LMFDB - Embedded newform 294.4.e.g.67.1

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 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	294.67
Dual form			294.4.e.g.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-6.00000 + 10.3923i) q^{10} +(-6.00000 + 10.3923i) q^{11} +(-6.00000 - 10.3923i) q^{12} -38.0000 q^{13} -18.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-63.0000 + 109.119i) q^{17} +(9.00000 - 15.5885i) q^{18} +(10.0000 + 17.3205i) q^{19} -24.0000 q^{20} -24.0000 q^{22} +(-84.0000 - 145.492i) q^{23} +(12.0000 - 20.7846i) q^{24} +(44.5000 - 77.0763i) q^{25} +(-38.0000 - 65.8179i) q^{26} +27.0000 q^{27} +30.0000 q^{29} +(-18.0000 - 31.1769i) q^{30} +(-44.0000 + 76.2102i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-18.0000 - 31.1769i) q^{33} -252.000 q^{34} +36.0000 q^{36} +(-127.000 - 219.970i) q^{37} +(-20.0000 + 34.6410i) q^{38} +(57.0000 - 98.7269i) q^{39} +(-24.0000 - 41.5692i) q^{40} -42.0000 q^{41} -52.0000 q^{43} +(-24.0000 - 41.5692i) q^{44} +(27.0000 - 46.7654i) q^{45} +(168.000 - 290.985i) q^{46} +(-48.0000 - 83.1384i) q^{47} +48.0000 q^{48} +178.000 q^{50} +(-189.000 - 327.358i) q^{51} +(76.0000 - 131.636i) q^{52} +(-99.0000 + 171.473i) q^{53} +(27.0000 + 46.7654i) q^{54} -72.0000 q^{55} -60.0000 q^{57} +(30.0000 + 51.9615i) q^{58} +(-330.000 + 571.577i) q^{59} +(36.0000 - 62.3538i) q^{60} +(-269.000 - 465.922i) q^{61} -176.000 q^{62} +64.0000 q^{64} +(-114.000 - 197.454i) q^{65} +(36.0000 - 62.3538i) q^{66} +(-442.000 + 765.566i) q^{67} +(-252.000 - 436.477i) q^{68} +504.000 q^{69} +792.000 q^{71} +(36.0000 + 62.3538i) q^{72} +(109.000 - 188.794i) q^{73} +(254.000 - 439.941i) q^{74} +(133.500 + 231.229i) q^{75} -80.0000 q^{76} +228.000 q^{78} +(260.000 + 450.333i) q^{79} +(48.0000 - 83.1384i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-42.0000 - 72.7461i) q^{82} +492.000 q^{83} -756.000 q^{85} +(-52.0000 - 90.0666i) q^{86} +(-45.0000 + 77.9423i) q^{87} +(48.0000 - 83.1384i) q^{88} +(405.000 + 701.481i) q^{89} +108.000 q^{90} +672.000 q^{92} +(-132.000 - 228.631i) q^{93} +(96.0000 - 166.277i) q^{94} +(-60.0000 + 103.923i) q^{95} +(48.0000 + 83.1384i) q^{96} -1154.00 q^{97} +108.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} + 6 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 + 6 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} + 6 q^{5} - 12 q^{6} - 16 q^{8} - 9 q^{9} - 12 q^{10} - 12 q^{11} - 12 q^{12} - 76 q^{13} - 36 q^{15} - 16 q^{16} - 126 q^{17} + 18 q^{18} + 20 q^{19} - 48 q^{20} - 48 q^{22} - 168 q^{23} + 24 q^{24} + 89 q^{25} - 76 q^{26} + 54 q^{27} + 60 q^{29} - 36 q^{30} - 88 q^{31} + 32 q^{32} - 36 q^{33} - 504 q^{34} + 72 q^{36} - 254 q^{37} - 40 q^{38} + 114 q^{39} - 48 q^{40} - 84 q^{41} - 104 q^{43} - 48 q^{44} + 54 q^{45} + 336 q^{46} - 96 q^{47} + 96 q^{48} + 356 q^{50} - 378 q^{51} + 152 q^{52} - 198 q^{53} + 54 q^{54} - 144 q^{55} - 120 q^{57} + 60 q^{58} - 660 q^{59} + 72 q^{60} - 538 q^{61} - 352 q^{62} + 128 q^{64} - 228 q^{65} + 72 q^{66} - 884 q^{67} - 504 q^{68} + 1008 q^{69} + 1584 q^{71} + 72 q^{72} + 218 q^{73} + 508 q^{74} + 267 q^{75} - 160 q^{76} + 456 q^{78} + 520 q^{79} + 96 q^{80} - 81 q^{81} - 84 q^{82} + 984 q^{83} - 1512 q^{85} - 104 q^{86} - 90 q^{87} + 96 q^{88} + 810 q^{89} + 216 q^{90} + 1344 q^{92} - 264 q^{93} + 192 q^{94} - 120 q^{95} + 96 q^{96} - 2308 q^{97} + 216 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 + 6 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9 - 12 * q^10 - 12 * q^11 - 12 * q^12 - 76 * q^13 - 36 * q^15 - 16 * q^16 - 126 * q^17 + 18 * q^18 + 20 * q^19 - 48 * q^20 - 48 * q^22 - 168 * q^23 + 24 * q^24 + 89 * q^25 - 76 * q^26 + 54 * q^27 + 60 * q^29 - 36 * q^30 - 88 * q^31 + 32 * q^32 - 36 * q^33 - 504 * q^34 + 72 * q^36 - 254 * q^37 - 40 * q^38 + 114 * q^39 - 48 * q^40 - 84 * q^41 - 104 * q^43 - 48 * q^44 + 54 * q^45 + 336 * q^46 - 96 * q^47 + 96 * q^48 + 356 * q^50 - 378 * q^51 + 152 * q^52 - 198 * q^53 + 54 * q^54 - 144 * q^55 - 120 * q^57 + 60 * q^58 - 660 * q^59 + 72 * q^60 - 538 * q^61 - 352 * q^62 + 128 * q^64 - 228 * q^65 + 72 * q^66 - 884 * q^67 - 504 * q^68 + 1008 * q^69 + 1584 * q^71 + 72 * q^72 + 218 * q^73 + 508 * q^74 + 267 * q^75 - 160 * q^76 + 456 * q^78 + 520 * q^79 + 96 * q^80 - 81 * q^81 - 84 * q^82 + 984 * q^83 - 1512 * q^85 - 104 * q^86 - 90 * q^87 + 96 * q^88 + 810 * q^89 + 216 * q^90 + 1344 * q^92 - 264 * q^93 + 192 * q^94 - 120 * q^95 + 96 * q^96 - 2308 * q^97 + 216 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$199$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	3.00000	+	5.19615i	0.268328	+	0.464758i	0.968430	−	0.249285i	$-0.0801955\pi$
$5$	3.00000	+	5.19615i	0.268328	+	0.464758i	−0.700102	+	0.714043i	$0.746862\pi$
$6$	−6.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	−8.00000			−0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−6.00000	+	10.3923i	−0.189737	+	0.328634i
$11$	−6.00000	+	10.3923i	−0.164461	+	0.284854i	−0.936464	−	0.350765i	$-0.885922\pi$
$11$	−6.00000	+	10.3923i	−0.164461	+	0.284854i	0.772003	+	0.635619i	$0.219255\pi$
$12$	−6.00000	−	10.3923i	−0.144338	−	0.250000i
$13$	−38.0000			−0.810716			−0.405358	−	0.914158i	$-0.632853\pi$
$13$	−38.0000			−0.810716			−0.405358	+	0.914158i	$0.632853\pi$
$14$		0			0
$15$	−18.0000			−0.309839
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−63.0000	+	109.119i	−0.898808	+	1.55678i	−0.0697893	+	0.997562i	$0.522233\pi$
$17$	−63.0000	+	109.119i	−0.898808	+	1.55678i	−0.829019	+	0.559220i	$0.811101\pi$
$18$	9.00000	−	15.5885i	0.117851	−	0.204124i
$19$	10.0000	+	17.3205i	0.120745	+	0.209137i	0.920062	−	0.391773i	$-0.128138\pi$
$19$	10.0000	+	17.3205i	0.120745	+	0.209137i	−0.799317	+	0.600910i	$0.794805\pi$
$20$	−24.0000			−0.268328
$21$		0			0
$22$	−24.0000			−0.232583
$23$	−84.0000	−	145.492i	−0.761531	−	1.31901i	−0.942061	−	0.335441i	$-0.891115\pi$
$23$	−84.0000	−	145.492i	−0.761531	−	1.31901i	0.180530	−	0.983569i	$-0.442219\pi$
$24$	12.0000	−	20.7846i	0.102062	−	0.176777i
$25$	44.5000	−	77.0763i	0.356000	−	0.616610i
$26$	−38.0000	−	65.8179i	−0.286631	−	0.496460i
$27$	27.0000			0.192450
$28$		0			0
$29$	30.0000			0.192099			0.0960493	−	0.995377i	$-0.469379\pi$
$29$	30.0000			0.192099			0.0960493	+	0.995377i	$0.469379\pi$
$30$	−18.0000	−	31.1769i	−0.109545	−	0.189737i
$31$	−44.0000	+	76.2102i	−0.254924	+	0.441541i	−0.964875	−	0.262710i	$-0.915384\pi$
$31$	−44.0000	+	76.2102i	−0.254924	+	0.441541i	0.709951	+	0.704251i	$0.248717\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	−18.0000	−	31.1769i	−0.0949514	−	0.164461i
$34$	−252.000			−1.27111
$35$		0			0
$36$	36.0000			0.166667
$37$	−127.000	−	219.970i	−0.564288	−	0.977376i	−0.997115	−	0.0758992i	$-0.975817\pi$
$37$	−127.000	−	219.970i	−0.564288	−	0.977376i	0.432827	−	0.901477i	$-0.357516\pi$
$38$	−20.0000	+	34.6410i	−0.0853797	+	0.147882i
$39$	57.0000	−	98.7269i	0.234033	−	0.405358i
$40$	−24.0000	−	41.5692i	−0.0948683	−	0.164317i
$41$	−42.0000			−0.159983			−0.0799914	−	0.996796i	$-0.525489\pi$
$41$	−42.0000			−0.159983			−0.0799914	+	0.996796i	$0.525489\pi$
$42$		0			0
$43$	−52.0000			−0.184417			−0.0922084	−	0.995740i	$-0.529393\pi$
$43$	−52.0000			−0.184417			−0.0922084	+	0.995740i	$0.529393\pi$
$44$	−24.0000	−	41.5692i	−0.0822304	−	0.142427i
$45$	27.0000	−	46.7654i	0.0894427	−	0.154919i
$46$	168.000	−	290.985i	0.538484	−	0.932681i
$47$	−48.0000	−	83.1384i	−0.148969	−	0.258021i	0.781878	−	0.623431i	$-0.214262\pi$
$47$	−48.0000	−	83.1384i	−0.148969	−	0.258021i	−0.930846	+	0.365410i	$0.880929\pi$
$48$	48.0000			0.144338
$49$		0			0
$50$	178.000			0.503460
$51$	−189.000	−	327.358i	−0.518927	−	0.898808i
$52$	76.0000	−	131.636i	0.202679	−	0.351050i
$53$	−99.0000	+	171.473i	−0.256579	+	0.444408i	−0.965323	−	0.261058i	$-0.915929\pi$
$53$	−99.0000	+	171.473i	−0.256579	+	0.444408i	0.708744	+	0.705466i	$0.249262\pi$
$54$	27.0000	+	46.7654i	0.0680414	+	0.117851i
$55$	−72.0000			−0.176518
$56$		0			0
$57$	−60.0000			−0.139424
$58$	30.0000	+	51.9615i	0.0679171	+	0.117636i
$59$	−330.000	+	571.577i	−0.728175	+	1.26124i	0.229478	+	0.973314i	$0.426298\pi$
$59$	−330.000	+	571.577i	−0.728175	+	1.26124i	−0.957654	+	0.287923i	$0.907035\pi$
$60$	36.0000	−	62.3538i	0.0774597	−	0.134164i
$61$	−269.000	−	465.922i	−0.564622	−	0.977953i	−0.997085	−	0.0763018i	$-0.975689\pi$
$61$	−269.000	−	465.922i	−0.564622	−	0.977953i	0.432463	−	0.901652i	$-0.357645\pi$
$62$	−176.000			−0.360516
$63$		0			0
$64$	64.0000			0.125000
$65$	−114.000	−	197.454i	−0.217538	−	0.376787i
$66$	36.0000	−	62.3538i	0.0671408	−	0.116291i
$67$	−442.000	+	765.566i	−0.805954	+	1.39595i	0.109692	+	0.993966i	$0.465014\pi$
$67$	−442.000	+	765.566i	−0.805954	+	1.39595i	−0.915645	+	0.401987i	$0.868320\pi$
$68$	−252.000	−	436.477i	−0.449404	−	0.778391i
$69$	504.000			0.879340
$70$		0			0
$71$	792.000			1.32385			0.661923	−	0.749572i	$-0.269740\pi$
$71$	792.000			1.32385			0.661923	+	0.749572i	$0.269740\pi$
$72$	36.0000	+	62.3538i	0.0589256	+	0.102062i
$73$	109.000	−	188.794i	0.174760	−	0.302693i	−0.765318	−	0.643652i	$-0.777418\pi$
$73$	109.000	−	188.794i	0.174760	−	0.302693i	0.940078	+	0.340959i	$0.110752\pi$
$74$	254.000	−	439.941i	0.399012	−	0.691109i
$75$	133.500	+	231.229i	0.205537	+	0.356000i
$76$	−80.0000			−0.120745
$77$		0			0
$78$	228.000			0.330973
$79$	260.000	+	450.333i	0.370282	+	0.641347i	0.989609	−	0.143786i	$-0.0459277\pi$
$79$	260.000	+	450.333i	0.370282	+	0.641347i	−0.619327	+	0.785133i	$0.712594\pi$
$80$	48.0000	−	83.1384i	0.0670820	−	0.116190i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−42.0000	−	72.7461i	−0.0565625	−	0.0979691i
$83$	492.000			0.650651			0.325325	−	0.945602i	$-0.394526\pi$
$83$	492.000			0.650651			0.325325	+	0.945602i	$0.394526\pi$
$84$		0			0
$85$	−756.000			−0.964703
$86$	−52.0000	−	90.0666i	−0.0652012	−	0.112932i
$87$	−45.0000	+	77.9423i	−0.0554541	+	0.0960493i
$88$	48.0000	−	83.1384i	0.0581456	−	0.100711i
$89$	405.000	+	701.481i	0.482359	+	0.835470i	0.999795	−	0.0202521i	$-0.00644690\pi$
$89$	405.000	+	701.481i	0.482359	+	0.835470i	−0.517436	+	0.855722i	$0.673114\pi$
$90$	108.000			0.126491
$91$		0			0
$92$	672.000			0.761531
$93$	−132.000	−	228.631i	−0.147180	−	0.254924i
$94$	96.0000	−	166.277i	0.105337	−	0.182448i
$95$	−60.0000	+	103.923i	−0.0647986	+	0.112235i
$96$	48.0000	+	83.1384i	0.0510310	+	0.0883883i
$97$	−1154.00			−1.20795			−0.603974	−	0.797004i	$-0.706417\pi$
$97$	−1154.00			−1.20795			−0.603974	+	0.797004i	$0.706417\pi$
$98$		0			0
$99$	108.000			0.109640
$100$	178.000	+	308.305i	0.178000	+	0.308305i
$101$	−309.000	+	535.204i	−0.304422	+	0.527275i	−0.977133	−	0.212631i	$-0.931797\pi$
$101$	−309.000	+	535.204i	−0.304422	+	0.527275i	0.672710	+	0.739906i	$0.265130\pi$
$102$	378.000	−	654.715i	0.366937	−	0.635554i
$103$	64.0000	+	110.851i	0.0612243	+	0.106044i	0.895013	−	0.446040i	$-0.147166\pi$
$103$	64.0000	+	110.851i	0.0612243	+	0.106044i	−0.833789	+	0.552084i	$0.813833\pi$
$104$	304.000			0.286631
$105$		0			0
$106$	−396.000			−0.362858
$107$	738.000	+	1278.25i	0.666777	+	1.15489i	0.978800	+	0.204817i	$0.0656600\pi$
$107$	738.000	+	1278.25i	0.666777	+	1.15489i	−0.312023	+	0.950075i	$0.601007\pi$
$108$	−54.0000	+	93.5307i	−0.0481125	+	0.0833333i
$109$	−595.000	+	1030.57i	−0.522850	+	0.905603i	0.476796	+	0.879014i	$0.341798\pi$
$109$	−595.000	+	1030.57i	−0.522850	+	0.905603i	−0.999646	+	0.0265892i	$0.991535\pi$
$110$	−72.0000	−	124.708i	−0.0624085	−	0.108095i
$111$	762.000			0.651584
$112$		0			0
$113$	−462.000			−0.384613			−0.192307	−	0.981335i	$-0.561597\pi$
$113$	−462.000			−0.384613			−0.192307	+	0.981335i	$0.561597\pi$
$114$	−60.0000	−	103.923i	−0.0492940	−	0.0853797i
$115$	504.000	−	872.954i	0.408680	−	0.707855i
$116$	−60.0000	+	103.923i	−0.0480247	+	0.0831811i
$117$	171.000	+	296.181i	0.135119	+	0.234033i
$118$	−1320.00			−1.02980
$119$		0			0
$120$	144.000			0.109545
$121$	593.500	+	1027.97i	0.445905	+	0.772331i
$122$	538.000	−	931.843i	0.399248	−	0.691517i
$123$	63.0000	−	109.119i	0.0461831	−	0.0799914i
$124$	−176.000	−	304.841i	−0.127462	−	0.220770i
$125$	1284.00			0.918756
$126$		0			0
$127$	−2536.00			−1.77192			−0.885959	−	0.463763i	$-0.846499\pi$
$127$	−2536.00			−1.77192			−0.885959	+	0.463763i	$0.846499\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	78.0000	−	135.100i	0.0532366	−	0.0922084i
$130$	228.000	−	394.908i	0.153822	−	0.266428i
$131$	1146.00	+	1984.93i	0.764324	+	1.32385i	0.940603	+	0.339508i	$0.110261\pi$
$131$	1146.00	+	1984.93i	0.764324	+	1.32385i	−0.176279	+	0.984340i	$0.556406\pi$
$132$	144.000			0.0949514
$133$		0			0
$134$	−1768.00			−1.13979
$135$	81.0000	+	140.296i	0.0516398	+	0.0894427i
$136$	504.000	−	872.954i	0.317777	−	0.550406i
$137$	363.000	−	628.734i	0.226374	−	0.392091i	−0.730357	−	0.683066i	$-0.760646\pi$
$137$	363.000	−	628.734i	0.226374	−	0.392091i	0.956731	+	0.290975i	$0.0939796\pi$
$138$	504.000	+	872.954i	0.310894	+	0.538484i
$139$	−380.000			−0.231879			−0.115939	−	0.993256i	$-0.536988\pi$
$139$	−380.000			−0.231879			−0.115939	+	0.993256i	$0.536988\pi$
$140$		0			0
$141$	288.000			0.172014
$142$	792.000	+	1371.78i	0.468050	+	0.810687i
$143$	228.000	−	394.908i	0.133331	−	0.230936i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	90.0000	+	155.885i	0.0515455	+	0.0892794i
$146$	436.000			0.247148
$147$		0			0
$148$	1016.00			0.564288
$149$	−795.000	−	1376.98i	−0.437107	−	0.757091i	0.560358	−	0.828251i	$-0.310664\pi$
$149$	−795.000	−	1376.98i	−0.437107	−	0.757091i	−0.997465	+	0.0711590i	$0.977330\pi$
$150$	−267.000	+	462.458i	−0.145336	+	0.251730i
$151$	−1216.00	+	2106.17i	−0.655342	+	1.13509i	0.326466	+	0.945209i	$0.394142\pi$
$151$	−1216.00	+	2106.17i	−0.655342	+	1.13509i	−0.981808	+	0.189877i	$0.939191\pi$
$152$	−80.0000	−	138.564i	−0.0426898	−	0.0739410i
$153$	1134.00			0.599206
$154$		0			0
$155$	−528.000			−0.273613
$156$	228.000	+	394.908i	0.117017	+	0.202679i
$157$	307.000	−	531.740i	0.156059	−	0.270302i	−0.777385	−	0.629025i	$-0.783454\pi$
$157$	307.000	−	531.740i	0.156059	−	0.270302i	0.933444	+	0.358723i	$0.116788\pi$
$158$	−520.000	+	900.666i	−0.261829	+	0.453501i
$159$	−297.000	−	514.419i	−0.148136	−	0.256579i
$160$	192.000			0.0948683
$161$		0			0
$162$	−162.000			−0.0785674
$163$	926.000	+	1603.88i	0.444969	+	0.770709i	0.998050	−	0.0624187i	$-0.0198814\pi$
$163$	926.000	+	1603.88i	0.444969	+	0.770709i	−0.553081	+	0.833127i	$0.686548\pi$
$164$	84.0000	−	145.492i	0.0399957	−	0.0692746i
$165$	108.000	−	187.061i	0.0509563	−	0.0882589i
$166$	492.000	+	852.169i	0.230040	+	0.398441i
$167$	2136.00			0.989752			0.494876	−	0.868964i	$-0.335213\pi$
$167$	2136.00			0.989752			0.494876	+	0.868964i	$0.335213\pi$
$168$		0			0
$169$	−753.000			−0.342740
$170$	−756.000	−	1309.43i	−0.341074	−	0.590757i
$171$	90.0000	−	155.885i	0.0402484	−	0.0697122i
$172$	104.000	−	180.133i	0.0461042	−	0.0798548i
$173$	879.000	+	1522.47i	0.386296	+	0.669084i	0.991948	−	0.126646i	$-0.0404211\pi$
$173$	879.000	+	1522.47i	0.386296	+	0.669084i	−0.605652	+	0.795729i	$0.707088\pi$
$174$	−180.000			−0.0784239
$175$		0			0
$176$	192.000			0.0822304
$177$	−990.000	−	1714.73i	−0.420412	−	0.728175i
$178$	−810.000	+	1402.96i	−0.341079	+	0.590766i
$179$	270.000	−	467.654i	0.112742	−	0.195274i	−0.804133	−	0.594449i	$-0.797370\pi$
$179$	270.000	−	467.654i	0.112742	−	0.195274i	0.916875	+	0.399175i	$0.130703\pi$
$180$	108.000	+	187.061i	0.0447214	+	0.0774597i
$181$	−1982.00			−0.813928			−0.406964	−	0.913444i	$-0.633412\pi$
$181$	−1982.00			−0.813928			−0.406964	+	0.913444i	$0.633412\pi$
$182$		0			0
$183$	1614.00			0.651969
$184$	672.000	+	1163.94i	0.269242	+	0.466341i
$185$	762.000	−	1319.82i	0.302829	−	0.524515i
$186$	264.000	−	457.261i	0.104072	−	0.180258i
$187$	−756.000	−	1309.43i	−0.295637	−	0.512059i
$188$	384.000			0.148969
$189$		0			0
$190$	−240.000			−0.0916391
$191$	1344.00	+	2327.88i	0.509154	+	0.881881i	0.999944	+	0.0106027i	$0.00337499\pi$
$191$	1344.00	+	2327.88i	0.509154	+	0.881881i	−0.490790	+	0.871278i	$0.663292\pi$
$192$	−96.0000	+	166.277i	−0.0360844	+	0.0625000i
$193$	1151.00	−	1993.59i	0.429279	−	0.743533i	−0.567531	−	0.823352i	$-0.692101\pi$
$193$	1151.00	−	1993.59i	0.429279	−	0.743533i	0.996809	+	0.0798198i	$0.0254345\pi$
$194$	−1154.00	−	1998.79i	−0.427074	−	0.739714i
$195$	684.000			0.251191
$196$		0			0
$197$	4374.00			1.58190			0.790951	−	0.611880i	$-0.209586\pi$
$197$	4374.00			1.58190			0.790951	+	0.611880i	$0.209586\pi$
$198$	108.000	+	187.061i	0.0387638	+	0.0671408i
$199$	−800.000	+	1385.64i	−0.284977	+	0.493595i	−0.972604	−	0.232469i	$-0.925319\pi$
$199$	−800.000	+	1385.64i	−0.284977	+	0.493595i	0.687626	+	0.726065i	$0.258653\pi$
$200$	−356.000	+	616.610i	−0.125865	+	0.218005i
$201$	−1326.00	−	2296.70i	−0.465318	−	0.805954i
$202$	−1236.00			−0.430518
$203$		0			0
$204$	1512.00			0.518927
$205$	−126.000	−	218.238i	−0.0429279	−	0.0743533i
$206$	−128.000	+	221.703i	−0.0432921	+	0.0749842i
$207$	−756.000	+	1309.43i	−0.253844	+	0.439670i
$208$	304.000	+	526.543i	0.101339	+	0.175525i
$209$	−240.000			−0.0794313
$210$		0			0
$211$	3332.00			1.08713			0.543565	−	0.839367i	$-0.317074\pi$
$211$	3332.00			1.08713			0.543565	+	0.839367i	$0.317074\pi$
$212$	−396.000	−	685.892i	−0.128290	−	0.222204i
$213$	−1188.00	+	2057.68i	−0.382162	+	0.661923i
$214$	−1476.00	+	2556.51i	−0.471483	+	0.816632i
$215$	−156.000	−	270.200i	−0.0494842	−	0.0857092i
$216$	−216.000			−0.0680414
$217$		0			0
$218$	−2380.00			−0.739422
$219$	327.000	+	566.381i	0.100898	+	0.174760i
$220$	144.000	−	249.415i	0.0441294	−	0.0764344i
$221$	2394.00	−	4146.53i	0.728678	−	1.26211i
$222$	762.000	+	1319.82i	0.230370	+	0.399012i
$223$	−2648.00			−0.795171			−0.397586	−	0.917565i	$-0.630152\pi$
$223$	−2648.00			−0.795171			−0.397586	+	0.917565i	$0.630152\pi$
$224$		0			0
$225$	−801.000			−0.237333
$226$	−462.000	−	800.207i	−0.135981	−	0.235527i
$227$	1122.00	−	1943.36i	0.328061	−	0.568218i	−0.654066	−	0.756437i	$-0.726938\pi$
$227$	1122.00	−	1943.36i	0.328061	−	0.568218i	0.982127	+	0.188220i	$0.0602716\pi$
$228$	120.000	−	207.846i	0.0348561	−	0.0603726i
$229$	−2825.00	−	4893.04i	−0.815202	−	1.41197i	−0.909183	−	0.416397i	$-0.863293\pi$
$229$	−2825.00	−	4893.04i	−0.815202	−	1.41197i	0.0939808	−	0.995574i	$-0.470041\pi$
$230$	2016.00			0.577961
$231$		0			0
$232$	−240.000			−0.0679171
$233$	−2349.00	−	4068.59i	−0.660464	−	1.14396i	−0.980494	−	0.196550i	$-0.937026\pi$
$233$	−2349.00	−	4068.59i	−0.660464	−	1.14396i	0.320030	−	0.947407i	$-0.396307\pi$
$234$	−342.000	+	592.361i	−0.0955438	+	0.165487i
$235$	288.000	−	498.831i	0.0799449	−	0.138469i
$236$	−1320.00	−	2286.31i	−0.364088	−	0.630618i
$237$	−1560.00			−0.427565
$238$		0			0
$239$	−1200.00			−0.324776			−0.162388	−	0.986727i	$-0.551920\pi$
$239$	−1200.00			−0.324776			−0.162388	+	0.986727i	$0.551920\pi$
$240$	144.000	+	249.415i	0.0387298	+	0.0670820i
$241$	−359.000	+	621.806i	−0.0959553	+	0.166199i	−0.910007	−	0.414593i	$-0.863924\pi$
$241$	−359.000	+	621.806i	−0.0959553	+	0.166199i	0.814052	+	0.580793i	$0.197257\pi$
$242$	−1187.00	+	2055.94i	−0.315303	+	0.546120i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	2152.00			0.564622
$245$		0			0
$246$	252.000			0.0653127
$247$	−380.000	−	658.179i	−0.0978900	−	0.169550i
$248$	352.000	−	609.682i	0.0901291	−	0.156108i
$249$	−738.000	+	1278.25i	−0.187827	+	0.325325i
$250$	1284.00	+	2223.95i	0.324829	+	0.562621i
$251$	−6012.00			−1.51185			−0.755924	−	0.654659i	$-0.772812\pi$
$251$	−6012.00			−1.51185			−0.755924	+	0.654659i	$0.772812\pi$
$252$		0			0
$253$	2016.00			0.500968
$254$	−2536.00	−	4392.48i	−0.626468	−	1.08507i
$255$	1134.00	−	1964.15i	0.278486	−	0.482351i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1023.00	−	1771.89i	−0.248300	−	0.430067i	0.714755	−	0.699375i	$-0.246538\pi$
$257$	−1023.00	−	1771.89i	−0.248300	−	0.430067i	−0.963054	+	0.269308i	$0.913205\pi$
$258$	312.000			0.0752879
$259$		0			0
$260$	912.000			0.217538
$261$	−135.000	−	233.827i	−0.0320164	−	0.0554541i
$262$	−2292.00	+	3969.86i	−0.540459	+	0.936102i
$263$	3036.00	−	5258.51i	0.711817	−	1.23290i	−0.252358	−	0.967634i	$-0.581206\pi$
$263$	3036.00	−	5258.51i	0.711817	−	1.23290i	0.964175	−	0.265269i	$-0.0854606\pi$
$264$	144.000	+	249.415i	0.0335704	+	0.0581456i
$265$	−1188.00			−0.275390
$266$		0			0
$267$	−2430.00			−0.556980
$268$	−1768.00	−	3062.27i	−0.402977	−	0.697976i
$269$	−3465.00	+	6001.56i	−0.785371	+	1.36030i	0.143406	+	0.989664i	$0.454194\pi$
$269$	−3465.00	+	6001.56i	−0.785371	+	1.36030i	−0.928777	+	0.370638i	$0.879139\pi$
$270$	−162.000	+	280.592i	−0.0365148	+	0.0632456i
$271$	676.000	+	1170.87i	0.151528	+	0.262454i	0.931789	−	0.362999i	$-0.118247\pi$
$271$	676.000	+	1170.87i	0.151528	+	0.262454i	−0.780261	+	0.625454i	$0.784914\pi$
$272$	2016.00			0.449404
$273$		0			0
$274$	1452.00			0.320141
$275$	534.000	+	924.915i	0.117096	+	0.202816i
$276$	−1008.00	+	1745.91i	−0.219835	+	0.380765i
$277$	593.000	−	1027.11i	0.128628	−	0.222790i	−0.794517	−	0.607241i	$-0.792276\pi$
$277$	593.000	−	1027.11i	0.128628	−	0.222790i	0.923145	+	0.384451i	$0.125609\pi$
$278$	−380.000	−	658.179i	−0.0819816	−	0.141996i
$279$	792.000			0.169949
$280$		0			0
$281$	2442.00			0.518425			0.259213	−	0.965820i	$-0.416537\pi$
$281$	2442.00			0.518425			0.259213	+	0.965820i	$0.416537\pi$
$282$	288.000	+	498.831i	0.0608161	+	0.105337i
$283$	1414.00	−	2449.12i	0.297009	−	0.514435i	−0.678441	−	0.734655i	$-0.737344\pi$
$283$	1414.00	−	2449.12i	0.297009	−	0.514435i	0.975450	+	0.220220i	$0.0706775\pi$
$284$	−1584.00	+	2743.57i	−0.330962	+	0.573242i
$285$	−180.000	−	311.769i	−0.0374115	−	0.0647986i
$286$	912.000			0.188558
$287$		0			0
$288$	−288.000			−0.0589256
$289$	−5481.50	−	9494.24i	−1.11571	−	1.93247i
$290$	−180.000	+	311.769i	−0.0364482	+	0.0631301i
$291$	1731.00	−	2998.18i	0.348705	−	0.603974i
$292$	436.000	+	755.174i	0.0873800	+	0.151347i
$293$	−4758.00			−0.948687			−0.474344	−	0.880340i	$-0.657315\pi$
$293$	−4758.00			−0.948687			−0.474344	+	0.880340i	$0.657315\pi$
$294$		0			0
$295$	−3960.00			−0.781560
$296$	1016.00	+	1759.76i	0.199506	+	0.345555i
$297$	−162.000	+	280.592i	−0.0316505	+	0.0548202i
$298$	1590.00	−	2753.96i	0.309081	−	0.535345i
$299$	3192.00	+	5528.71i	0.617385	+	1.06934i
$300$	−1068.00			−0.205537
$301$		0			0
$302$	−4864.00			−0.926794
$303$	−927.000	−	1605.61i	−0.175758	−	0.304422i
$304$	160.000	−	277.128i	0.0301863	−	0.0522842i
$305$	1614.00	−	2795.53i	0.303008	−	0.524825i
$306$	1134.00	+	1964.15i	0.211851	+	0.366937i
$307$	8476.00			1.57574			0.787868	−	0.615844i	$-0.211185\pi$
$307$	8476.00			1.57574			0.787868	+	0.615844i	$0.211185\pi$
$308$		0			0
$309$	−384.000			−0.0706958
$310$	−528.000	−	914.523i	−0.0967367	−	0.167553i
$311$	2316.00	−	4011.43i	0.422278	−	0.731406i	−0.573884	−	0.818936i	$-0.694564\pi$
$311$	2316.00	−	4011.43i	0.422278	−	0.731406i	0.996162	+	0.0875302i	$0.0278974\pi$
$312$	−456.000	+	789.815i	−0.0827433	+	0.143316i
$313$	−2411.00	−	4175.97i	−0.435392	−	0.754122i	0.561935	−	0.827181i	$-0.310057\pi$
$313$	−2411.00	−	4175.97i	−0.435392	−	0.754122i	−0.997328	+	0.0730597i	$0.976724\pi$
$314$	1228.00			0.220701
$315$		0			0
$316$	−2080.00			−0.370282
$317$	1713.00	+	2967.00i	0.303507	+	0.525689i	0.976928	−	0.213570i	$-0.0685091\pi$
$317$	1713.00	+	2967.00i	0.303507	+	0.525689i	−0.673421	+	0.739259i	$0.735176\pi$
$318$	594.000	−	1028.84i	0.104748	−	0.181429i
$319$	−180.000	+	311.769i	−0.0315927	+	0.0547201i
$320$	192.000	+	332.554i	0.0335410	+	0.0580948i
$321$	−4428.00			−0.769928
$322$		0			0
$323$	−2520.00			−0.434107
$324$	−162.000	−	280.592i	−0.0277778	−	0.0481125i
$325$	−1691.00	+	2928.90i	−0.288615	+	0.499895i
$326$	−1852.00	+	3207.76i	−0.314640	+	0.544973i
$327$	−1785.00	−	3091.71i	−0.301868	−	0.522850i
$328$	336.000			0.0565625
$329$		0			0
$330$	432.000			0.0720631
$331$	1394.00	+	2414.48i	0.231484	+	0.400942i	0.958245	−	0.285948i	$-0.0923086\pi$
$331$	1394.00	+	2414.48i	0.231484	+	0.400942i	−0.726761	+	0.686890i	$0.758975\pi$
$332$	−984.000	+	1704.34i	−0.162663	+	0.281740i
$333$	−1143.00	+	1979.73i	−0.188096	+	0.325792i
$334$	2136.00	+	3699.66i	0.349930	+	0.606097i
$335$	−5304.00			−0.865040
$336$		0			0
$337$	434.000			0.0701528			0.0350764	−	0.999385i	$-0.488833\pi$
$337$	434.000			0.0701528			0.0350764	+	0.999385i	$0.488833\pi$
$338$	−753.000	−	1304.23i	−0.121177	−	0.209885i
$339$	693.000	−	1200.31i	0.111028	−	0.192307i
$340$	1512.00	−	2618.86i	0.241176	−	0.417728i
$341$	−528.000	−	914.523i	−0.0838499	−	0.145232i
$342$	360.000			0.0569198
$343$		0			0
$344$	416.000			0.0652012
$345$	1512.00	+	2618.86i	0.235952	+	0.408680i
$346$	−1758.00	+	3044.95i	−0.273152	+	0.473114i
$347$	−3342.00	+	5788.51i	−0.517026	+	0.895515i	0.482779	+	0.875742i	$0.339628\pi$
$347$	−3342.00	+	5788.51i	−0.517026	+	0.895515i	−0.999805	+	0.0197726i	$0.993706\pi$
$348$	−180.000	−	311.769i	−0.0277270	−	0.0480247i
$349$	−2630.00			−0.403383			−0.201692	−	0.979449i	$-0.564644\pi$
$349$	−2630.00			−0.403383			−0.201692	+	0.979449i	$0.564644\pi$
$350$		0			0
$351$	−1026.00			−0.156022
$352$	192.000	+	332.554i	0.0290728	+	0.0503556i
$353$	−3711.00	+	6427.64i	−0.559537	+	0.969147i	0.437998	+	0.898976i	$0.355688\pi$
$353$	−3711.00	+	6427.64i	−0.559537	+	0.969147i	−0.997535	+	0.0701707i	$0.977646\pi$
$354$	1980.00	−	3429.46i	0.297276	−	0.514898i
$355$	2376.00	+	4115.35i	0.355225	+	0.615268i
$356$	−3240.00			−0.482359
$357$		0			0
$358$	1080.00			0.159441
$359$	5220.00	+	9041.31i	0.767412	+	1.32920i	0.938962	+	0.344022i	$0.111789\pi$
$359$	5220.00	+	9041.31i	0.767412	+	1.32920i	−0.171549	+	0.985176i	$0.554877\pi$
$360$	−216.000	+	374.123i	−0.0316228	+	0.0547723i
$361$	3229.50	−	5593.66i	0.470841	−	0.815521i
$362$	−1982.00	−	3432.92i	−0.287767	−	0.498427i
$363$	−3561.00			−0.514887
$364$		0			0
$365$	1308.00			0.187572
$366$	1614.00	+	2795.53i	0.230506	+	0.399248i
$367$	5212.00	−	9027.45i	0.741319	−	1.28400i	−0.210575	−	0.977578i	$-0.567534\pi$
$367$	5212.00	−	9027.45i	0.741319	−	1.28400i	0.951895	−	0.306425i	$-0.0991329\pi$
$368$	−1344.00	+	2327.88i	−0.190383	+	0.329753i
$369$	189.000	+	327.358i	0.0266638	+	0.0461831i
$370$	3048.00			0.428265
$371$		0			0
$372$	1056.00			0.147180
$373$	−1639.00	−	2838.83i	−0.227518	−	0.394073i	0.729554	−	0.683923i	$-0.239728\pi$
$373$	−1639.00	−	2838.83i	−0.227518	−	0.394073i	−0.957072	+	0.289851i	$0.906394\pi$
$374$	1512.00	−	2618.86i	0.209047	−	0.362080i
$375$	−1926.00	+	3335.93i	−0.265222	+	0.459378i
$376$	384.000	+	665.108i	0.0526683	+	0.0912242i
$377$	−1140.00			−0.155737
$378$		0			0
$379$	6140.00			0.832165			0.416083	−	0.909327i	$-0.363403\pi$
$379$	6140.00			0.832165			0.416083	+	0.909327i	$0.363403\pi$
$380$	−240.000	−	415.692i	−0.0323993	−	0.0561173i
$381$	3804.00	−	6588.72i	0.511509	−	0.885959i
$382$	−2688.00	+	4655.75i	−0.360026	+	0.623584i
$383$	−1536.00	−	2660.43i	−0.204924	−	0.354939i	0.745184	−	0.666858i	$-0.232361\pi$
$383$	−1536.00	−	2660.43i	−0.204924	−	0.354939i	−0.950109	+	0.311919i	$0.899028\pi$
$384$	−384.000			−0.0510310
$385$		0			0
$386$	4604.00			0.607092
$387$	234.000	+	405.300i	0.0307361	+	0.0532366i
$388$	2308.00	−	3997.57i	0.301987	−	0.523057i
$389$	−3075.00	+	5326.06i	−0.400794	+	0.694195i	−0.993822	−	0.110987i	$-0.964599\pi$
$389$	−3075.00	+	5326.06i	−0.400794	+	0.694195i	0.593028	+	0.805182i	$0.297932\pi$
$390$	684.000	+	1184.72i	0.0888095	+	0.153822i
$391$	21168.0			2.73788
$392$		0			0
$393$	−6876.00			−0.882566
$394$	4374.00	+	7575.99i	0.559287	+	0.968713i
$395$	−1560.00	+	2702.00i	−0.198714	+	0.344183i
$396$	−216.000	+	374.123i	−0.0274101	+	0.0474757i
$397$	−53.0000	−	91.7987i	−0.00670024	−	0.0116051i	0.862656	−	0.505791i	$-0.168799\pi$
$397$	−53.0000	−	91.7987i	−0.00670024	−	0.0116051i	−0.869356	+	0.494186i	$0.835466\pi$
$398$	−3200.00			−0.403019
$399$		0			0
$400$	−1424.00			−0.178000
$401$	879.000	+	1522.47i	0.109464	+	0.189598i	0.915553	−	0.402197i	$-0.131753\pi$
$401$	879.000	+	1522.47i	0.109464	+	0.189598i	−0.806089	+	0.591794i	$0.798420\pi$
$402$	2652.00	−	4593.40i	0.329029	−	0.569895i
$403$	1672.00	−	2895.99i	0.206671	−	0.357964i
$404$	−1236.00	−	2140.81i	−0.152211	−	0.263637i
$405$	−486.000			−0.0596285
$406$		0			0
$407$	3048.00			0.371213
$408$	1512.00	+	2618.86i	0.183469	+	0.317777i
$409$	−1835.00	+	3178.31i	−0.221846	+	0.384248i	−0.955368	−	0.295417i	$-0.904541\pi$
$409$	−1835.00	+	3178.31i	−0.221846	+	0.384248i	0.733523	+	0.679665i	$0.237875\pi$
$410$	252.000	−	436.477i	0.0303546	−	0.0525757i
$411$	1089.00	+	1886.20i	0.130697	+	0.226374i
$412$	−512.000			−0.0612243
$413$		0			0
$414$	−3024.00			−0.358989
$415$	1476.00	+	2556.51i	0.174588	+	0.302395i
$416$	−608.000	+	1053.09i	−0.0716578	+	0.124115i
$417$	570.000	−	987.269i	0.0669377	−	0.115939i
$418$	−240.000	−	415.692i	−0.0280832	−	0.0486416i
$419$	9660.00			1.12631			0.563153	−	0.826353i	$-0.309588\pi$
$419$	9660.00			1.12631			0.563153	+	0.826353i	$0.309588\pi$
$420$		0			0
$421$	8462.00			0.979602			0.489801	−	0.871834i	$-0.337069\pi$
$421$	8462.00			0.979602			0.489801	+	0.871834i	$0.337069\pi$
$422$	3332.00	+	5771.19i	0.384358	+	0.665728i
$423$	−432.000	+	748.246i	−0.0496562	+	0.0860070i
$424$	792.000	−	1371.78i	0.0907144	−	0.157122i
$425$	5607.00	+	9711.61i	0.639952	+	1.10843i
$426$	−4752.00			−0.540458
$427$		0			0
$428$	−5904.00			−0.666777
$429$	684.000	+	1184.72i	0.0769786	+	0.133331i
$430$	312.000	−	540.400i	0.0349906	−	0.0606056i
$431$	−4896.00	+	8480.12i	−0.547174	+	0.947733i	0.451293	+	0.892376i	$0.350963\pi$
$431$	−4896.00	+	8480.12i	−0.547174	+	0.947733i	−0.998467	+	0.0553572i	$0.982370\pi$
$432$	−216.000	−	374.123i	−0.0240563	−	0.0416667i
$433$	7342.00			0.814859			0.407430	−	0.913237i	$-0.366425\pi$
$433$	7342.00			0.814859			0.407430	+	0.913237i	$0.366425\pi$
$434$		0			0
$435$	−540.000			−0.0595196
$436$	−2380.00	−	4122.28i	−0.261425	−	0.452801i
$437$	1680.00	−	2909.85i	0.183902	−	0.318528i
$438$	−654.000	+	1132.76i	−0.0713455	+	0.123574i
$439$	5320.00	+	9214.51i	0.578382	+	1.00179i	0.995665	+	0.0930106i	$0.0296491\pi$
$439$	5320.00	+	9214.51i	0.578382	+	1.00179i	−0.417283	+	0.908777i	$0.637018\pi$
$440$	576.000			0.0624085
$441$		0			0
$442$	9576.00			1.03051
$443$	8706.00	+	15079.2i	0.933712	+	1.61724i	0.776914	+	0.629606i	$0.216784\pi$
$443$	8706.00	+	15079.2i	0.933712	+	1.61724i	0.156798	+	0.987631i	$0.449883\pi$
$444$	−1524.00	+	2639.65i	−0.162896	+	0.282144i
$445$	−2430.00	+	4208.88i	−0.258861	+	0.448360i
$446$	−2648.00	−	4586.47i	−0.281136	−	0.486941i
$447$	4770.00			0.504728
$448$		0			0
$449$	−1710.00			−0.179732			−0.0898662	−	0.995954i	$-0.528644\pi$
$449$	−1710.00			−0.179732			−0.0898662	+	0.995954i	$0.528644\pi$
$450$	−801.000	−	1387.37i	−0.0839100	−	0.145336i
$451$	252.000	−	436.477i	0.0263109	−	0.0455718i
$452$	924.000	−	1600.41i	0.0961533	−	0.166542i
$453$	−3648.00	−	6318.52i	−0.378362	−	0.655342i
$454$	4488.00			0.463948
$455$		0			0
$456$	480.000			0.0492940
$457$	323.000	+	559.452i	0.0330619	+	0.0572649i	0.882083	−	0.471094i	$-0.156141\pi$
$457$	323.000	+	559.452i	0.0330619	+	0.0572649i	−0.849021	+	0.528359i	$0.822807\pi$
$458$	5650.00	−	9786.09i	0.576435	−	0.998414i
$459$	−1701.00	+	2946.22i	−0.172976	+	0.299603i
$460$	2016.00	+	3491.81i	0.204340	+	0.353928i
$461$	6018.00			0.607996			0.303998	−	0.952673i	$-0.401678\pi$
$461$	6018.00			0.607996			0.303998	+	0.952673i	$0.401678\pi$
$462$		0			0
$463$	−6712.00			−0.673722			−0.336861	−	0.941554i	$-0.609365\pi$
$463$	−6712.00			−0.673722			−0.336861	+	0.941554i	$0.609365\pi$
$464$	−240.000	−	415.692i	−0.0240123	−	0.0415906i
$465$	792.000	−	1371.78i	0.0789852	−	0.136806i
$466$	4698.00	−	8137.17i	0.467019	−	0.808900i
$467$	2682.00	+	4645.36i	0.265756	+	0.460303i	0.967761	−	0.251868i	$-0.0810450\pi$
$467$	2682.00	+	4645.36i	0.265756	+	0.460303i	−0.702005	+	0.712172i	$0.747712\pi$
$468$	−1368.00			−0.135119
$469$		0			0
$470$	1152.00			0.113059
$471$	921.000	+	1595.22i	0.0901007	+	0.156059i
$472$	2640.00	−	4572.61i	0.257449	−	0.445914i
$473$	312.000	−	540.400i	0.0303293	−	0.0525319i
$474$	−1560.00	−	2702.00i	−0.151167	−	0.261829i
$475$	1780.00			0.171941
$476$		0			0
$477$	1782.00			0.171053
$478$	−1200.00	−	2078.46i	−0.114826	−	0.198884i
$479$	4920.00	−	8521.69i	0.469312	−	0.812873i	−0.530072	−	0.847952i	$-0.677835\pi$
$479$	4920.00	−	8521.69i	0.469312	−	0.812873i	0.999385	+	0.0350799i	$0.0111686\pi$
$480$	−288.000	+	498.831i	−0.0273861	+	0.0474342i
$481$	4826.00	+	8358.88i	0.457477	+	0.792374i
$482$	−1436.00			−0.135701
$483$		0			0
$484$	−4748.00			−0.445905
$485$	−3462.00	−	5996.36i	−0.324126	−	0.561403i
$486$	243.000	−	420.888i	0.0226805	−	0.0392837i
$487$	−712.000	+	1233.22i	−0.0662501	+	0.114749i	−0.897248	−	0.441527i	$-0.854437\pi$
$487$	−712.000	+	1233.22i	−0.0662501	+	0.114749i	0.830998	+	0.556276i	$0.187770\pi$
$488$	2152.00	+	3727.37i	0.199624	+	0.345759i
$489$	−5556.00			−0.513806
$490$		0			0
$491$	−4548.00			−0.418021			−0.209011	−	0.977913i	$-0.567024\pi$
$491$	−4548.00			−0.418021			−0.209011	+	0.977913i	$0.567024\pi$
$492$	252.000	+	436.477i	0.0230915	+	0.0399957i
$493$	−1890.00	+	3273.58i	−0.172660	+	0.299056i
$494$	760.000	−	1316.36i	0.0692187	−	0.119890i
$495$	324.000	+	561.184i	0.0294196	+	0.0509563i
$496$	1408.00			0.127462
$497$		0			0
$498$	−2952.00			−0.265627
$499$	−3250.00	−	5629.17i	−0.291563	−	0.505002i	0.682616	−	0.730777i	$-0.260842\pi$
$499$	−3250.00	−	5629.17i	−0.291563	−	0.505002i	−0.974180	+	0.225775i	$0.927509\pi$
$500$	−2568.00	+	4447.91i	−0.229689	+	0.397833i
$501$	−3204.00	+	5549.49i	−0.285717	+	0.494876i
$502$	−6012.00	−	10413.1i	−0.534519	−	0.925815i
$503$	−12168.0			−1.07862			−0.539308	−	0.842108i	$-0.681314\pi$
$503$	−12168.0			−1.07862			−0.539308	+	0.842108i	$0.681314\pi$
$504$		0			0
$505$	−3708.00			−0.326740
$506$	2016.00	+	3491.81i	0.177119	+	0.306779i
$507$	1129.50	−	1956.35i	0.0989405	−	0.171370i
$508$	5072.00	−	8784.96i	0.442980	−	0.767263i
$509$	−10545.0	−	18264.5i	−0.918269	−	1.59049i	−0.802043	−	0.597266i	$-0.796254\pi$
$509$	−10545.0	−	18264.5i	−0.918269	−	1.59049i	−0.116226	−	0.993223i	$-0.537080\pi$
$510$	4536.00			0.393838
$511$		0			0
$512$	−512.000			−0.0441942
$513$	270.000	+	467.654i	0.0232374	+	0.0402484i
$514$	2046.00	−	3543.78i	0.175574	−	0.304104i
$515$	−384.000	+	665.108i	−0.0328564	+	0.0569090i
$516$	312.000	+	540.400i	0.0266183	+	0.0461042i
$517$	1152.00			0.0979979
$518$		0			0
$519$	−5274.00			−0.446056
$520$	912.000	+	1579.63i	0.0769112	+	0.133214i
$521$	−2619.00	+	4536.24i	−0.220231	+	0.381452i	−0.954878	−	0.296998i	$-0.904015\pi$
$521$	−2619.00	+	4536.24i	−0.220231	+	0.381452i	0.734647	+	0.678450i	$0.237348\pi$
$522$	270.000	−	467.654i	0.0226390	−	0.0392120i
$523$	4294.00	+	7437.43i	0.359012	+	0.621828i	0.987796	−	0.155752i	$-0.0497802\pi$
$523$	4294.00	+	7437.43i	0.359012	+	0.621828i	−0.628784	+	0.777580i	$0.716447\pi$
$524$	−9168.00			−0.764324
$525$		0			0
$526$	12144.0			1.00666
$527$	−5544.00	−	9602.49i	−0.458255	−	0.793721i
$528$	−288.000	+	498.831i	−0.0237379	+	0.0411152i
$529$	−8028.50	+	13905.8i	−0.659859	+	1.14291i
$530$	−1188.00	−	2057.68i	−0.0973649	−	0.168641i
$531$	5940.00			0.485450
$532$		0			0
$533$	1596.00			0.129701
$534$	−2430.00	−	4208.88i	−0.196922	−	0.341079i
$535$	−4428.00	+	7669.52i	−0.357830	+	0.619780i
$536$	3536.00	−	6124.53i	0.284948	−	0.493544i
$537$	810.000	+	1402.96i	0.0650914	+	0.112742i
$538$	−13860.0			−1.11068
$539$		0			0
$540$	−648.000			−0.0516398
$541$	−1531.00	−	2651.77i	−0.121669	−	0.210737i	0.798757	−	0.601654i	$-0.205491\pi$
$541$	−1531.00	−	2651.77i	−0.121669	−	0.210737i	−0.920426	+	0.390917i	$0.872158\pi$
$542$	−1352.00	+	2341.73i	−0.107146	+	0.185583i
$543$	2973.00	−	5149.39i	0.234961	−	0.406964i
$544$	2016.00	+	3491.81i	0.158888	+	0.275203i
$545$	−7140.00			−0.561182
$546$		0			0
$547$	−8476.00			−0.662537			−0.331268	−	0.943537i	$-0.607477\pi$
$547$	−8476.00			−0.662537			−0.331268	+	0.943537i	$0.607477\pi$
$548$	1452.00	+	2514.94i	0.113187	+	0.196045i
$549$	−2421.00	+	4193.30i	−0.188207	+	0.325984i
$550$	−1068.00	+	1849.83i	−0.0827994	+	0.143413i
$551$	300.000	+	519.615i	0.0231950	+	0.0401749i
$552$	−4032.00			−0.310894
$553$		0			0
$554$	2372.00			0.181907
$555$	2286.00	+	3959.47i	0.174838	+	0.302829i
$556$	760.000	−	1316.36i	0.0579697	−	0.100407i
$557$	6273.00	−	10865.2i	0.477191	−	0.826520i	−0.522467	−	0.852659i	$-0.674988\pi$
$557$	6273.00	−	10865.2i	0.477191	−	0.826520i	0.999658	+	0.0261400i	$0.00832156\pi$
$558$	792.000	+	1371.78i	0.0600861	+	0.104072i
$559$	1976.00			0.149510
$560$		0			0
$561$	4536.00			0.341373
$562$	2442.00	+	4229.67i	0.183291	+	0.317469i
$563$	−6.00000	+	10.3923i	−0.000449147	+	0.000777946i	−0.866250	−	0.499611i	$-0.833476\pi$
$563$	−6.00000	+	10.3923i	−0.000449147	+	0.000777946i	0.865801	+	0.500389i	$0.166810\pi$
$564$	−576.000	+	997.661i	−0.0430035	+	0.0744843i
$565$	−1386.00	−	2400.62i	−0.103203	−	0.178752i
$566$	5656.00			0.420034
$567$		0			0
$568$	−6336.00			−0.468050
$569$	−9645.00	−	16705.6i	−0.710614	−	1.23082i	−0.964627	−	0.263619i	$-0.915084\pi$
$569$	−9645.00	−	16705.6i	−0.710614	−	1.23082i	0.254013	−	0.967201i	$-0.418249\pi$
$570$	360.000	−	623.538i	0.0264539	−	0.0458196i
$571$	6074.00	−	10520.5i	0.445165	−	0.771048i	−0.552899	−	0.833248i	$-0.686478\pi$
$571$	6074.00	−	10520.5i	0.445165	−	0.771048i	0.998064	+	0.0622005i	$0.0198118\pi$
$572$	912.000	+	1579.63i	0.0666654	+	0.115468i
$573$	−8064.00			−0.587920
$574$		0			0
$575$	−14952.0			−1.08442
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	−5183.00	+	8977.22i	−0.373953	+	0.647706i	−0.990170	−	0.139871i	$-0.955331\pi$
$577$	−5183.00	+	8977.22i	−0.373953	+	0.647706i	0.616216	+	0.787577i	$0.288665\pi$
$578$	10963.0	−	18988.5i	0.788929	−	1.36646i
$579$	3453.00	+	5980.77i	0.247844	+	0.429279i
$580$	−720.000			−0.0515455
$581$		0			0
$582$	6924.00			0.493143
$583$	−1188.00	−	2057.68i	−0.0843944	−	0.146175i
$584$	−872.000	+	1510.35i	−0.0617870	+	0.107018i
$585$	−1026.00	+	1777.08i	−0.0725126	+	0.125596i
$586$	−4758.00	−	8241.10i	−0.335412	−	0.580950i
$587$	−7644.00			−0.537482			−0.268741	−	0.963213i	$-0.586607\pi$
$587$	−7644.00			−0.537482			−0.268741	+	0.963213i	$0.586607\pi$
$588$		0			0
$589$	−1760.00			−0.123123
$590$	−3960.00	−	6858.92i	−0.276323	−	0.478606i
$591$	−6561.00	+	11364.0i	−0.456656	+	0.790951i
$592$	−2032.00	+	3519.53i	−0.141072	+	0.244344i
$593$	4329.00	+	7498.05i	0.299782	+	0.519238i	0.976086	−	0.217385i	$-0.0697527\pi$
$593$	4329.00	+	7498.05i	0.299782	+	0.519238i	−0.676304	+	0.736623i	$0.736419\pi$
$594$	−648.000			−0.0447605
$595$		0			0
$596$	6360.00			0.437107
$597$	−2400.00	−	4156.92i	−0.164532	−	0.284977i
$598$	−6384.00	+	11057.4i	−0.436557	+	0.756139i
$599$	−12900.0	+	22343.5i	−0.879933	+	1.52409i	−0.0285192	+	0.999593i	$0.509079\pi$
$599$	−12900.0	+	22343.5i	−0.879933	+	1.52409i	−0.851414	+	0.524495i	$0.824254\pi$
$600$	−1068.00	−	1849.83i	−0.0726682	−	0.125865i
$601$	−16202.0			−1.09966			−0.549828	−	0.835278i	$-0.685307\pi$
$601$	−16202.0			−1.09966			−0.549828	+	0.835278i	$0.685307\pi$
$602$		0			0
$603$	7956.00			0.537302
$604$	−4864.00	−	8424.70i	−0.327671	−	0.567543i
$605$	−3561.00	+	6167.83i	−0.239298	+	0.414476i
$606$	1854.00	−	3211.22i	0.124280	−	0.215259i
$607$	−12068.0	−	20902.4i	−0.806960	−	1.39770i	−0.914960	−	0.403546i	$-0.867778\pi$
$607$	−12068.0	−	20902.4i	−0.806960	−	1.39770i	0.107999	−	0.994151i	$-0.465556\pi$
$608$	640.000			0.0426898
$609$		0			0
$610$	6456.00			0.428518
$611$	1824.00	+	3159.26i	0.120771	+	0.209182i
$612$	−2268.00	+	3928.29i	−0.149801	+	0.259464i
$613$	2321.00	−	4020.09i	0.152927	−	0.264877i	−0.779375	−	0.626557i	$-0.784463\pi$
$613$	2321.00	−	4020.09i	0.152927	−	0.264877i	0.932302	+	0.361680i	$0.117797\pi$
$614$	8476.00	+	14680.9i	0.557107	+	0.964937i
$615$	756.000			0.0495689
$616$		0			0
$617$	−6726.00			−0.438863			−0.219432	−	0.975628i	$-0.570420\pi$
$617$	−6726.00			−0.438863			−0.219432	+	0.975628i	$0.570420\pi$
$618$	−384.000	−	665.108i	−0.0249947	−	0.0432921i
$619$	−10610.0	+	18377.1i	−0.688937	+	1.19327i	0.283245	+	0.959047i	$0.408589\pi$
$619$	−10610.0	+	18377.1i	−0.688937	+	1.19327i	−0.972182	+	0.234226i	$0.924744\pi$
$620$	1056.00	−	1829.05i	0.0684032	−	0.118478i
$621$	−2268.00	−	3928.29i	−0.146557	−	0.253844i
$622$	9264.00			0.597191
$623$		0			0
$624$	−1824.00			−0.117017
$625$	−1710.50	−	2962.67i	−0.109472	−	0.189611i
$626$	4822.00	−	8351.95i	0.307869	−	0.533244i
$627$	360.000	−	623.538i	0.0229298	−	0.0397157i
$628$	1228.00	+	2126.96i	0.0780295	+	0.135151i
$629$	32004.0			2.02875
$630$		0			0
$631$	29792.0			1.87956			0.939779	−	0.341783i	$-0.111031\pi$
$631$	29792.0			1.87956			0.939779	+	0.341783i	$0.111031\pi$
$632$	−2080.00	−	3602.67i	−0.130914	−	0.226751i
$633$	−4998.00	+	8656.79i	−0.313827	+	0.543565i
$634$	−3426.00	+	5934.01i	−0.214612	+	0.371718i
$635$	−7608.00	−	13177.4i	−0.475456	−	0.823513i
$636$	2376.00			0.148136
$637$		0			0
$638$	−720.000			−0.0446788
$639$	−3564.00	−	6173.03i	−0.220641	−	0.382162i
$640$	−384.000	+	665.108i	−0.0237171	+	0.0410792i
$641$	5079.00	−	8797.09i	0.312962	−	0.542066i	−0.666040	−	0.745916i	$-0.732012\pi$
$641$	5079.00	−	8797.09i	0.312962	−	0.542066i	0.979002	+	0.203850i	$0.0653455\pi$
$642$	−4428.00	−	7669.52i	−0.272211	−	0.471483i
$643$	−29828.0			−1.82940			−0.914698	−	0.404138i	$-0.867571\pi$
$643$	−29828.0			−1.82940			−0.914698	+	0.404138i	$0.867571\pi$
$644$		0			0
$645$	936.000			0.0571395
$646$	−2520.00	−	4364.77i	−0.153480	−	0.265835i
$647$	972.000	−	1683.55i	0.0590622	−	0.102299i	−0.834982	−	0.550277i	$-0.814522\pi$
$647$	972.000	−	1683.55i	0.0590622	−	0.102299i	0.894045	+	0.447978i	$0.147856\pi$
$648$	324.000	−	561.184i	0.0196419	−	0.0340207i
$649$	−3960.00	−	6858.92i	−0.239512	−	0.414848i
$650$	−6764.00			−0.408163
$651$		0			0
$652$	−7408.00			−0.444969
$653$	−13359.0	−	23138.5i	−0.800579	−	1.38664i	−0.919236	−	0.393708i	$-0.871192\pi$
$653$	−13359.0	−	23138.5i	−0.800579	−	1.38664i	0.118657	−	0.992935i	$-0.462141\pi$
$654$	3570.00	−	6183.42i	0.213453	−	0.369711i
$655$	−6876.00	+	11909.6i	−0.410179	+	0.710452i
$656$	336.000	+	581.969i	0.0199979	+	0.0346373i
$657$	−1962.00			−0.116507
$658$		0			0
$659$	4260.00			0.251815			0.125907	−	0.992042i	$-0.459816\pi$
$659$	4260.00			0.251815			0.125907	+	0.992042i	$0.459816\pi$
$660$	432.000	+	748.246i	0.0254781	+	0.0441294i
$661$	11431.0	−	19799.1i	0.672639	−	1.16504i	−0.304514	−	0.952508i	$-0.598494\pi$
$661$	11431.0	−	19799.1i	0.672639	−	1.16504i	0.977153	−	0.212537i	$-0.0681726\pi$
$662$	−2788.00	+	4828.96i	−0.163684	+	0.283509i
$663$	7182.00	+	12439.6i	0.420703	+	0.728678i
$664$	−3936.00			−0.230040
$665$		0			0
$666$	−4572.00			−0.266008
$667$	−2520.00	−	4364.77i	−0.146289	−	0.253380i
$668$	−4272.00	+	7399.32i	−0.247438	+	0.428575i
$669$	3972.00	−	6879.71i	0.229546	−	0.397586i
$670$	−5304.00	−	9186.80i	−0.305838	−	0.529727i
$671$	6456.00			0.371432
$672$		0			0
$673$	−32542.0			−1.86390			−0.931948	−	0.362592i	$-0.881892\pi$
$673$	−32542.0			−1.86390			−0.931948	+	0.362592i	$0.881892\pi$
$674$	434.000	+	751.710i	0.0248028	+	0.0429596i
$675$	1201.50	−	2081.06i	0.0685122	−	0.118667i
$676$	1506.00	−	2608.47i	0.0856850	−	0.148411i
$677$	7107.00	+	12309.7i	0.403463	+	0.698818i	0.994141	−	0.108089i	$-0.0344732\pi$
$677$	7107.00	+	12309.7i	0.403463	+	0.698818i	−0.590679	+	0.806907i	$0.701140\pi$
$678$	2772.00			0.157018
$679$		0			0
$680$	6048.00			0.341074
$681$	3366.00	+	5830.08i	0.189406	+	0.328061i
$682$	1056.00	−	1829.05i	0.0592908	−	0.102695i
$683$	3546.00	−	6141.85i	0.198659	−	0.344087i	−0.749435	−	0.662078i	$-0.769675\pi$
$683$	3546.00	−	6141.85i	0.198659	−	0.344087i	0.948094	+	0.317991i	$0.103008\pi$
$684$	360.000	+	623.538i	0.0201242	+	0.0348561i
$685$	4356.00			0.242970
$686$		0			0
$687$	16950.0			0.941314
$688$	416.000	+	720.533i	0.0230521	+	0.0399274i
$689$	3762.00	−	6515.98i	0.208013	−	0.360289i
$690$	−3024.00	+	5237.72i	−0.166843	+	0.288981i
$691$	−6614.00	−	11455.8i	−0.364122	−	0.630678i	0.624513	−	0.781015i	$-0.285298\pi$
$691$	−6614.00	−	11455.8i	−0.364122	−	0.630678i	−0.988635	+	0.150337i	$0.951964\pi$
$692$	−7032.00			−0.386296
$693$		0			0
$694$	−13368.0			−0.731185
$695$	−1140.00	−	1974.54i	−0.0622197	−	0.107768i
$696$	360.000	−	623.538i	0.0196060	−	0.0339586i
$697$	2646.00	−	4583.01i	0.143794	−	0.249058i
$698$	−2630.00	−	4555.29i	−0.142617	−	0.247021i
$699$	14094.0			0.762638
$700$		0			0
$701$	28062.0			1.51196			0.755982	−	0.654592i	$-0.227160\pi$
$701$	28062.0			1.51196			0.755982	+	0.654592i	$0.227160\pi$
$702$	−1026.00	−	1777.08i	−0.0551622	−	0.0955438i
$703$	2540.00	−	4399.41i	0.136270	−	0.236027i
$704$	−384.000	+	665.108i	−0.0205576	+	0.0356068i
$705$	864.000	+	1496.49i	0.0461562	+	0.0799449i
$706$	−14844.0			−0.791305
$707$		0			0
$708$	7920.00			0.420412
$709$	13625.0	+	23599.2i	0.721717	+	1.25005i	0.960311	+	0.278932i	$0.0899803\pi$
$709$	13625.0	+	23599.2i	0.721717	+	1.25005i	−0.238594	+	0.971120i	$0.576686\pi$
$710$	−4752.00	+	8230.71i	−0.251182	+	0.435060i
$711$	2340.00	−	4053.00i	0.123427	−	0.213782i
$712$	−3240.00	−	5611.84i	−0.170540	−	0.295383i
$713$	14784.0			0.776529
$714$		0			0
$715$	2736.00			0.143106
$716$	1080.00	+	1870.61i	0.0563708	+	0.0976371i
$717$	1800.00	−	3117.69i	0.0937549	−	0.162388i
$718$	−10440.0	+	18082.6i	−0.542643	+	0.939884i
$719$	−7200.00	−	12470.8i	−0.373456	−	0.646844i	0.616639	−	0.787246i	$-0.288494\pi$
$719$	−7200.00	−	12470.8i	−0.373456	−	0.646844i	−0.990095	+	0.140402i	$0.955161\pi$
$720$	−864.000			−0.0447214
$721$		0			0
$722$	12918.0			0.665870
$723$	−1077.00	−	1865.42i	−0.0553998	−	0.0959553i
$724$	3964.00	−	6865.85i	0.203482	−	0.352441i
$725$	1335.00	−	2312.29i	0.0683871	−	0.118450i
$726$	−3561.00	−	6167.83i	−0.182040	−	0.315303i
$727$	−17984.0			−0.917455			−0.458727	−	0.888577i	$-0.651695\pi$
$727$	−17984.0			−0.917455			−0.458727	+	0.888577i	$0.651695\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$	1308.00	+	2265.52i	0.0663168	+	0.114864i
$731$	3276.00	−	5674.20i	0.165755	−	0.287097i
$732$	−3228.00	+	5591.06i	−0.162992	+	0.282311i
$733$	8299.00	+	14374.3i	0.418186	+	0.724320i	0.995757	−	0.0920207i	$-0.0293326\pi$
$733$	8299.00	+	14374.3i	0.418186	+	0.724320i	−0.577571	+	0.816341i	$0.695999\pi$
$734$	20848.0			1.04838
$735$		0			0
$736$	−5376.00			−0.269242
$737$	−5304.00	−	9186.80i	−0.265095	−	0.459159i
$738$	−378.000	+	654.715i	−0.0188542	+	0.0326564i
$739$	−730.000	+	1264.40i	−0.0363376	+	0.0629386i	−0.883622	−	0.468201i	$-0.844902\pi$
$739$	−730.000	+	1264.40i	−0.0363376	+	0.0629386i	0.847285	+	0.531139i	$0.178236\pi$
$740$	3048.00	+	5279.29i	0.151414	+	0.262258i
$741$	2280.00			0.113034
$742$		0			0
$743$	−30072.0			−1.48484			−0.742419	−	0.669936i	$-0.766322\pi$
$743$	−30072.0			−1.48484			−0.742419	+	0.669936i	$0.766322\pi$
$744$	1056.00	+	1829.05i	0.0520361	+	0.0901291i
$745$	4770.00	−	8261.88i	0.234576	−	0.406298i
$746$	3278.00	−	5677.66i	0.160880	−	0.278651i
$747$	−2214.00	−	3834.76i	−0.108442	−	0.187827i
$748$	6048.00			0.295637
$749$		0			0
$750$	−7704.00			−0.375080
$751$	9044.00	+	15664.7i	0.439441	+	0.761134i	0.997646	−	0.0685686i	$-0.0218432\pi$
$751$	9044.00	+	15664.7i	0.439441	+	0.761134i	−0.558205	+	0.829703i	$0.688510\pi$
$752$	−768.000	+	1330.22i	−0.0372421	+	0.0645053i
$753$	9018.00	−	15619.6i	0.436433	−	0.755924i
$754$	−1140.00	−	1974.54i	−0.0550615	−	0.0953693i
$755$	−14592.0			−0.703387
$756$		0			0
$757$	24734.0			1.18755			0.593773	−	0.804633i	$-0.297638\pi$
$757$	24734.0			1.18755			0.593773	+	0.804633i	$0.297638\pi$
$758$	6140.00	+	10634.8i	0.294215	+	0.509595i
$759$	−3024.00	+	5237.72i	−0.144617	+	0.250484i
$760$	480.000	−	831.384i	0.0229098	−	0.0396809i
$761$	−11139.0	−	19293.3i	−0.530602	−	0.919030i	−0.999362	−	0.0357047i	$-0.988632\pi$
$761$	−11139.0	−	19293.3i	−0.530602	−	0.919030i	0.468760	−	0.883326i	$-0.344701\pi$
$762$	15216.0			0.723383
$763$		0			0
$764$	−10752.0			−0.509154
$765$	3402.00	+	5892.44i	0.160784	+	0.278486i
$766$	3072.00	−	5320.86i	0.144903	−	0.250980i
$767$	12540.0	−	21719.9i	0.590343	−	1.02250i
$768$	−384.000	−	665.108i	−0.0180422	−	0.0312500i
$769$	−16130.0			−0.756388			−0.378194	−	0.925726i	$-0.623455\pi$
$769$	−16130.0			−0.756388			−0.378194	+	0.925726i	$0.623455\pi$
$770$		0			0
$771$	6138.00			0.286712
$772$	4604.00	+	7974.36i	0.214639	+	0.371766i
$773$	14859.0	−	25736.5i	0.691386	−	1.19752i	−0.279998	−	0.960000i	$-0.590334\pi$
$773$	14859.0	−	25736.5i	0.691386	−	1.19752i	0.971384	−	0.237515i	$-0.0763327\pi$
$774$	−468.000	+	810.600i	−0.0217337	+	0.0376439i
$775$	3916.00	+	6782.71i	0.181506	+	0.314377i
$776$	9232.00			0.427074
$777$		0			0
$778$	−12300.0			−0.566808
$779$	−420.000	−	727.461i	−0.0193172	−	0.0334583i
$780$	−1368.00	+	2369.45i	−0.0627978	+	0.108769i
$781$	−4752.00	+	8230.71i	−0.217721	+	0.377103i
$782$	21168.0	+	36664.1i	0.967987	+	1.67660i
$783$	810.000			0.0369694
$784$		0			0
$785$	3684.00			0.167500
$786$	−6876.00	−	11909.6i	−0.312034	−	0.540459i
$787$	4762.00	−	8248.03i	0.215689	−	0.373584i	−0.737797	−	0.675023i	$-0.764134\pi$
$787$	4762.00	−	8248.03i	0.215689	−	0.373584i	0.953485	+	0.301439i	$0.0974670\pi$
$788$	−8748.00	+	15152.0i	−0.395475	+	0.684983i
$789$	9108.00	+	15775.5i	0.410968	+	0.711817i
$790$	−6240.00			−0.281024
$791$		0			0
$792$	−864.000			−0.0387638
$793$	10222.0	+	17705.0i	0.457748	+	0.792842i
$794$	106.000	−	183.597i	0.00473778	−	0.00820608i
$795$	1782.00	−	3086.51i	0.0794981	−	0.137695i
$796$	−3200.00	−	5542.56i	−0.142489	−	0.246798i
$797$	33906.0			1.50692			0.753458	−	0.657496i	$-0.228384\pi$
$797$	33906.0			1.50692			0.753458	+	0.657496i	$0.228384\pi$
$798$		0			0
$799$	12096.0			0.535577
$800$	−1424.00	−	2466.44i	−0.0629325	−	0.109002i
$801$	3645.00	−	6313.33i	0.160786	−	0.278490i
$802$	−1758.00	+	3044.95i	−0.0774029	+	0.134066i
$803$	1308.00	+	2265.52i	0.0574823	+	0.0995623i
$804$	10608.0			0.465318
$805$		0			0
$806$	6688.00			0.292276
$807$	−10395.0	−	18004.7i	−0.453434	−	0.785371i
$808$	2472.00	−	4281.63i	0.107630	−	0.186420i
$809$	315.000	−	545.596i	0.0136895	−	0.0237109i	−0.859099	−	0.511809i	$-0.828976\pi$
$809$	315.000	−	545.596i	0.0136895	−	0.0237109i	0.872789	+	0.488098i	$0.162309\pi$
$810$	−486.000	−	841.777i	−0.0210819	−	0.0365148i
$811$	20788.0			0.900081			0.450040	−	0.893008i	$-0.351410\pi$
$811$	20788.0			0.900081			0.450040	+	0.893008i	$0.351410\pi$
$812$		0			0
$813$	−4056.00			−0.174969
$814$	3048.00	+	5279.29i	0.131244	+	0.227321i
$815$	−5556.00	+	9623.27i	−0.238795	+	0.413606i
$816$	−3024.00	+	5237.72i	−0.129732	+	0.224702i
$817$	−520.000	−	900.666i	−0.0222674	−	0.0385683i
$818$	−7340.00			−0.313737
$819$		0			0
$820$	1008.00			0.0429279
$821$	21549.0	+	37324.0i	0.916036	+	1.58662i	0.805378	+	0.592762i	$0.201962\pi$
$821$	21549.0	+	37324.0i	0.916036	+	1.58662i	0.110658	+	0.993859i	$0.464704\pi$
$822$	−2178.00	+	3772.41i	−0.0924166	+	0.160070i
$823$	7136.00	−	12359.9i	0.302242	−	0.523499i	−0.674401	−	0.738365i	$-0.735598\pi$
$823$	7136.00	−	12359.9i	0.302242	−	0.523499i	0.976644	+	0.214866i	$0.0689315\pi$
$824$	−512.000	−	886.810i	−0.0216461	−	0.0374921i
$825$	−3204.00			−0.135211
$826$		0			0
$827$	13644.0			0.573698			0.286849	−	0.957976i	$-0.407392\pi$
$827$	13644.0			0.573698			0.286849	+	0.957976i	$0.407392\pi$
$828$	−3024.00	−	5237.72i	−0.126922	−	0.219835i
$829$	−1205.00	+	2087.12i	−0.0504842	+	0.0874412i	−0.890163	−	0.455642i	$-0.849410\pi$
$829$	−1205.00	+	2087.12i	−0.0504842	+	0.0874412i	0.839679	+	0.543083i	$0.182743\pi$
$830$	−2952.00	+	5113.01i	−0.123452	+	0.213826i
$831$	1779.00	+	3081.32i	0.0742633	+	0.128628i
$832$	−2432.00			−0.101339
$833$		0			0
$834$	2280.00			0.0946642
$835$	6408.00	+	11099.0i	0.265578	+	0.459995i
$836$	480.000	−	831.384i	0.0198578	−	0.0343948i
$837$	−1188.00	+	2057.68i	−0.0490601	+	0.0849746i
$838$	9660.00	+	16731.6i	0.398209	+	0.689718i
$839$	−23160.0			−0.953006			−0.476503	−	0.879173i	$-0.658096\pi$
$839$	−23160.0			−0.953006			−0.476503	+	0.879173i	$0.658096\pi$
$840$		0			0
$841$	−23489.0			−0.963098
$842$	8462.00	+	14656.6i	0.346342	+	0.599882i
$843$	−3663.00	+	6344.50i	−0.149656	+	0.259213i
$844$	−6664.00	+	11542.4i	−0.271782	+	0.470741i
$845$	−2259.00	−	3912.70i	−0.0919668	−	0.159291i
$846$	−1728.00			−0.0702244
$847$		0			0
$848$	3168.00			0.128290
$849$	4242.00	+	7347.36i	0.171478	+	0.297009i
$850$	−11214.0	+	19423.2i	−0.452514	+	0.783777i
$851$	−21336.0	+	36955.0i	−0.859446	+	1.48860i
$852$	−4752.00	−	8230.71i	−0.191081	−	0.330962i
$853$	−32078.0			−1.28761			−0.643804	−	0.765190i	$-0.722645\pi$
$853$	−32078.0			−1.28761			−0.643804	+	0.765190i	$0.722645\pi$
$854$		0			0
$855$	1080.00			0.0431991
$856$	−5904.00	−	10226.0i	−0.235741	−	0.408316i
$857$	−7203.00	+	12476.0i	−0.287106	+	0.497282i	−0.973118	−	0.230308i	$-0.926027\pi$
$857$	−7203.00	+	12476.0i	−0.287106	+	0.497282i	0.686012	+	0.727590i	$0.259360\pi$
$858$	−1368.00	+	2369.45i	−0.0544321	+	0.0942792i
$859$	15310.0	+	26517.7i	0.608115	+	1.05329i	0.991551	+	0.129718i	$0.0414072\pi$
$859$	15310.0	+	26517.7i	0.608115	+	1.05329i	−0.383436	+	0.923567i	$0.625259\pi$
$860$	1248.00			0.0494842
$861$		0			0
$862$	−19584.0			−0.773821
$863$	−8784.00	−	15214.3i	−0.346478	−	0.600118i	0.639143	−	0.769088i	$-0.279289\pi$
$863$	−8784.00	−	15214.3i	−0.346478	−	0.600118i	−0.985621	+	0.168970i	$0.945956\pi$
$864$	432.000	−	748.246i	0.0170103	−	0.0294628i
$865$	−5274.00	+	9134.84i	−0.207308	+	0.359068i
$866$	7342.00	+	12716.7i	0.288096	+	0.498997i
$867$	32889.0			1.28831
$868$		0			0
$869$	−6240.00			−0.243587
$870$	−540.000	−	935.307i	−0.0210434	−	0.0364482i
$871$	16796.0	−	29091.5i	0.653399	−	1.13172i
$872$	4760.00	−	8244.56i	0.184855	−	0.320179i
$873$	5193.00	+	8994.54i	0.201325	+	0.348705i
$874$	6720.00			0.260077
$875$		0			0
$876$	−2616.00			−0.100898
$877$	10853.0	+	18797.9i	0.417879	+	0.723787i	0.995726	−	0.0923577i	$-0.0294403\pi$
$877$	10853.0	+	18797.9i	0.417879	+	0.723787i	−0.577847	+	0.816145i	$0.696107\pi$
$878$	−10640.0	+	18429.0i	−0.408978	+	0.708371i
$879$	7137.00	−	12361.6i	0.273862	−	0.474344i
$880$	576.000	+	997.661i	0.0220647	+	0.0382172i
$881$	14958.0			0.572018			0.286009	−	0.958227i	$-0.407671\pi$
$881$	14958.0			0.572018			0.286009	+	0.958227i	$0.407671\pi$
$882$		0			0
$883$	−32812.0			−1.25052			−0.625261	−	0.780415i	$-0.715008\pi$
$883$	−32812.0			−1.25052			−0.625261	+	0.780415i	$0.715008\pi$
$884$	9576.00	+	16586.1i	0.364339	+	0.631054i
$885$	5940.00	−	10288.4i	0.225617	−	0.390780i
$886$	−17412.0	+	30158.5i	−0.660234	+	1.14356i
$887$	−19428.0	−	33650.3i	−0.735432	−	1.27381i	−0.954533	−	0.298104i	$-0.903646\pi$
$887$	−19428.0	−	33650.3i	−0.735432	−	1.27381i	0.219101	−	0.975702i	$-0.429688\pi$
$888$	−6096.00			−0.230370
$889$		0			0
$890$	−9720.00			−0.366084
$891$	−486.000	−	841.777i	−0.0182734	−	0.0316505i
$892$	5296.00	−	9172.94i	0.198793	−	0.344319i
$893$	960.000	−	1662.77i	0.0359744	−	0.0623096i
$894$	4770.00	+	8261.88i	0.178448	+	0.309081i
$895$	3240.00			0.121007
$896$		0			0
$897$	−19152.0			−0.712895
$898$	−1710.00	−	2961.81i	−0.0635450	−	0.110063i
$899$	−1320.00	+	2286.31i	−0.0489705	+	0.0848194i
$900$	1602.00	−	2774.75i	0.0593333	−	0.102768i
$901$	−12474.0	−	21605.6i	−0.461231	−	0.798876i
$902$	1008.00			0.0372092
$903$		0			0
$904$	3696.00			0.135981
$905$	−5946.00	−	10298.8i	−0.218400	−	0.378279i
$906$	7296.00	−	12637.0i	0.267542	−	0.463397i
$907$	14138.0	−	24487.7i	0.517579	−	0.896474i	−0.482212	−	0.876055i	$-0.660167\pi$
$907$	14138.0	−	24487.7i	0.517579	−	0.896474i	0.999792	−	0.0204194i	$-0.00650015\pi$
$908$	4488.00	+	7773.44i	0.164030	+	0.284109i
$909$	5562.00			0.202948
$910$		0			0
$911$	8112.00			0.295019			0.147510	−	0.989061i	$-0.452874\pi$
$911$	8112.00			0.295019			0.147510	+	0.989061i	$0.452874\pi$
$912$	480.000	+	831.384i	0.0174281	+	0.0301863i
$913$	−2952.00	+	5113.01i	−0.107007	+	0.185341i
$914$	−646.000	+	1118.90i	−0.0233783	+	0.0404924i
$915$	4842.00	+	8386.59i	0.174942	+	0.303008i
$916$	22600.0			0.815202
$917$		0			0
$918$	−6804.00			−0.244625
$919$	13040.0	+	22585.9i	0.468063	+	0.810709i	0.999334	−	0.0364931i	$-0.0116187\pi$
$919$	13040.0	+	22585.9i	0.468063	+	0.810709i	−0.531271	+	0.847202i	$0.678285\pi$
$920$	−4032.00	+	6983.63i	−0.144490	+	0.250265i
$921$	−12714.0	+	22021.3i	−0.454876	+	0.787868i
$922$	6018.00	+	10423.5i	0.214959	+	0.372320i
$923$	−30096.0			−1.07326
$924$		0			0
$925$	−22606.0			−0.803547
$926$	−6712.00	−	11625.5i	−0.238197	−	0.412569i
$927$	576.000	−	997.661i	0.0204081	−	0.0353479i
$928$	480.000	−	831.384i	0.0169793	−	0.0294090i
$929$	24585.0	+	42582.5i	0.868254	+	1.50386i	0.863780	+	0.503870i	$0.168091\pi$
$929$	24585.0	+	42582.5i	0.868254	+	1.50386i	0.00447392	+	0.999990i	$0.498576\pi$
$930$	3168.00			0.111702
$931$		0			0
$932$	18792.0			0.660464
$933$	6948.00	+	12034.3i	0.243802	+	0.422278i
$934$	−5364.00	+	9290.72i	−0.187918	+	0.325484i
$935$	4536.00	−	7856.58i	0.158656	−	0.274800i
$936$	−1368.00	−	2369.45i	−0.0477719	−	0.0827433i
$937$	−48314.0			−1.68447			−0.842236	−	0.539110i	$-0.818761\pi$
$937$	−48314.0			−1.68447			−0.842236	+	0.539110i	$0.818761\pi$
$938$		0			0
$939$	14466.0			0.502748
$940$	1152.00	+	1995.32i	0.0399724	+	0.0692343i
$941$	17391.0	−	30122.1i	0.602477	−	1.04352i	−0.389968	−	0.920828i	$-0.627514\pi$
$941$	17391.0	−	30122.1i	0.602477	−	1.04352i	0.992445	−	0.122692i	$-0.0391526\pi$
$942$	−1842.00	+	3190.44i	−0.0637108	+	0.110350i
$943$	3528.00	+	6110.68i	0.121832	+	0.211019i
$944$	10560.0			0.364088
$945$		0			0
$946$	1248.00			0.0428922
$947$	12558.0	+	21751.1i	0.430919	+	0.746373i	0.996953	−	0.0780087i	$-0.0248562\pi$
$947$	12558.0	+	21751.1i	0.430919	+	0.746373i	−0.566034	+	0.824382i	$0.691523\pi$
$948$	3120.00	−	5404.00i	0.106891	−	0.185141i
$949$	−4142.00	+	7174.15i	−0.141681	+	0.245398i
$950$	1780.00	+	3083.05i	0.0607903	+	0.105292i
$951$	−10278.0			−0.350460
$952$		0			0
$953$	−15462.0			−0.525565			−0.262782	−	0.964855i	$-0.584640\pi$
$953$	−15462.0			−0.525565			−0.262782	+	0.964855i	$0.584640\pi$
$954$	1782.00	+	3086.51i	0.0604763	+	0.104748i
$955$	−8064.00	+	13967.3i	−0.273241	+	0.473267i
$956$	2400.00	−	4156.92i	0.0811941	−	0.140632i
$957$	−540.000	−	935.307i	−0.0182400	−	0.0315927i
$958$	19680.0			0.663708
$959$		0			0
$960$	−1152.00			−0.0387298
$961$	11023.5	+	19093.3i	0.370028	+	0.640907i
$962$	−9652.00	+	16717.8i	−0.323485	+	0.560293i
$963$	6642.00	−	11504.3i	0.222259	−	0.384964i
$964$	−1436.00	−	2487.22i	−0.0479776	−	0.0830997i
$965$	13812.0			0.460750
$966$		0			0
$967$	−736.000			−0.0244759			−0.0122379	−	0.999925i	$-0.503896\pi$
$967$	−736.000			−0.0244759			−0.0122379	+	0.999925i	$0.503896\pi$
$968$	−4748.00	−	8223.78i	−0.157651	−	0.273060i
$969$	3780.00	−	6547.15i	0.125316	−	0.217053i
$970$	6924.00	−	11992.7i	0.229192	−	0.396972i
$971$	−14634.0	−	25346.8i	−0.483653	−	0.837712i	0.516170	−	0.856486i	$-0.327357\pi$
$971$	−14634.0	−	25346.8i	−0.483653	−	0.837712i	−0.999824	+	0.0187737i	$0.994024\pi$
$972$	972.000			0.0320750
$973$		0			0
$974$	−2848.00			−0.0936918
$975$	−5073.00	−	8786.69i	−0.166632	−	0.288615i
$976$	−4304.00	+	7454.75i	−0.141155	+	0.244488i
$977$	−8337.00	+	14440.1i	−0.273003	+	0.472856i	−0.969629	−	0.244579i	$-0.921350\pi$
$977$	−8337.00	+	14440.1i	−0.273003	+	0.472856i	0.696626	+	0.717434i	$0.254684\pi$
$978$	−5556.00	−	9623.27i	−0.181658	−	0.314640i
$979$	−9720.00			−0.317316
$980$		0			0
$981$	10710.0			0.348567
$982$	−4548.00	−	7877.37i	−0.147793	−	0.255985i
$983$	−15636.0	+	27082.3i	−0.507336	+	0.878731i	0.492628	+	0.870240i	$0.336036\pi$
$983$	−15636.0	+	27082.3i	−0.507336	+	0.878731i	−0.999964	+	0.00849130i	$0.997297\pi$
$984$	−504.000	+	872.954i	−0.0163282	+	0.0282812i
$985$	13122.0	+	22728.0i	0.424469	+	0.735201i
$986$	−7560.00			−0.244178
$987$		0			0
$988$	3040.00			0.0978900
$989$	4368.00	+	7565.60i	0.140439	+	0.243248i
$990$	−648.000	+	1122.37i	−0.0208028	+	0.0360315i
$991$	7964.00	−	13794.1i	0.255282	−	0.442162i	−0.709690	−	0.704514i	$-0.751165\pi$
$991$	7964.00	−	13794.1i	0.255282	−	0.442162i	0.964972	+	0.262352i	$0.0844982\pi$
$992$	1408.00	+	2438.73i	0.0450646	+	0.0780541i
$993$	−8364.00			−0.267295
$994$		0			0
$995$	−9600.00			−0.305870
$996$	−2952.00	−	5113.01i	−0.0939134	−	0.162663i
$997$	21007.0	−	36385.2i	0.667300	−	1.15580i	−0.311356	−	0.950293i	$-0.600783\pi$
$997$	21007.0	−	36385.2i	0.667300	−	1.15580i	0.978656	−	0.205505i	$-0.0658835\pi$
$998$	6500.00	−	11258.3i	0.206166	−	0.357090i
$999$	−3429.00	−	5939.20i	−0.108597	−	0.188096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.4.e.g.67.1		2
3.2	odd	2		882.4.g.f.361.1		2
7.2	even	3	inner	294.4.e.g.79.1		2
7.3	odd	6		6.4.a.a.1.1	✓	1
7.4	even	3		294.4.a.e.1.1		1
7.5	odd	6		294.4.e.h.79.1		2
7.6	odd	2		294.4.e.h.67.1		2
21.2	odd	6		882.4.g.f.667.1		2
21.5	even	6		882.4.g.i.667.1		2
21.11	odd	6		882.4.a.n.1.1		1
21.17	even	6		18.4.a.a.1.1		1
21.20	even	2		882.4.g.i.361.1		2
28.3	even	6		48.4.a.c.1.1		1
28.11	odd	6		2352.4.a.e.1.1		1
35.3	even	12		150.4.c.d.49.2		2
35.17	even	12		150.4.c.d.49.1		2
35.24	odd	6		150.4.a.i.1.1		1
56.3	even	6		192.4.a.c.1.1		1
56.45	odd	6		192.4.a.i.1.1		1
63.31	odd	6		162.4.c.f.55.1		2
63.38	even	6		162.4.c.c.109.1		2
63.52	odd	6		162.4.c.f.109.1		2
63.59	even	6		162.4.c.c.55.1		2
77.10	even	6		726.4.a.f.1.1		1
84.59	odd	6		144.4.a.c.1.1		1
91.31	even	12		1014.4.b.d.337.2		2
91.38	odd	6		1014.4.a.g.1.1		1
91.73	even	12		1014.4.b.d.337.1		2
105.17	odd	12		450.4.c.e.199.2		2
105.38	odd	12		450.4.c.e.199.1		2
105.59	even	6		450.4.a.h.1.1		1
112.3	even	12		768.4.d.c.385.2		2
112.45	odd	12		768.4.d.n.385.1		2
112.59	even	12		768.4.d.c.385.1		2
112.101	odd	12		768.4.d.n.385.2		2
119.101	odd	6		1734.4.a.d.1.1		1
133.94	even	6		2166.4.a.i.1.1		1
140.3	odd	12		1200.4.f.j.49.2		2
140.59	even	6		1200.4.a.b.1.1		1
140.87	odd	12		1200.4.f.j.49.1		2
168.59	odd	6		576.4.a.r.1.1		1
168.101	even	6		576.4.a.q.1.1		1
231.164	odd	6		2178.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.4.a.a.1.1	✓	1	7.3	odd	6
18.4.a.a.1.1		1	21.17	even	6
48.4.a.c.1.1		1	28.3	even	6
144.4.a.c.1.1		1	84.59	odd	6
150.4.a.i.1.1		1	35.24	odd	6
150.4.c.d.49.1		2	35.17	even	12
150.4.c.d.49.2		2	35.3	even	12
162.4.c.c.55.1		2	63.59	even	6
162.4.c.c.109.1		2	63.38	even	6
162.4.c.f.55.1		2	63.31	odd	6
162.4.c.f.109.1		2	63.52	odd	6
192.4.a.c.1.1		1	56.3	even	6
192.4.a.i.1.1		1	56.45	odd	6
294.4.a.e.1.1		1	7.4	even	3
294.4.e.g.67.1		2	1.1	even	1	trivial
294.4.e.g.79.1		2	7.2	even	3	inner
294.4.e.h.67.1		2	7.6	odd	2
294.4.e.h.79.1		2	7.5	odd	6
450.4.a.h.1.1		1	105.59	even	6
450.4.c.e.199.1		2	105.38	odd	12
450.4.c.e.199.2		2	105.17	odd	12
576.4.a.q.1.1		1	168.101	even	6
576.4.a.r.1.1		1	168.59	odd	6
726.4.a.f.1.1		1	77.10	even	6
768.4.d.c.385.1		2	112.59	even	12
768.4.d.c.385.2		2	112.3	even	12
768.4.d.n.385.1		2	112.45	odd	12
768.4.d.n.385.2		2	112.101	odd	12
882.4.a.n.1.1		1	21.11	odd	6
882.4.g.f.361.1		2	3.2	odd	2
882.4.g.f.667.1		2	21.2	odd	6
882.4.g.i.361.1		2	21.20	even	2
882.4.g.i.667.1		2	21.5	even	6
1014.4.a.g.1.1		1	91.38	odd	6
1014.4.b.d.337.1		2	91.73	even	12
1014.4.b.d.337.2		2	91.31	even	12
1200.4.a.b.1.1		1	140.59	even	6
1200.4.f.j.49.1		2	140.87	odd	12
1200.4.f.j.49.2		2	140.3	odd	12
1734.4.a.d.1.1		1	119.101	odd	6
2166.4.a.i.1.1		1	133.94	even	6
2178.4.a.e.1.1		1	231.164	odd	6
2352.4.a.e.1.1		1	28.11	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	294.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(3.00000 + 5.19615i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-6.00000 + 10.3923i) q^{10} +(-6.00000 + 10.3923i) q^{11} +(-6.00000 - 10.3923i) q^{12} -38.0000 q^{13} -18.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-63.0000 + 109.119i) q^{17} +(9.00000 - 15.5885i) q^{18} +(10.0000 + 17.3205i) q^{19} -24.0000 q^{20} -24.0000 q^{22} +(-84.0000 - 145.492i) q^{23} +(12.0000 - 20.7846i) q^{24} +(44.5000 - 77.0763i) q^{25} +(-38.0000 - 65.8179i) q^{26} +27.0000 q^{27} +30.0000 q^{29} +(-18.0000 - 31.1769i) q^{30} +(-44.0000 + 76.2102i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-18.0000 - 31.1769i) q^{33} -252.000 q^{34} +36.0000 q^{36} +(-127.000 - 219.970i) q^{37} +(-20.0000 + 34.6410i) q^{38} +(57.0000 - 98.7269i) q^{39} +(-24.0000 - 41.5692i) q^{40} -42.0000 q^{41} -52.0000 q^{43} +(-24.0000 - 41.5692i) q^{44} +(27.0000 - 46.7654i) q^{45} +(168.000 - 290.985i) q^{46} +(-48.0000 - 83.1384i) q^{47} +48.0000 q^{48} +178.000 q^{50} +(-189.000 - 327.358i) q^{51} +(76.0000 - 131.636i) q^{52} +(-99.0000 + 171.473i) q^{53} +(27.0000 + 46.7654i) q^{54} -72.0000 q^{55} -60.0000 q^{57} +(30.0000 + 51.9615i) q^{58} +(-330.000 + 571.577i) q^{59} +(36.0000 - 62.3538i) q^{60} +(-269.000 - 465.922i) q^{61} -176.000 q^{62} +64.0000 q^{64} +(-114.000 - 197.454i) q^{65} +(36.0000 - 62.3538i) q^{66} +(-442.000 + 765.566i) q^{67} +(-252.000 - 436.477i) q^{68} +504.000 q^{69} +792.000 q^{71} +(36.0000 + 62.3538i) q^{72} +(109.000 - 188.794i) q^{73} +(254.000 - 439.941i) q^{74} +(133.500 + 231.229i) q^{75} -80.0000 q^{76} +228.000 q^{78} +(260.000 + 450.333i) q^{79} +(48.0000 - 83.1384i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-42.0000 - 72.7461i) q^{82} +492.000 q^{83} -756.000 q^{85} +(-52.0000 - 90.0666i) q^{86} +(-45.0000 + 77.9423i) q^{87} +(48.0000 - 83.1384i) q^{88} +(405.000 + 701.481i) q^{89} +108.000 q^{90} +672.000 q^{92} +(-132.000 - 228.631i) q^{93} +(96.0000 - 166.277i) q^{94} +(-60.0000 + 103.923i) q^{95} +(48.0000 + 83.1384i) q^{96} -1154.00 q^{97} +108.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} + 6 q^{5} - 12 q^{6} - 16 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 + 6 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} + 6 q^{5} - 12 q^{6} - 16 q^{8} - 9 q^{9} - 12 q^{10} - 12 q^{11} - 12 q^{12} - 76 q^{13} - 36 q^{15} - 16 q^{16} - 126 q^{17} + 18 q^{18} + 20 q^{19} - 48 q^{20} - 48 q^{22} - 168 q^{23} + 24 q^{24} + 89 q^{25} - 76 q^{26} + 54 q^{27} + 60 q^{29} - 36 q^{30} - 88 q^{31} + 32 q^{32} - 36 q^{33} - 504 q^{34} + 72 q^{36} - 254 q^{37} - 40 q^{38} + 114 q^{39} - 48 q^{40} - 84 q^{41} - 104 q^{43} - 48 q^{44} + 54 q^{45} + 336 q^{46} - 96 q^{47} + 96 q^{48} + 356 q^{50} - 378 q^{51} + 152 q^{52} - 198 q^{53} + 54 q^{54} - 144 q^{55} - 120 q^{57} + 60 q^{58} - 660 q^{59} + 72 q^{60} - 538 q^{61} - 352 q^{62} + 128 q^{64} - 228 q^{65} + 72 q^{66} - 884 q^{67} - 504 q^{68} + 1008 q^{69} + 1584 q^{71} + 72 q^{72} + 218 q^{73} + 508 q^{74} + 267 q^{75} - 160 q^{76} + 456 q^{78} + 520 q^{79} + 96 q^{80} - 81 q^{81} - 84 q^{82} + 984 q^{83} - 1512 q^{85} - 104 q^{86} - 90 q^{87} + 96 q^{88} + 810 q^{89} + 216 q^{90} + 1344 q^{92} - 264 q^{93} + 192 q^{94} - 120 q^{95} + 96 q^{96} - 2308 q^{97} + 216 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 4 * q^4 + 6 * q^5 - 12 * q^6 - 16 * q^8 - 9 * q^9 - 12 * q^10 - 12 * q^11 - 12 * q^12 - 76 * q^13 - 36 * q^15 - 16 * q^16 - 126 * q^17 + 18 * q^18 + 20 * q^19 - 48 * q^20 - 48 * q^22 - 168 * q^23 + 24 * q^24 + 89 * q^25 - 76 * q^26 + 54 * q^27 + 60 * q^29 - 36 * q^30 - 88 * q^31 + 32 * q^32 - 36 * q^33 - 504 * q^34 + 72 * q^36 - 254 * q^37 - 40 * q^38 + 114 * q^39 - 48 * q^40 - 84 * q^41 - 104 * q^43 - 48 * q^44 + 54 * q^45 + 336 * q^46 - 96 * q^47 + 96 * q^48 + 356 * q^50 - 378 * q^51 + 152 * q^52 - 198 * q^53 + 54 * q^54 - 144 * q^55 - 120 * q^57 + 60 * q^58 - 660 * q^59 + 72 * q^60 - 538 * q^61 - 352 * q^62 + 128 * q^64 - 228 * q^65 + 72 * q^66 - 884 * q^67 - 504 * q^68 + 1008 * q^69 + 1584 * q^71 + 72 * q^72 + 218 * q^73 + 508 * q^74 + 267 * q^75 - 160 * q^76 + 456 * q^78 + 520 * q^79 + 96 * q^80 - 81 * q^81 - 84 * q^82 + 984 * q^83 - 1512 * q^85 - 104 * q^86 - 90 * q^87 + 96 * q^88 + 810 * q^89 + 216 * q^90 + 1344 * q^92 - 264 * q^93 + 192 * q^94 - 120 * q^95 + 96 * q^96 - 2308 * q^97 + 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more