297523	+	0.515325i
$725$	15367.0	+	26616.4i	0.787195	+	1.36346i
$726$	3801.00	−	6583.53i	0.194309	−	0.336553i
$727$	−23072.0			−1.17702			−0.588510	−	0.808490i	$-0.700285\pi$
$727$	−23072.0			−1.17702			−0.588510	+	0.808490i	$0.700285\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	−836.000	+	1447.99i	−0.0423860	+	0.0734146i
$731$	212.000	+	367.195i	0.0107265	+	0.0185789i
$732$	−180.000	−	311.769i	−0.00908879	−	0.0157422i
$733$	−15891.0	+	27524.0i	−0.800747	+	1.38693i	0.118378	+	0.992969i	$0.462230\pi$
$733$	−15891.0	+	27524.0i	−0.800747	+	1.38693i	−0.919125	+	0.393966i	$0.871103\pi$
$734$	24832.0			1.24873
$735$		0			0
$736$	2432.00			0.121800
$737$	−3056.00	+	5293.15i	−0.152740	+	0.264553i
$738$	−4158.00	−	7201.87i	−0.207396	−	0.359220i
$739$	12198.0	+	21127.6i	0.607186	+	1.05168i	0.991702	+	0.128559i	$0.0410352\pi$
$739$	12198.0	+	21127.6i	0.607186	+	1.05168i	−0.384516	+	0.923119i	$0.625631\pi$
$740$	−1592.00	+	2757.42i	−0.0790852	+	0.136980i
$741$	15624.0			0.774578
$742$		0			0
$743$	−32604.0			−1.60986			−0.804929	−	0.593371i	$-0.797797\pi$
$743$	−32604.0			−1.60986			−0.804929	+	0.593371i	$0.797797\pi$
$744$	864.000	−	1496.49i	0.0425750	−	0.0737420i
$745$	2850.00	+	4936.34i	0.140156	+	0.242757i
$746$	7442.00	+	12889.9i	0.365243	+	0.632619i
$747$	−4662.00	+	8074.82i	−0.228345	+	0.395505i
$748$	64.0000			0.00312844
$749$		0			0
$750$	−2952.00			−0.143722
$751$	3840.00	−	6651.08i	0.186583	−	0.323171i	−0.757526	−	0.652805i	$-0.773592\pi$
$751$	3840.00	−	6651.08i	0.186583	−	0.323171i	0.944109	+	0.329634i	$0.106925\pi$
$752$	2112.00	+	3658.09i	0.102416	+	0.177389i
$753$	−1890.00	−	3273.58i	−0.0914680	−	0.158427i
$754$	10668.0	−	18477.5i	0.515259	−	0.892456i
$755$	3344.00			0.161193
$756$		0			0
$757$	366.000			0.0175727			0.00878633	−	0.999961i	$-0.497203\pi$
$757$	366.000			0.0175727			0.00878633	+	0.999961i	$0.497203\pi$
$758$	−100.000	+	173.205i	−0.00479177	+	0.00829959i
$759$	912.000	+	1579.63i	0.0436146	+	0.0755428i
$760$	992.000	+	1718.19i	0.0473469	+	0.0820072i
$761$	−14687.0	+	25438.6i	−0.699610	+	1.21176i	0.268992	+	0.963143i	$0.413310\pi$
$761$	−14687.0	+	25438.6i	−0.699610	+	1.21176i	−0.968602	+	0.248618i	$0.920024\pi$
$762$	12528.0			0.595593
$763$		0			0
$764$	10608.0			0.502335
$765$	18.0000	−	31.1769i	0.000850708	−	0.00147347i
$766$	−8080.00	−	13995.0i	−0.381126	−	0.660129i
$767$	−16212.0	−	28080.0i	−0.763209	−	1.32192i
$768$	−384.000	+	665.108i	−0.0180422	+	0.0312500i
$769$	−38990.0			−1.82837			−0.914184	−	0.405299i	$-0.867167\pi$
$769$	−38990.0			−1.82837			−0.914184	+	0.405299i	$0.867167\pi$
$770$		0			0
$771$	17730.0			0.828185
$772$	−292.000	+	505.759i	−0.0136131	+	0.0235786i
$773$	10235.0	+	17727.5i	0.476232	+	0.824858i	0.999629	−	0.0272308i	$-0.00866890\pi$
$773$	10235.0	+	17727.5i	0.476232	+	0.824858i	−0.523397	+	0.852089i	$0.675336\pi$
$774$	−1908.00	−	3304.75i	−0.0886068	−	0.153471i
$775$	−4356.00	+	7544.81i	−0.201900	+	0.349700i
$776$	−9520.00			−0.440397
$777$		0			0
$778$	−10964.0			−0.505242
$779$	28644.0	−	49612.9i	1.31743	−	2.28186i
$780$	504.000	+	872.954i	0.0231360	+	0.0400728i
$781$	−944.000	−	1635.06i	−0.0432509	−	0.0749128i
$782$	152.000	−	263.272i	0.00695078	−	0.0120391i
$783$	6858.00			0.313008
$784$		0			0
$785$	892.000			0.0405565
$786$	876.000	−	1517.28i	0.0397530	−	0.0688543i
$787$	−14958.0	−	25908.0i	−0.677503	−	1.17347i	−0.975730	−	0.218975i	$-0.929729\pi$
$787$	−14958.0	−	25908.0i	−0.677503	−	1.17347i	0.298227	−	0.954495i	$-0.403605\pi$
$788$	5092.00	+	8819.60i	0.230197	+	0.398712i
$789$	−4482.00	+	7763.05i	−0.202235	+	0.350281i
$790$	2208.00			0.0994394
$791$		0			0
$792$	−576.000			−0.0258425
$793$	630.000	−	1091.19i	0.0282118	−	0.0488643i
$794$	−10446.0	−	18093.0i	−0.466895	−	0.808686i
$795$	486.000	+	841.777i	0.0216813	+	0.0375531i
$796$	5072.00	−	8784.96i	0.225845	−	0.391174i
$797$	4914.00			0.218398			0.109199	−	0.994020i	$-0.465172\pi$
$797$	4914.00			0.218398			0.109199	+	0.994020i	$0.465172\pi$
$798$		0			0
$799$	528.000			0.0233783
$800$	1936.00	−	3353.25i	0.0855599	−	0.148194i
$801$	−135.000	−	233.827i	−0.00595504	−	0.0103144i
$802$	11334.0	+	19631.1i	0.499024	+	0.864335i
$803$	1672.00	−	2895.99i	0.0734790	−	0.127269i
$804$	−9168.00			−0.402152
$805$		0			0
$806$	6048.00			0.264307
$807$	1977.00	−	3424.26i	0.0862375	−	0.149368i
$808$	−5480.00	−	9491.64i	−0.238596	−	0.413261i
$809$	−17125.0	−	29661.4i	−0.744231	−	1.28905i	−0.950553	−	0.310562i	$-0.899483\pi$
$809$	−17125.0	−	29661.4i	−0.744231	−	1.28905i	0.206322	−	0.978484i	$-0.433851\pi$
$810$	−162.000	+	280.592i	−0.00702728	+	0.0121716i
$811$	−41804.0			−1.81003			−0.905017	−	0.425376i	$-0.860142\pi$
$811$	−41804.0			−1.81003			−0.905017	+	0.425376i	$0.860142\pi$
$812$		0			0
$813$	−16920.0			−0.729902
$814$	3184.00	−	5514.85i	0.137100	−	0.237464i
$815$	−2708.00	−	4690.39i	−0.116389	−	0.201592i
$816$	48.0000	+	83.1384i	0.00205924	+	0.00356670i
$817$	13144.0	−	22766.1i	0.562852	−	0.974889i
$818$	17188.0			0.734675
$819$		0			0
$820$	3696.00			0.157402
$821$	−15431.0	+	26727.3i	−0.655963	+	1.13616i	0.325688	+	0.945477i	$0.394404\pi$
$821$	−15431.0	+	26727.3i	−0.655963	+	1.13616i	−0.981651	+	0.190684i	$0.938929\pi$
$822$	−2454.00	−	4250.45i	−0.104128	−	0.180355i
$823$	−5288.00	−	9159.08i	−0.223971	−	0.387929i	0.732039	−	0.681262i	$-0.238569\pi$
$823$	−5288.00	−	9159.08i	−0.223971	−	0.387929i	−0.956010	+	0.293333i	$0.905235\pi$
$824$	−1856.00	+	3214.69i	−0.0784670	+	0.135909i
$825$	2904.00			0.122551
$826$		0			0
$827$	−10680.0			−0.449069			−0.224534	−	0.974466i	$-0.572086\pi$
$827$	−10680.0			−0.449069			−0.224534	+	0.974466i	$0.572086\pi$
$828$	−1368.00	+	2369.45i	−0.0574170	+	0.0994492i
$829$	589.000	+	1020.18i	0.0246765	+	0.0427409i	0.878100	−	0.478477i	$-0.158811\pi$
$829$	589.000	+	1020.18i	0.0246765	+	0.0427409i	−0.853423	+	0.521218i	$0.825478\pi$
$830$	−2072.00	−	3588.81i	−0.0866508	−	0.150084i
$831$	−9669.00	+	16747.2i	−0.403627	+	0.699102i
$832$	−2688.00			−0.112007
$833$		0			0
$834$	−12936.0			−0.537095
$835$	−896.000	+	1551.92i	−0.0371346	+	0.0643189i
$836$	−1984.00	−	3436.39i	−0.0820790	−	0.142165i
$837$	972.000	+	1683.55i	0.0401401	+	0.0695246i
$838$	−10500.0	+	18186.5i	−0.432836	+	0.749694i
$839$	−5600.00			−0.230433			−0.115217	−	0.993340i	$-0.536756\pi$
$839$	−5600.00			−0.230433			−0.115217	+	0.993340i	$0.536756\pi$
$840$		0			0
$841$	40127.0			1.64529
$842$	12066.0	−	20898.9i	0.493850	−	0.855374i
$843$	−7395.00	−	12808.5i	−0.302132	−	0.523308i
$844$	2600.00	+	4503.33i	0.106038	+	0.183662i
$845$	433.000	−	749.978i	0.0176280	−	0.0305326i
$846$	−4752.00			−0.193117
$847$		0			0
$848$	−2592.00			−0.104964
$849$	9390.00	−	16264.0i	0.379581	−	0.657453i
$850$	−242.000	−	419.156i	−0.00976533	−	0.0169140i
$851$	−15124.0	−	26195.5i	−0.609217	−	1.05520i
$852$	1416.00	−	2452.58i	0.0569382	−	0.0986199i
$853$	−826.000			−0.0331556			−0.0165778	−	0.999863i	$-0.505277\pi$
$853$	−826.000			−0.0331556			−0.0165778	+	0.999863i	$0.505277\pi$
$854$		0			0
$855$	−2232.00			−0.0892781
$856$	8544.00	−	14798.6i	0.341154	−	0.590896i
$857$	−22959.0	−	39766.2i	−0.915128	−	1.58505i	−0.806714	−	0.590942i	$-0.798756\pi$
$857$	−22959.0	−	39766.2i	−0.915128	−	1.58505i	−0.108414	−	0.994106i	$-0.534577\pi$
$858$	−1008.00	−	1745.91i	−0.0401079	−	0.0694689i
$859$	−21190.0	+	36702.2i	−0.841669	+	1.45781i	0.0468143	+	0.998904i	$0.485093\pi$
$859$	−21190.0	+	36702.2i	−0.841669	+	1.45781i	−0.888483	+	0.458909i	$0.848240\pi$
$860$	1696.00			0.0672478
$861$		0			0
$862$	8664.00			0.342340
$863$	13262.0	−	22970.5i	0.523110	−	0.906053i	−0.476529	−	0.879159i	$-0.658105\pi$
$863$	13262.0	−	22970.5i	0.523110	−	0.906053i	0.999638	−	0.0268937i	$-0.00856156\pi$
$864$	−432.000	−	748.246i	−0.0170103	−	0.0294628i
$865$	−4034.00	−	6987.09i	−0.158567	−	0.274645i
$866$	1918.00	−	3322.07i	0.0752613	−	0.130356i
$867$	−14727.0			−0.576880
$868$		0			0
$869$	−4416.00			−0.172385
$870$	−1524.00	+	2639.65i	−0.0593890	+	0.102865i
$871$	−16044.0	−	27789.0i	−0.624145	−	1.08105i
$872$	4904.00	+	8493.98i	0.190448	+	0.329865i
$873$	5355.00	−	9275.13i	0.207605	−	0.359583i
$874$	−18848.0			−0.729454
$875$		0			0
$876$	5016.00			0.193465
$877$	−10307.0	+	17852.2i	−0.396856	+	0.687375i	−0.993336	−	0.115253i	$-0.963232\pi$
$877$	−10307.0	+	17852.2i	−0.396856	+	0.687375i	0.596480	+	0.802628i	$0.296565\pi$
$878$	7992.00	+	13842.6i	0.307195	+	0.532077i
$879$	3465.00	+	6001.56i	0.132960	+	0.230293i
$880$	128.000	−	221.703i	0.00490327	−	0.00849272i
$881$	−23730.0			−0.907473			−0.453737	−	0.891136i	$-0.649909\pi$
$881$	−23730.0			−0.907473			−0.453737	+	0.891136i	$0.649909\pi$
$882$		0			0
$883$	−9028.00			−0.344073			−0.172036	−	0.985091i	$-0.555035\pi$
$883$	−9028.00			−0.344073			−0.172036	+	0.985091i	$0.555035\pi$
$884$	−168.000	+	290.985i	−0.00639191	+	0.0110711i
$885$	2316.00	+	4011.43i	0.0879678	+	0.152365i
$886$	−3184.00	−	5514.85i	−0.120732	−	0.209114i
$887$	−18600.0	+	32216.1i	−0.704089	+	1.21952i	0.262930	+	0.964815i	$0.415311\pi$
$887$	−18600.0	+	32216.1i	−0.704089	+	1.21952i	−0.967019	+	0.254703i	$0.918022\pi$
$888$	9552.00			0.360973
$889$		0			0
$890$	120.000			0.00451956
$891$	324.000	−	561.184i	0.0121823	−	0.0211003i
$892$	−5152.00	−	8923.53i	−0.193388	−	0.334957i
$893$	−16368.0	−	28350.2i	−0.613364	−	1.06238i
$894$	8550.00	−	14809.0i	0.319860	−	0.554014i
$895$	−6960.00			−0.259941
$896$		0			0
$897$	−9576.00			−0.356447
$898$	−11426.0	+	19790.4i	−0.424600	+	0.735428i
$899$	9144.00	+	15837.9i	0.339232	+	0.587567i
$900$	2178.00	+	3772.41i	0.0806667	+	0.139719i
$901$	−162.000	+	280.592i	−0.00599001	+	0.0103750i
$902$	−7392.00			−0.272868
$903$		0			0
$904$	2704.00			0.0994842
$905$	2898.00	−	5019.48i	0.106445	−	0.184368i
$906$	−5016.00	−	8687.97i	−0.183935	−	0.318585i
$907$	−11994.0	−	20774.2i	−0.439090	−	0.760525i	0.558530	−	0.829484i	$-0.311366\pi$
$907$	−11994.0	−	20774.2i	−0.439090	−	0.760525i	−0.997619	+	0.0689589i	$0.978032\pi$
$908$	3672.00	−	6360.09i	0.134207	−	0.232453i
$909$	12330.0			0.449901
$910$		0			0
$911$	15276.0			0.555561			0.277781	−	0.960645i	$-0.410401\pi$
$911$	15276.0			0.555561			0.277781	+	0.960645i	$0.410401\pi$
$912$	2976.00	−	5154.58i	0.108054	−	0.187155i
$913$	4144.00	+	7177.62i	0.150215	+	0.260180i
$914$	16934.0	+	29330.5i	0.612830	+	1.06145i
$915$	−90.0000	+	155.885i	−0.00325170	+	0.00563211i
$916$	−7496.00			−0.270387
$917$		0			0
$918$	−108.000			−0.00388293
$919$	5380.00	−	9318.43i	0.193112	−	0.334480i	−0.753168	−	0.657828i	$-0.771475\pi$
$919$	5380.00	−	9318.43i	0.193112	−	0.334480i	0.946280	+	0.323349i	$0.104809\pi$
$920$	−608.000	−	1053.09i	−0.0217882	−	0.0377383i
$921$	−294.000	−	509.223i	−0.0105186	−	0.0182187i
$922$	17038.0	−	29510.7i	0.608586	−	1.05410i
$923$	9912.00			0.353475
$924$		0			0
$925$	−48158.0			−1.71181
$926$	13592.0	−	23542.0i	0.482355	−	0.835464i
$927$	−2088.00	−	3616.52i	−0.0739794	−	0.128136i
$928$	−4064.00	−	7039.05i	−0.143758	−	0.248996i
$929$	26445.0	−	45804.1i	0.933942	−	1.61764i	0.157433	−	0.987530i	$-0.449678\pi$
$929$	26445.0	−	45804.1i	0.933942	−	1.61764i	0.776509	−	0.630106i	$-0.216988\pi$
$930$	−864.000			−0.0304642
$931$		0			0
$932$	14920.0			0.524379
$933$	10104.0	−	17500.6i	0.354545	−	0.614089i
$934$	−8612.00	−	14916.4i	−0.301706	−	0.522570i
$935$	−16.0000	−	27.7128i	−0.000559632	−	0.000969311i
$936$	1512.00	−	2618.86i	0.0528005	−	0.0914531i
$937$	−6118.00			−0.213305			−0.106652	−	0.994296i	$-0.534013\pi$
$937$	−6118.00			−0.213305			−0.106652	+	0.994296i	$0.534013\pi$
$938$		0			0
$939$	1182.00			0.0410789
$940$	1056.00	−	1829.05i	0.0366414	−	0.0634648i
$941$	16115.0	+	27912.0i	0.558272	+	0.966956i	0.997641	+	0.0686488i	$0.0218688\pi$
$941$	16115.0	+	27912.0i	0.558272	+	0.966956i	−0.439369	+	0.898307i	$0.644798\pi$
$942$	−1338.00	−	2317.48i	−0.0462786	−	0.0801568i
$943$	−17556.0	+	30407.9i	−0.606259	+	1.05007i
$944$	−12352.0			−0.425872
$945$		0			0
$946$	−3392.00			−0.116579
$947$	9272.00	−	16059.6i	0.318162	−	0.551073i	−0.661942	−	0.749555i	$-0.730268\pi$
$947$	9272.00	−	16059.6i	0.318162	−	0.551073i	0.980105	+	0.198482i	$0.0636010\pi$
$948$	−3312.00	−	5736.55i	−0.113469	−	0.196534i
$949$	8778.00	+	15203.9i	0.300259	+	0.520064i
$950$	−15004.0	+	25987.7i	−0.512415	+	0.887528i
$951$	−20142.0			−0.686802
$952$		0			0
$953$	25930.0			0.881380			0.440690	−	0.897659i	$-0.354734\pi$
$953$	25930.0			0.881380			0.440690	+	0.897659i	$0.354734\pi$
$954$	1458.00	−	2525.33i	0.0494806	−	0.0857029i
$955$	−2652.00	−	4593.40i	−0.0898604	−	0.155643i
$956$	−4008.00	−	6942.06i	−0.135594	−	0.234856i
$957$	3048.00	−	5279.29i	0.102955	−	0.178323i
$958$	14864.0			0.501288
$959$		0			0
$960$	384.000			0.0129099
$961$	12303.5	−	21310.3i	0.412994	−	0.715326i
$962$	16716.0	+	28953.0i	0.560234	+	0.970354i
$963$	9612.00	+	16648.5i	0.321643	+	0.557102i
$964$	1292.00	−	2237.81i	0.0431665	−	0.0747666i
$965$	292.000			0.00974074
$966$		0			0
$967$	8192.00			0.272427			0.136214	−	0.990680i	$-0.456507\pi$
$967$	8192.00			0.272427			0.136214	+	0.990680i	$0.456507\pi$
$968$	5068.00	−	8778.03i	0.168277	−	0.291464i
$969$	−372.000	−	644.323i	−0.0123327	−	0.0213608i
$970$	2380.00	+	4122.28i	0.0787806	+	0.136452i
$971$	27222.0	−	47149.9i	0.899686	−	1.55830i	0.0717914	−	0.997420i	$-0.477128\pi$
$971$	27222.0	−	47149.9i	0.899686	−	1.55830i	0.827895	−	0.560883i	$-0.189538\pi$
$972$	972.000			0.0320750
$973$		0			0
$974$	−13232.0			−0.435298
$975$	−7623.00	+	13203.4i	−0.250391	+	0.433690i
$976$	−240.000	−	415.692i	−0.00787112	−	0.0136332i
$977$	12723.0	+	22036.9i	0.416627	+	0.721620i	0.995598	−	0.0937289i	$-0.0298787\pi$
$977$	12723.0	+	22036.9i	0.416627	+	0.721620i	−0.578970	+	0.815348i	$0.696545\pi$
$978$	−8124.00	+	14071.2i	−0.265621	+	0.460068i
$979$	−240.000			−0.00783497
$980$		0			0
$981$	−11034.0			−0.359112
$982$	−17040.0	+	29514.1i	−0.553735	+	0.959098i
$983$	−16596.0	−	28745.1i	−0.538484	−	0.932682i	−0.998986	−	0.0450235i	$-0.985664\pi$
$983$	−16596.0	−	28745.1i	−0.538484	−	0.932682i	0.460502	−	0.887659i	$-0.347670\pi$
$984$	−5544.00	−	9602.49i	−0.179610	−	0.311094i
$985$	2546.00	−	4409.80i	0.0823577	−	0.142648i
$986$	−1016.00			−0.0328154
$987$		0			0
$988$	20832.0			0.670804
$989$	−8056.00	+	13953.4i	−0.259015	+	0.448627i
$990$	144.000	+	249.415i	0.00462285	+	0.00800701i
$991$	−5512.00	−	9547.06i	−0.176685	−	0.306027i	0.764058	−	0.645147i	$-0.223204\pi$
$991$	−5512.00	−	9547.06i	−0.176685	−	0.306027i	−0.940743	+	0.339120i	$0.889871\pi$
$992$	1152.00	−	1995.32i	0.0368710	−	0.0638625i
$993$	2076.00			0.0663443
$994$		0			0
$995$	−5072.00			−0.161601
$996$	−6216.00	+	10766.4i	−0.197753	+	0.342517i
$997$	20357.0	+	35259.4i	0.646653	+	1.12004i	0.983917	+	0.178625i	$0.0571650\pi$
$997$	20357.0	+	35259.4i	0.646653	+	1.12004i	−0.337265	+	0.941410i	$0.609502\pi$
$998$	2948.00	+	5106.09i	0.0935043	+	0.161954i
$999$	−5373.00	+	9306.31i	−0.170164	+	0.294733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.e.a.79.1		2
3.2	odd	2		882.4.g.s.667.1		2
7.2	even	3		42.4.a.b.1.1	✓	1
7.3	odd	6		294.4.e.d.67.1		2
7.4	even	3	inner	294.4.e.a.67.1		2
7.5	odd	6		294.4.a.h.1.1		1
7.6	odd	2		294.4.e.d.79.1		2
21.2	odd	6		126.4.a.c.1.1		1
21.5	even	6		882.4.a.d.1.1		1
21.11	odd	6		882.4.g.s.361.1		2
21.17	even	6		882.4.g.r.361.1		2
21.20	even	2		882.4.g.r.667.1		2
28.19	even	6		2352.4.a.ba.1.1		1
28.23	odd	6		336.4.a.d.1.1		1
35.2	odd	12		1050.4.g.n.799.2		2
35.9	even	6		1050.4.a.d.1.1		1
35.23	odd	12		1050.4.g.n.799.1		2
56.37	even	6		1344.4.a.f.1.1		1
56.51	odd	6		1344.4.a.t.1.1		1
84.23	even	6		1008.4.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.a.b.1.1	✓	1	7.2	even	3
126.4.a.c.1.1		1	21.2	odd	6
294.4.a.h.1.1		1	7.5	odd	6
294.4.e.a.67.1		2	7.4	even	3	inner
294.4.e.a.79.1		2	1.1	even	1	trivial
294.4.e.d.67.1		2	7.3	odd	6
294.4.e.d.79.1		2	7.6	odd	2
336.4.a.d.1.1		1	28.23	odd	6
882.4.a.d.1.1		1	21.5	even	6
882.4.g.r.361.1		2	21.17	even	6
882.4.g.r.667.1		2	21.20	even	2
882.4.g.s.361.1		2	21.11	odd	6
882.4.g.s.667.1		2	3.2	odd	2
1008.4.a.j.1.1		1	84.23	even	6
1050.4.a.d.1.1		1	35.9	even	6
1050.4.g.n.799.1		2	35.23	odd	12
1050.4.g.n.799.2		2	35.2	odd	12
1344.4.a.f.1.1		1	56.37	even	6
1344.4.a.t.1.1		1	56.51	odd	6
2352.4.a.ba.1.1		1	28.19	even	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.00000 + 1.73205i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-1.00000 + 1.73205i) q^{5} +6.00000 q^{6} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-2.00000 - 3.46410i) q^{10} +(4.00000 + 6.92820i) q^{11} +(-6.00000 + 10.3923i) q^{12} -42.0000 q^{13} +6.00000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(62.0000 - 107.387i) q^{19} +8.00000 q^{20} -16.0000 q^{22} +(-38.0000 + 65.8179i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(60.5000 + 104.789i) q^{25} +(42.0000 - 72.7461i) q^{26} +27.0000 q^{27} +254.000 q^{29} +(-6.00000 + 10.3923i) q^{30} +(36.0000 + 62.3538i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(12.0000 - 20.7846i) q^{33} -4.00000 q^{34} +36.0000 q^{36} +(-199.000 + 344.678i) q^{37} +(124.000 + 214.774i) q^{38} +(63.0000 + 109.119i) q^{39} +(-8.00000 + 13.8564i) q^{40} +462.000 q^{41} +212.000 q^{43} +(16.0000 - 27.7128i) q^{44} +(-9.00000 - 15.5885i) q^{45} +(-76.0000 - 131.636i) q^{46} +(132.000 - 228.631i) q^{47} +48.0000 q^{48} -242.000 q^{50} +(3.00000 - 5.19615i) q^{51} +(84.0000 + 145.492i) q^{52} +(81.0000 + 140.296i) q^{53} +(-27.0000 + 46.7654i) q^{54} -16.0000 q^{55} -372.000 q^{57} +(-254.000 + 439.941i) q^{58} +(386.000 + 668.572i) q^{59} +(-12.0000 - 20.7846i) q^{60} +(-15.0000 + 25.9808i) q^{61} -144.000 q^{62} +64.0000 q^{64} +(42.0000 - 72.7461i) q^{65} +(24.0000 + 41.5692i) q^{66} +(382.000 + 661.643i) q^{67} +(4.00000 - 6.92820i) q^{68} +228.000 q^{69} -236.000 q^{71} +(-36.0000 + 62.3538i) q^{72} +(-209.000 - 361.999i) q^{73} +(-398.000 - 689.356i) q^{74} +(181.500 - 314.367i) q^{75} -496.000 q^{76} -252.000 q^{78} +(-276.000 + 478.046i) q^{79} +(-16.0000 - 27.7128i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-462.000 + 800.207i) q^{82} +1036.00 q^{83} -4.00000 q^{85} +(-212.000 + 367.195i) q^{86} +(-381.000 - 659.911i) q^{87} +(32.0000 + 55.4256i) q^{88} +(-15.0000 + 25.9808i) q^{89} +36.0000 q^{90} +304.000 q^{92} +(108.000 - 187.061i) q^{93} +(264.000 + 457.261i) q^{94} +(124.000 + 214.774i) q^{95} +(-48.0000 + 83.1384i) q^{96} -1190.00 q^{97} -72.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 3 q^{3} - 4 q^{4} - 2 q^{5} + 12 q^{6} + 16 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 - 2 * q^5 + 12 * q^6 + 16 * q^8 - 9 * q^9	\( 2 q - 2 q^{2} - 3 q^{3} - 4 q^{4} - 2 q^{5} + 12 q^{6} + 16 q^{8} - 9 q^{9} - 4 q^{10} + 8 q^{11} - 12 q^{12} - 84 q^{13} + 12 q^{15} - 16 q^{16} + 2 q^{17} - 18 q^{18} + 124 q^{19} + 16 q^{20} - 32 q^{22} - 76 q^{23} - 24 q^{24} + 121 q^{25} + 84 q^{26} + 54 q^{27} + 508 q^{29} - 12 q^{30} + 72 q^{31} - 32 q^{32} + 24 q^{33} - 8 q^{34} + 72 q^{36} - 398 q^{37} + 248 q^{38} + 126 q^{39} - 16 q^{40} + 924 q^{41} + 424 q^{43} + 32 q^{44} - 18 q^{45} - 152 q^{46} + 264 q^{47} + 96 q^{48} - 484 q^{50} + 6 q^{51} + 168 q^{52} + 162 q^{53} - 54 q^{54} - 32 q^{55} - 744 q^{57} - 508 q^{58} + 772 q^{59} - 24 q^{60} - 30 q^{61} - 288 q^{62} + 128 q^{64} + 84 q^{65} + 48 q^{66} + 764 q^{67} + 8 q^{68} + 456 q^{69} - 472 q^{71} - 72 q^{72} - 418 q^{73} - 796 q^{74} + 363 q^{75} - 992 q^{76} - 504 q^{78} - 552 q^{79} - 32 q^{80} - 81 q^{81} - 924 q^{82} + 2072 q^{83} - 8 q^{85} - 424 q^{86} - 762 q^{87} + 64 q^{88} - 30 q^{89} + 72 q^{90} + 608 q^{92} + 216 q^{93} + 528 q^{94} + 248 q^{95} - 96 q^{96} - 2380 q^{97} - 144 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 3 * q^3 - 4 * q^4 - 2 * q^5 + 12 * q^6 + 16 * q^8 - 9 * q^9 - 4 * q^10 + 8 * q^11 - 12 * q^12 - 84 * q^13 + 12 * q^15 - 16 * q^16 + 2 * q^17 - 18 * q^18 + 124 * q^19 + 16 * q^20 - 32 * q^22 - 76 * q^23 - 24 * q^24 + 121 * q^25 + 84 * q^26 + 54 * q^27 + 508 * q^29 - 12 * q^30 + 72 * q^31 - 32 * q^32 + 24 * q^33 - 8 * q^34 + 72 * q^36 - 398 * q^37 + 248 * q^38 + 126 * q^39 - 16 * q^40 + 924 * q^41 + 424 * q^43 + 32 * q^44 - 18 * q^45 - 152 * q^46 + 264 * q^47 + 96 * q^48 - 484 * q^50 + 6 * q^51 + 168 * q^52 + 162 * q^53 - 54 * q^54 - 32 * q^55 - 744 * q^57 - 508 * q^58 + 772 * q^59 - 24 * q^60 - 30 * q^61 - 288 * q^62 + 128 * q^64 + 84 * q^65 + 48 * q^66 + 764 * q^67 + 8 * q^68 + 456 * q^69 - 472 * q^71 - 72 * q^72 - 418 * q^73 - 796 * q^74 + 363 * q^75 - 992 * q^76 - 504 * q^78 - 552 * q^79 - 32 * q^80 - 81 * q^81 - 924 * q^82 + 2072 * q^83 - 8 * q^85 - 424 * q^86 - 762 * q^87 + 64 * q^88 - 30 * q^89 + 72 * q^90 + 608 * q^92 + 216 * q^93 + 528 * q^94 + 248 * q^95 - 96 * q^96 - 2380 * q^97 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more