LMFDB - Embedded newform 150.3.d.c.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,3,Mod(101,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("150.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	150.d (of order $2$, degree $1$, 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:	$4.08720396540$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 9 $ x^4 - 4*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.3
Root			$1.58114 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	150.101
Dual form			150.3.d.c.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(-2.58114 - 1.52896i) q^{3} -2.00000 q^{4} +(2.16228 - 3.65028i) q^{6} +7.48683 q^{7} -2.82843i q^{8} +(4.32456 + 7.89292i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(-2.58114 - 1.52896i) q^{3} -2.00000 q^{4} +(2.16228 - 3.65028i) q^{6} +7.48683 q^{7} -2.82843i q^{8} +(4.32456 + 7.89292i) q^{9} +8.48528i q^{11} +(5.16228 + 3.05792i) q^{12} +10.0000 q^{13} +10.5880i q^{14} +4.00000 q^{16} +30.3870i q^{17} +(-11.1623 + 6.11584i) q^{18} +26.9737 q^{19} +(-19.3246 - 11.4471i) q^{21} -12.0000 q^{22} -9.17377i q^{23} +(-4.32456 + 7.30056i) q^{24} +14.1421i q^{26} +(0.905694 - 26.9848i) q^{27} -14.9737 q^{28} -26.8328i q^{29} +8.00000 q^{31} +5.65685i q^{32} +(12.9737 - 21.9017i) q^{33} -42.9737 q^{34} +(-8.64911 - 15.7858i) q^{36} -15.9473 q^{37} +38.1465i q^{38} +(-25.8114 - 15.2896i) q^{39} +47.3575i q^{41} +(16.1886 - 27.3290i) q^{42} +14.4605 q^{43} -16.9706i q^{44} +12.9737 q^{46} -45.8688i q^{47} +(-10.3246 - 6.11584i) q^{48} +7.05267 q^{49} +(46.4605 - 78.4330i) q^{51} -20.0000 q^{52} +30.3870i q^{53} +(38.1623 + 1.28084i) q^{54} -21.1760i q^{56} +(-69.6228 - 41.2417i) q^{57} +37.9473 q^{58} -24.0789i q^{59} -53.9473 q^{61} +11.3137i q^{62} +(32.3772 + 59.0930i) q^{63} -8.00000 q^{64} +(30.9737 + 18.3475i) q^{66} +110.460 q^{67} -60.7739i q^{68} +(-14.0263 + 23.6788i) q^{69} +15.5936i q^{71} +(22.3246 - 12.2317i) q^{72} -87.9473 q^{73} -22.5529i q^{74} -53.9473 q^{76} +63.5279i q^{77} +(21.6228 - 36.5028i) q^{78} -46.9737 q^{79} +(-43.5964 + 68.2668i) q^{81} -66.9737 q^{82} -26.1443i q^{83} +(38.6491 + 22.8942i) q^{84} +20.4502i q^{86} +(-41.0263 + 69.2592i) q^{87} +24.0000 q^{88} +60.7739i q^{89} +74.8683 q^{91} +18.3475i q^{92} +(-20.6491 - 12.2317i) q^{93} +64.8683 q^{94} +(8.64911 - 14.6011i) q^{96} -36.0527 q^{97} +9.97398i q^{98} +(-66.9737 + 36.6951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 8 * q^9	$ 4 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 8 q^{9} + 8 q^{12} + 40 q^{13} + 16 q^{16} - 32 q^{18} + 32 q^{19} - 52 q^{21} - 48 q^{22} + 8 q^{24} - 28 q^{27} + 16 q^{28} + 32 q^{31} - 24 q^{33} - 96 q^{34} + 16 q^{36} + 88 q^{37} - 40 q^{39} + 128 q^{42} - 56 q^{43} - 24 q^{46} - 16 q^{48} + 180 q^{49} + 72 q^{51} - 80 q^{52} + 140 q^{54} - 152 q^{57} - 64 q^{61} + 256 q^{63} - 32 q^{64} + 48 q^{66} + 328 q^{67} - 132 q^{69} + 64 q^{72} - 200 q^{73} - 64 q^{76} - 40 q^{78} - 112 q^{79} + 28 q^{81} - 192 q^{82} + 104 q^{84} - 240 q^{87} + 96 q^{88} - 80 q^{91} - 32 q^{93} - 120 q^{94} - 16 q^{96} - 296 q^{97} - 192 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 8 * q^9 + 8 * q^12 + 40 * q^13 + 16 * q^16 - 32 * q^18 + 32 * q^19 - 52 * q^21 - 48 * q^22 + 8 * q^24 - 28 * q^27 + 16 * q^28 + 32 * q^31 - 24 * q^33 - 96 * q^34 + 16 * q^36 + 88 * q^37 - 40 * q^39 + 128 * q^42 - 56 * q^43 - 24 * q^46 - 16 * q^48 + 180 * q^49 + 72 * q^51 - 80 * q^52 + 140 * q^54 - 152 * q^57 - 64 * q^61 + 256 * q^63 - 32 * q^64 + 48 * q^66 + 328 * q^67 - 132 * q^69 + 64 * q^72 - 200 * q^73 - 64 * q^76 - 40 * q^78 - 112 * q^79 + 28 * q^81 - 192 * q^82 + 104 * q^84 - 240 * q^87 + 96 * q^88 - 80 * q^91 - 32 * q^93 - 120 * q^94 - 16 * q^96 - 296 * q^97 - 192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$	−2.58114	−	1.52896i	−0.860380	−	0.509654i
$3$	−2.58114	−	1.52896i	−0.860380	−	0.509654i
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	2.16228	−	3.65028i	0.360380	−	0.608380i
$7$	7.48683			1.06955			0.534774	−	0.844995i	$-0.320397\pi$
$7$	7.48683			1.06955			0.534774	+	0.844995i	$0.320397\pi$
$8$		−	2.82843i		−	0.353553i
$9$	4.32456	+	7.89292i	0.480506	+	0.876991i
$10$		0			0
$11$			8.48528i			0.771389i	0.922627	+	0.385695i	$0.126038\pi$
$11$			8.48528i			0.771389i	−0.922627	+	0.385695i	$0.873962\pi$
$12$	5.16228	+	3.05792i	0.430190	+	0.254827i
$13$	10.0000			0.769231			0.384615	−	0.923077i	$-0.374334\pi$
$13$	10.0000			0.769231			0.384615	+	0.923077i	$0.374334\pi$
$14$			10.5880i			0.756284i
$15$		0			0
$16$	4.00000			0.250000
$17$			30.3870i			1.78747i	0.448596	+	0.893734i	$0.351924\pi$
$17$			30.3870i			1.78747i	−0.448596	+	0.893734i	$0.648076\pi$
$18$	−11.1623	+	6.11584i	−0.620127	+	0.339769i
$19$	26.9737			1.41967			0.709833	−	0.704370i	$-0.248770\pi$
$19$	26.9737			1.41967			0.709833	+	0.704370i	$0.248770\pi$
$20$		0			0
$21$	−19.3246	−	11.4471i	−0.920217	−	0.545099i
$22$	−12.0000			−0.545455
$23$		−	9.17377i		−	0.398859i	−0.979912	−	0.199430i	$-0.936091\pi$
$23$		−	9.17377i		−	0.398859i	0.979912	−	0.199430i	$-0.0639090\pi$
$24$	−4.32456	+	7.30056i	−0.180190	+	0.304190i
$25$		0			0
$26$			14.1421i			0.543928i
$27$	0.905694	−	26.9848i	0.0335442	−	0.999437i
$28$	−14.9737			−0.534774
$29$		−	26.8328i		−	0.925270i	−0.886549	−	0.462635i	$-0.846904\pi$
$29$		−	26.8328i		−	0.925270i	0.886549	−	0.462635i	$-0.153096\pi$
$30$		0			0
$31$	8.00000			0.258065			0.129032	−	0.991640i	$-0.458813\pi$
$31$	8.00000			0.258065			0.129032	+	0.991640i	$0.458813\pi$
$32$			5.65685i			0.176777i
$33$	12.9737	−	21.9017i	0.393141	−	0.663688i
$34$	−42.9737			−1.26393
$35$		0			0
$36$	−8.64911	−	15.7858i	−0.240253	−	0.438496i
$37$	−15.9473			−0.431009			−0.215504	−	0.976503i	$-0.569140\pi$
$37$	−15.9473			−0.431009			−0.215504	+	0.976503i	$0.569140\pi$
$38$			38.1465i			1.00386i
$39$	−25.8114	−	15.2896i	−0.661830	−	0.392041i
$40$		0			0
$41$			47.3575i			1.15506i	0.816369	+	0.577531i	$0.195984\pi$
$41$			47.3575i			1.15506i	−0.816369	+	0.577531i	$0.804016\pi$
$42$	16.1886	−	27.3290i	0.385443	−	0.650692i
$43$	14.4605			0.336291			0.168145	−	0.985762i	$-0.446222\pi$
$43$	14.4605			0.336291			0.168145	+	0.985762i	$0.446222\pi$
$44$		−	16.9706i		−	0.385695i
$45$		0			0
$46$	12.9737			0.282036
$47$		−	45.8688i		−	0.975933i	−0.872862	−	0.487966i	$-0.837739\pi$
$47$		−	45.8688i		−	0.975933i	0.872862	−	0.487966i	$-0.162261\pi$
$48$	−10.3246	−	6.11584i	−0.215095	−	0.127413i
$49$	7.05267			0.143932
$50$		0			0
$51$	46.4605	−	78.4330i	0.910990	−	1.53790i
$52$	−20.0000			−0.384615
$53$			30.3870i			0.573339i	0.958030	+	0.286670i	$0.0925482\pi$
$53$			30.3870i			0.573339i	−0.958030	+	0.286670i	$0.907452\pi$
$54$	38.1623	+	1.28084i	0.706709	+	0.0237194i
$55$		0			0
$56$		−	21.1760i		−	0.378142i
$57$	−69.6228	−	41.2417i	−1.22145	−	0.723538i
$58$	37.9473			0.654264
$59$		−	24.0789i		−	0.408116i	−0.978959	−	0.204058i	$-0.934587\pi$
$59$		−	24.0789i		−	0.408116i	0.978959	−	0.204058i	$-0.0654132\pi$
$60$		0			0
$61$	−53.9473			−0.884382			−0.442191	−	0.896921i	$-0.645799\pi$
$61$	−53.9473			−0.884382			−0.442191	+	0.896921i	$0.645799\pi$
$62$			11.3137i			0.182479i
$63$	32.3772	+	59.0930i	0.513924	+	0.937984i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	30.9737	+	18.3475i	0.469298	+	0.277993i
$67$	110.460			1.64866			0.824332	−	0.566107i	$-0.191551\pi$
$67$	110.460			1.64866			0.824332	+	0.566107i	$0.191551\pi$
$68$		−	60.7739i		−	0.893734i
$69$	−14.0263	+	23.6788i	−0.203280	+	0.343171i
$70$		0			0
$71$			15.5936i			0.219628i	0.993952	+	0.109814i	$0.0350255\pi$
$71$			15.5936i			0.219628i	−0.993952	+	0.109814i	$0.964974\pi$
$72$	22.3246	−	12.2317i	0.310063	−	0.169885i
$73$	−87.9473			−1.20476			−0.602379	−	0.798210i	$-0.705780\pi$
$73$	−87.9473			−1.20476			−0.602379	+	0.798210i	$0.705780\pi$
$74$		−	22.5529i		−	0.304769i
$75$		0			0
$76$	−53.9473			−0.709833
$77$			63.5279i			0.825037i
$78$	21.6228	−	36.5028i	0.277215	−	0.467985i
$79$	−46.9737			−0.594603			−0.297302	−	0.954784i	$-0.596087\pi$
$79$	−46.9737			−0.594603			−0.297302	+	0.954784i	$0.596087\pi$
$80$		0			0
$81$	−43.5964	+	68.2668i	−0.538228	+	0.842799i
$82$	−66.9737			−0.816752
$83$		−	26.1443i		−	0.314992i	−0.987520	−	0.157496i	$-0.949658\pi$
$83$		−	26.1443i		−	0.314992i	0.987520	−	0.157496i	$-0.0503421\pi$
$84$	38.6491	+	22.8942i	0.460108	+	0.272549i
$85$		0			0
$86$			20.4502i			0.237793i
$87$	−41.0263	+	69.2592i	−0.471567	+	0.796083i
$88$	24.0000			0.272727
$89$			60.7739i			0.682853i	0.939908	+	0.341427i	$0.110910\pi$
$89$			60.7739i			0.682853i	−0.939908	+	0.341427i	$0.889090\pi$
$90$		0			0
$91$	74.8683			0.822729
$92$			18.3475i			0.199430i
$93$	−20.6491	−	12.2317i	−0.222033	−	0.131524i
$94$	64.8683			0.690089
$95$		0			0
$96$	8.64911	−	14.6011i	0.0900949	−	0.152095i
$97$	−36.0527			−0.371677			−0.185838	−	0.982580i	$-0.559500\pi$
$97$	−36.0527			−0.371677			−0.185838	+	0.982580i	$0.559500\pi$
$98$			9.97398i			0.101775i
$99$	−66.9737	+	36.6951i	−0.676502	+	0.370657i
$100$		0			0
$101$		−	48.1577i		−	0.476809i	−0.971166	−	0.238405i	$-0.923376\pi$
$101$		−	48.1577i		−	0.476809i	0.971166	−	0.238405i	$-0.0766245\pi$
$102$	110.921	+	65.7051i	1.08746	+	0.644167i
$103$	−140.408			−1.36318			−0.681591	−	0.731733i	$-0.738712\pi$
$103$	−140.408			−1.36318			−0.681591	+	0.731733i	$0.738712\pi$
$104$		−	28.2843i		−	0.271964i
$105$		0			0
$106$	−42.9737			−0.405412
$107$			43.1149i			0.402943i	0.979494	+	0.201471i	$0.0645723\pi$
$107$			43.1149i			0.402943i	−0.979494	+	0.201471i	$0.935428\pi$
$108$	−1.81139	+	53.9696i	−0.0167721	+	0.499719i
$109$	133.842			1.22791			0.613954	−	0.789342i	$-0.289578\pi$
$109$	133.842			1.22791			0.613954	+	0.789342i	$0.289578\pi$
$110$		0			0
$111$	41.1623	+	24.3829i	0.370831	+	0.219665i
$112$	29.9473			0.267387
$113$		−	7.90852i		−	0.0699869i	−0.999388	−	0.0349935i	$-0.988859\pi$
$113$		−	7.90852i		−	0.0699869i	0.999388	−	0.0349935i	$-0.0111410\pi$
$114$	58.3246	−	98.4615i	0.511619	−	0.863697i
$115$		0			0
$116$			53.6656i			0.462635i
$117$	43.2456	+	78.9292i	0.369620	+	0.674609i
$118$	34.0527			0.288582
$119$			227.502i			1.91178i
$120$		0			0
$121$	49.0000			0.404959
$122$		−	76.2930i		−	0.625353i
$123$	72.4078	−	122.236i	0.588682	−	0.993792i
$124$	−16.0000			−0.129032
$125$		0			0
$126$	−83.5701	+	45.7883i	−0.663255	+	0.363399i
$127$	134.460			1.05874			0.529372	−	0.848390i	$-0.322428\pi$
$127$	134.460			1.05874			0.529372	+	0.848390i	$0.322428\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−37.3246	−	22.1095i	−0.289338	−	0.171392i
$130$		0			0
$131$		−	220.394i		−	1.68240i	−0.540727	−	0.841198i	$-0.681851\pi$
$131$		−	220.394i		−	1.68240i	0.540727	−	0.841198i	$-0.318149\pi$
$132$	−25.9473	+	43.8034i	−0.196571	+	0.331844i
$133$	201.947			1.51840
$134$			156.215i			1.16578i
$135$		0			0
$136$	85.9473			0.631966
$137$		−	95.5153i		−	0.697192i	−0.937273	−	0.348596i	$-0.886659\pi$
$137$		−	95.5153i		−	0.697192i	0.937273	−	0.348596i	$-0.113341\pi$
$138$	−33.4868	−	19.8362i	−0.242658	−	0.143741i
$139$	−76.8157			−0.552631			−0.276315	−	0.961067i	$-0.589113\pi$
$139$	−76.8157			−0.552631			−0.276315	+	0.961067i	$0.589113\pi$
$140$		0			0
$141$	−70.1317	+	118.394i	−0.497388	+	0.839673i
$142$	−22.0527			−0.155300
$143$			84.8528i			0.593376i
$144$	17.2982	+	31.5717i	0.120127	+	0.219248i
$145$		0			0
$146$		−	124.376i		−	0.851893i
$147$	−18.2039	−	10.7833i	−0.123836	−	0.0733555i
$148$	31.8947			0.215504
$149$		−	276.237i		−	1.85394i	−0.375139	−	0.926969i	$-0.622405\pi$
$149$		−	276.237i		−	1.85394i	0.375139	−	0.926969i	$-0.377595\pi$
$150$		0			0
$151$	18.0527			0.119554			0.0597770	−	0.998212i	$-0.480961\pi$
$151$	18.0527			0.119554			0.0597770	+	0.998212i	$0.480961\pi$
$152$		−	76.2930i		−	0.501928i
$153$	−239.842	+	131.410i	−1.56759	+	0.858890i
$154$	−89.8420			−0.583390
$155$		0			0
$156$	51.6228	+	30.5792i	0.330915	+	0.196021i
$157$	−103.842			−0.661414			−0.330707	−	0.943733i	$-0.607287\pi$
$157$	−103.842			−0.661414			−0.330707	+	0.943733i	$0.607287\pi$
$158$		−	66.4308i		−	0.420448i
$159$	46.4605	−	78.4330i	0.292204	−	0.493289i
$160$		0			0
$161$		−	68.6825i		−	0.426599i
$162$	−96.5438	−	61.6547i	−0.595949	−	0.380584i
$163$	11.3815			0.0698251			0.0349126	−	0.999390i	$-0.488885\pi$
$163$	11.3815			0.0698251			0.0349126	+	0.999390i	$0.488885\pi$
$164$		−	94.7151i		−	0.577531i
$165$		0			0
$166$	36.9737			0.222733
$167$		−	252.270i		−	1.51060i	−0.655382	−	0.755298i	$-0.727492\pi$
$167$		−	252.270i		−	1.51060i	0.655382	−	0.755298i	$-0.272508\pi$
$168$	−32.3772	+	54.6581i	−0.192722	+	0.325346i
$169$	−69.0000			−0.408284
$170$		0			0
$171$	116.649	+	212.901i	0.682159	+	1.24504i
$172$	−28.9210			−0.168145
$173$		−	11.8160i		−	0.0683005i	−0.999417	−	0.0341502i	$-0.989128\pi$
$173$		−	11.8160i		−	0.0683005i	0.999417	−	0.0341502i	$-0.0108725\pi$
$174$	−97.9473	−	58.0200i	−0.562916	−	0.333448i
$175$		0			0
$176$			33.9411i			0.192847i
$177$	−36.8157	+	62.1509i	−0.207998	+	0.351135i
$178$	−85.9473			−0.482850
$179$		−	69.0358i		−	0.385675i	−0.981231	−	0.192837i	$-0.938231\pi$
$179$		−	69.0358i		−	0.385675i	0.981231	−	0.192837i	$-0.0617690\pi$
$180$		0			0
$181$	−189.684			−1.04798			−0.523989	−	0.851725i	$-0.675557\pi$
$181$	−189.684			−1.04798			−0.523989	+	0.851725i	$0.675557\pi$
$182$			105.880i			0.581757i
$183$	139.246	+	82.4834i	0.760905	+	0.450729i
$184$	−25.9473			−0.141018
$185$		0			0
$186$	17.2982	−	29.2023i	0.0930012	−	0.157001i
$187$	−257.842			−1.37883
$188$			91.7377i			0.487966i
$189$	6.78078	−	202.031i	0.0358771	−	1.06895i
$190$		0			0
$191$			108.708i			0.569153i	0.958653	+	0.284577i	$0.0918530\pi$
$191$			108.708i			0.569153i	−0.958653	+	0.284577i	$0.908147\pi$
$192$	20.6491	+	12.2317i	0.107547	+	0.0637067i
$193$	167.947			0.870193			0.435097	−	0.900384i	$-0.356714\pi$
$193$	167.947			0.870193			0.435097	+	0.900384i	$0.356714\pi$
$194$		−	50.9862i		−	0.262815i
$195$		0			0
$196$	−14.1053			−0.0719660
$197$		−	171.659i		−	0.871367i	−0.900100	−	0.435684i	$-0.856507\pi$
$197$		−	171.659i		−	0.871367i	0.900100	−	0.435684i	$-0.143493\pi$
$198$	−51.8947	−	94.7151i	−0.262094	−	0.478359i
$199$	35.0790			0.176276			0.0881382	−	0.996108i	$-0.471908\pi$
$199$	35.0790			0.176276			0.0881382	+	0.996108i	$0.471908\pi$
$200$		0			0
$201$	−285.114	−	168.890i	−1.41848	−	0.840248i
$202$	68.1053			0.337155
$203$		−	200.893i		−	0.989620i
$204$	−92.9210	+	156.866i	−0.455495	+	0.768951i
$205$		0			0
$206$		−	198.567i		−	0.963916i
$207$	72.4078	−	39.6725i	0.349796	−	0.191654i
$208$	40.0000			0.192308
$209$			228.879i			1.09512i
$210$		0			0
$211$	−58.1580			−0.275630			−0.137815	−	0.990458i	$-0.544008\pi$
$211$	−58.1580			−0.275630			−0.137815	+	0.990458i	$0.544008\pi$
$212$		−	60.7739i		−	0.286670i
$213$	23.8420	−	40.2492i	0.111934	−	0.188963i
$214$	−60.9737			−0.284924
$215$		0			0
$216$	−76.3246	−	2.56169i	−0.353354	−	0.0118597i
$217$	59.8947			0.276012
$218$			189.281i			0.868262i
$219$	227.004	+	134.468i	1.03655	+	0.614009i
$220$		0			0
$221$			303.870i			1.37498i
$222$	−34.4826	+	58.2123i	−0.155327	+	0.262217i
$223$	−99.3815			−0.445657			−0.222828	−	0.974858i	$-0.571529\pi$
$223$	−99.3815			−0.445657			−0.222828	+	0.974858i	$0.571529\pi$
$224$			42.3519i			0.189071i
$225$		0			0
$226$	11.1843			0.0494882
$227$			216.951i			0.955733i	0.878432	+	0.477867i	$0.158590\pi$
$227$			216.951i			0.955733i	−0.878432	+	0.477867i	$0.841410\pi$
$228$	139.246	+	82.4834i	0.610726	+	0.361769i
$229$	325.684			1.42220			0.711100	−	0.703090i	$-0.248197\pi$
$229$	325.684			1.42220			0.711100	+	0.703090i	$0.248197\pi$
$230$		0			0
$231$	97.1317	−	163.974i	0.420483	−	0.709845i
$232$	−75.8947			−0.327132
$233$			51.7119i			0.221939i	0.993824	+	0.110970i	$0.0353957\pi$
$233$			51.7119i			0.221939i	−0.993824	+	0.110970i	$0.964604\pi$
$234$	−111.623	+	61.1584i	−0.477020	+	0.261361i
$235$		0			0
$236$			48.1577i			0.204058i
$237$	121.246	+	71.8209i	0.511585	+	0.303042i
$238$	−321.737			−1.35183
$239$		−	410.047i		−	1.71568i	−0.513917	−	0.857840i	$-0.671806\pi$
$239$		−	410.047i		−	1.71568i	0.513917	−	0.857840i	$-0.328194\pi$
$240$		0			0
$241$	445.526			1.84866			0.924328	−	0.381599i	$-0.124627\pi$
$241$	445.526			1.84866			0.924328	+	0.381599i	$0.124627\pi$
$242$			69.2965i			0.286349i
$243$	216.906	−	109.549i	0.892616	−	0.450818i
$244$	107.895			0.442191
$245$		0			0
$246$	172.868	+	102.400i	0.702717	+	0.416261i
$247$	269.737			1.09205
$248$		−	22.6274i		−	0.0912396i
$249$	−39.9737	+	67.4821i	−0.160537	+	0.271013i
$250$		0			0
$251$		−	237.364i		−	0.945675i	−0.881150	−	0.472838i	$-0.843230\pi$
$251$		−	237.364i		−	0.945675i	0.881150	−	0.472838i	$-0.156770\pi$
$252$	−64.7544	−	118.186i	−0.256962	−	0.468992i
$253$	77.8420			0.307676
$254$			190.156i			0.748645i
$255$		0			0
$256$	16.0000			0.0625000
$257$			318.887i			1.24080i	0.784284	+	0.620402i	$0.213030\pi$
$257$			318.887i			1.24080i	−0.784284	+	0.620402i	$0.786970\pi$
$258$	31.2676	−	52.7849i	0.121192	−	0.204593i
$259$	−119.395			−0.460985
$260$		0			0
$261$	211.789	−	116.040i	0.811453	−	0.444598i
$262$	311.684			1.18963
$263$			36.2300i			0.137757i	0.997625	+	0.0688784i	$0.0219420\pi$
$263$			36.2300i			0.137757i	−0.997625	+	0.0688784i	$0.978058\pi$
$264$	−61.9473	−	36.6951i	−0.234649	−	0.138996i
$265$		0			0
$266$			285.597i			1.07367i
$267$	92.9210	−	156.866i	0.348019	−	0.587513i
$268$	−220.921			−0.824332
$269$			528.041i			1.96298i	0.191518	+	0.981489i	$0.438659\pi$
$269$			528.041i			1.96298i	−0.191518	+	0.981489i	$0.561341\pi$
$270$		0			0
$271$	−475.895			−1.75607			−0.878034	−	0.478597i	$-0.841145\pi$
$271$	−475.895			−1.75607			−0.878034	+	0.478597i	$0.841145\pi$
$272$			121.548i			0.446867i
$273$	−193.246	−	114.471i	−0.707859	−	0.419307i
$274$	135.079			0.492989
$275$		0			0
$276$	28.0527	−	47.3575i	0.101640	−	0.171585i
$277$	−188.158			−0.679271			−0.339635	−	0.940557i	$-0.610304\pi$
$277$	−188.158			−0.679271			−0.339635	+	0.940557i	$0.610304\pi$
$278$		−	108.634i		−	0.390769i
$279$	34.5964	+	63.1434i	0.124002	+	0.226320i
$280$		0			0
$281$		−	24.4322i		−	0.0869473i	−0.999055	−	0.0434736i	$-0.986158\pi$
$281$		−	24.4322i		−	0.0869473i	0.999055	−	0.0434736i	$-0.0138424\pi$
$282$	−167.434	−	99.1812i	−0.593738	−	0.351706i
$283$	−198.460			−0.701274			−0.350637	−	0.936511i	$-0.614035\pi$
$283$	−198.460			−0.701274			−0.350637	+	0.936511i	$0.614035\pi$
$284$		−	31.1872i		−	0.109814i
$285$		0			0
$286$	−120.000			−0.419580
$287$			354.558i			1.23539i
$288$	−44.6491	+	24.4634i	−0.155032	+	0.0849423i
$289$	−634.368			−2.19504
$290$		0			0
$291$	93.0569	+	55.1231i	0.319783	+	0.189427i
$292$	175.895			0.602379
$293$		−	513.825i		−	1.75367i	−0.480794	−	0.876834i	$-0.659651\pi$
$293$		−	513.825i		−	1.75367i	0.480794	−	0.876834i	$-0.340349\pi$
$294$	15.2498	−	25.7442i	0.0518702	−	0.0875654i
$295$		0			0
$296$			45.1059i			0.152385i
$297$	228.974	+	7.68507i	0.770955	+	0.0258757i
$298$	390.658			1.31093
$299$		−	91.7377i		−	0.306815i
$300$		0			0
$301$	108.263			0.359679
$302$			25.5303i			0.0845375i
$303$	−73.6313	+	124.302i	−0.243008	+	0.410237i
$304$	107.895			0.354917
$305$		0			0
$306$	−185.842	−	339.188i	−0.607327	−	1.10846i
$307$	11.3815			0.0370733			0.0185366	−	0.999828i	$-0.494099\pi$
$307$	11.3815			0.0370733			0.0185366	+	0.999828i	$0.494099\pi$
$308$		−	127.056i		−	0.412519i
$309$	362.412	+	214.678i	1.17285	+	0.694751i
$310$		0			0
$311$			518.756i			1.66802i	0.551746	+	0.834012i	$0.313962\pi$
$311$			518.756i			1.66802i	−0.551746	+	0.834012i	$0.686038\pi$
$312$	−43.2456	+	73.0056i	−0.138608	+	0.233992i
$313$	46.3160			0.147974			0.0739872	−	0.997259i	$-0.476428\pi$
$313$	46.3160			0.147974			0.0739872	+	0.997259i	$0.476428\pi$
$314$		−	146.855i		−	0.467690i
$315$		0			0
$316$	93.9473			0.297302
$317$			39.0957i			0.123330i	0.998097	+	0.0616651i	$0.0196411\pi$
$317$			39.0957i			0.123330i	−0.998097	+	0.0616651i	$0.980359\pi$
$318$	110.921	+	65.7051i	0.348808	+	0.206620i
$319$	227.684			0.713743
$320$		0			0
$321$	65.9210	−	111.286i	0.205361	−	0.346684i
$322$	97.1317			0.301651
$323$			819.648i			2.53761i
$324$	87.1929	−	136.534i	0.269114	−	0.421400i
$325$		0			0
$326$			16.0959i			0.0493738i
$327$	−345.465	−	204.639i	−1.05647	−	0.625808i
$328$	133.947			0.408376
$329$		−	343.412i		−	1.04381i
$330$		0			0
$331$	−445.421			−1.34568			−0.672841	−	0.739787i	$-0.734926\pi$
$331$	−445.421			−1.34568			−0.672841	+	0.739787i	$0.734926\pi$
$332$			52.2887i			0.157496i
$333$	−68.9651	−	125.871i	−0.207102	−	0.377991i
$334$	356.763			1.06815
$335$		0			0
$336$	−77.2982	−	45.7883i	−0.230054	−	0.136275i
$337$	−325.684			−0.966421			−0.483211	−	0.875504i	$-0.660529\pi$
$337$	−325.684			−0.966421			−0.483211	+	0.875504i	$0.660529\pi$
$338$		−	97.5807i		−	0.288700i
$339$	−12.0918	+	20.4130i	−0.0356691	+	0.0602153i
$340$		0			0
$341$			67.8823i			0.199068i
$342$	−301.088	+	164.967i	−0.880373	+	0.482359i
$343$	−314.053			−0.915605
$344$		−	40.9005i		−	0.118897i
$345$		0			0
$346$	16.7103			0.0482957
$347$		−	51.8236i		−	0.149348i	−0.997208	−	0.0746738i	$-0.976208\pi$
$347$		−	51.8236i		−	0.149348i	0.997208	−	0.0746738i	$-0.0237916\pi$
$348$	82.0527	−	138.518i	0.235784	−	0.398042i
$349$	−97.5787			−0.279595			−0.139798	−	0.990180i	$-0.544645\pi$
$349$	−97.5787			−0.279595			−0.139798	+	0.990180i	$0.544645\pi$
$350$		0			0
$351$	9.05694	−	269.848i	0.0258033	−	0.768798i
$352$	−48.0000			−0.136364
$353$			569.797i			1.61416i	0.590445	+	0.807078i	$0.298952\pi$
$353$			569.797i			1.61416i	−0.590445	+	0.807078i	$0.701048\pi$
$354$	−87.8947	−	52.0652i	−0.248290	−	0.147077i
$355$		0			0
$356$		−	121.548i		−	0.341427i
$357$	347.842	−	587.215i	0.974347	−	1.64486i
$358$	97.6313			0.272713
$359$			274.283i			0.764019i	0.924158	+	0.382010i	$0.124768\pi$
$359$			274.283i			0.764019i	−0.924158	+	0.382010i	$0.875232\pi$
$360$		0			0
$361$	366.579			1.01545
$362$		−	268.254i		−	0.741032i
$363$	−126.476	−	74.9191i	−0.348418	−	0.206389i
$364$	−149.737			−0.411364
$365$		0			0
$366$	−116.649	+	196.923i	−0.318713	+	0.538041i
$367$	−461.828			−1.25839			−0.629194	−	0.777248i	$-0.716615\pi$
$367$	−461.828			−1.25839			−0.629194	+	0.777248i	$0.716615\pi$
$368$		−	36.6951i		−	0.0997149i
$369$	−373.789	+	204.800i	−1.01298	+	0.555014i
$370$		0			0
$371$			227.502i			0.613213i
$372$	41.2982	+	24.4634i	0.111017	+	0.0657618i
$373$	491.947			1.31889			0.659447	−	0.751751i	$-0.270791\pi$
$373$	491.947			1.31889			0.659447	+	0.751751i	$0.270791\pi$
$374$		−	364.644i		−	0.974983i
$375$		0			0
$376$	−129.737			−0.345044
$377$		−	268.328i		−	0.711746i
$378$	285.715	+	9.58947i	0.755859	+	0.0253690i
$379$	−258.763			−0.682752			−0.341376	−	0.939927i	$-0.610893\pi$
$379$	−258.763			−0.682752			−0.341376	+	0.939927i	$0.610893\pi$
$380$		0			0
$381$	−347.061	−	205.585i	−0.910922	−	0.539593i
$382$	−153.737			−0.402452
$383$		−	522.422i		−	1.36402i	−0.731341	−	0.682012i	$-0.761105\pi$
$383$		−	522.422i		−	1.36402i	0.731341	−	0.682012i	$-0.238895\pi$
$384$	−17.2982	+	29.2023i	−0.0450475	+	0.0760475i
$385$		0			0
$386$			237.513i			0.615320i
$387$	62.5352	+	114.136i	0.161590	+	0.294924i
$388$	72.1053			0.185838
$389$		−	610.847i		−	1.57030i	−0.619306	−	0.785150i	$-0.712586\pi$
$389$		−	610.847i		−	1.57030i	0.619306	−	0.785150i	$-0.287414\pi$
$390$		0			0
$391$	278.763			0.712949
$392$		−	19.9480i		−	0.0508876i
$393$	−336.974	+	568.867i	−0.857439	+	1.44750i
$394$	242.763			0.616150
$395$		0			0
$396$	133.947	−	73.3901i	0.338251	−	0.185329i
$397$	214.000			0.539043			0.269521	−	0.962994i	$-0.413135\pi$
$397$	214.000			0.539043			0.269521	+	0.962994i	$0.413135\pi$
$398$			49.6092i			0.124646i
$399$	−521.254	−	308.770i	−1.30640	−	0.773859i
$400$		0			0
$401$		−	454.557i		−	1.13356i	−0.823869	−	0.566780i	$-0.808189\pi$
$401$		−	454.557i		−	1.13356i	0.823869	−	0.566780i	$-0.191811\pi$
$402$	238.846	−	403.212i	0.594145	−	1.00301i
$403$	80.0000			0.198511
$404$			96.3155i			0.238405i
$405$		0			0
$406$	284.105			0.699767
$407$		−	135.318i		−	0.332476i
$408$	−221.842	−	131.410i	−0.543730	−	0.322084i
$409$	−573.842			−1.40304			−0.701518	−	0.712651i	$-0.747494\pi$
$409$	−573.842			−1.40304			−0.701518	+	0.712651i	$0.747494\pi$
$410$		0			0
$411$	−146.039	+	246.538i	−0.355326	+	0.599850i
$412$	280.816			0.681591
$413$		−	180.274i		−	0.436500i
$414$	56.1053	+	102.400i	0.135520	+	0.247343i
$415$		0			0
$416$			56.5685i			0.135982i
$417$	198.272	+	117.448i	0.475472	+	0.281650i
$418$	−323.684			−0.774364
$419$		−	97.9159i		−	0.233690i	−0.993150	−	0.116845i	$-0.962722\pi$
$419$		−	97.9159i		−	0.233690i	0.993150	−	0.116845i	$-0.0372780\pi$
$420$		0			0
$421$	717.315			1.70384			0.851918	−	0.523675i	$-0.175439\pi$
$421$	717.315			1.70384			0.851918	+	0.523675i	$0.175439\pi$
$422$		−	82.2478i		−	0.194900i
$423$	362.039	−	198.362i	0.855885	−	0.468942i
$424$	85.9473			0.202706
$425$		0			0
$426$	56.9210	+	33.7177i	0.133617	+	0.0791495i
$427$	−403.895			−0.945889
$428$		−	86.2298i		−	0.201471i
$429$	129.737	−	219.017i	0.302416	−	0.510529i
$430$		0			0
$431$		−	293.077i		−	0.679994i	−0.940427	−	0.339997i	$-0.889574\pi$
$431$		−	293.077i		−	0.679994i	0.940427	−	0.339997i	$-0.110426\pi$
$432$	3.62278	−	107.939i	0.00838606	−	0.249859i
$433$	−487.526			−1.12593			−0.562963	−	0.826482i	$-0.690339\pi$
$433$	−487.526			−1.12593			−0.562963	+	0.826482i	$0.690339\pi$
$434$			84.7038i			0.195170i
$435$		0			0
$436$	−267.684			−0.613954
$437$		−	247.450i		−	0.566247i
$438$	−190.167	+	321.033i	−0.434170	+	0.732951i
$439$	257.237			0.585961			0.292981	−	0.956118i	$-0.405353\pi$
$439$	257.237			0.585961			0.292981	+	0.956118i	$0.405353\pi$
$440$		0			0
$441$	30.4997	+	55.6662i	0.0691602	+	0.126227i
$442$	−429.737			−0.972255
$443$		−	293.096i		−	0.661615i	−0.943698	−	0.330808i	$-0.892679\pi$
$443$		−	293.096i		−	0.661615i	0.943698	−	0.330808i	$-0.107321\pi$
$444$	−82.3246	−	48.7657i	−0.185416	−	0.109833i
$445$		0			0
$446$		−	140.547i		−	0.315127i
$447$	−422.355	+	713.005i	−0.944866	+	1.59509i
$448$	−59.8947			−0.133693
$449$			585.614i			1.30426i	0.758106	+	0.652132i	$0.226125\pi$
$449$			585.614i			1.30426i	−0.758106	+	0.652132i	$0.773875\pi$
$450$		0			0
$451$	−401.842			−0.891002
$452$			15.8170i			0.0349935i
$453$	−46.5964	−	27.6018i	−0.102862	−	0.0609312i
$454$	−306.816			−0.675805
$455$		0			0
$456$	−116.649	+	196.923i	−0.255809	+	0.431849i
$457$	813.052			1.77911			0.889554	−	0.456831i	$-0.151016\pi$
$457$	813.052			1.77911			0.889554	+	0.456831i	$0.151016\pi$
$458$			460.587i			1.00565i
$459$	819.986	+	27.5213i	1.78646	+	0.0599593i
$460$		0			0
$461$		−	554.074i		−	1.20190i	−0.799288	−	0.600948i	$-0.794790\pi$
$461$		−	554.074i		−	1.20190i	0.799288	−	0.600948i	$-0.205210\pi$
$462$	231.895	+	137.365i	0.501937	+	0.297327i
$463$	449.723			0.971324			0.485662	−	0.874147i	$-0.338579\pi$
$463$	449.723			0.971324			0.485662	+	0.874147i	$0.338579\pi$
$464$		−	107.331i		−	0.231317i
$465$		0			0
$466$	−73.1317			−0.156935
$467$		−	30.7221i		−	0.0657862i	−0.999459	−	0.0328931i	$-0.989528\pi$
$467$		−	30.7221i		−	0.0657862i	0.999459	−	0.0328931i	$-0.0104721\pi$
$468$	−86.4911	−	157.858i	−0.184810	−	0.337304i
$469$	826.999			1.76332
$470$		0			0
$471$	268.031	+	158.770i	0.569067	+	0.337092i
$472$	−68.1053			−0.144291
$473$			122.701i			0.259411i
$474$	−101.570	+	171.467i	−0.214283	+	0.361745i
$475$		0			0
$476$		−	455.004i		−	0.955891i
$477$	−239.842	+	131.410i	−0.502813	+	0.275493i
$478$	579.895			1.21317
$479$			735.242i			1.53495i	0.641078	+	0.767476i	$0.278488\pi$
$479$			735.242i			1.53495i	−0.641078	+	0.767476i	$0.721512\pi$
$480$		0			0
$481$	−159.473			−0.331545
$482$			630.069i			1.30720i
$483$	−105.013	+	177.279i	−0.217418	+	0.367037i
$484$	−98.0000			−0.202479
$485$		0			0
$486$	154.925	+	306.751i	0.318776	+	0.631175i
$487$	92.6185			0.190182			0.0950909	−	0.995469i	$-0.469686\pi$
$487$	92.6185			0.190182			0.0950909	+	0.995469i	$0.469686\pi$
$488$			152.586i			0.312676i
$489$	−29.3772	−	17.4019i	−0.0600761	−	0.0355866i
$490$		0			0
$491$			898.323i			1.82958i	0.403933	+	0.914789i	$0.367643\pi$
$491$			898.323i			1.82958i	−0.403933	+	0.914789i	$0.632357\pi$
$492$	−144.816	+	244.473i	−0.294341	+	0.496896i
$493$	815.368			1.65389
$494$			381.465i			0.772197i
$495$		0			0
$496$	32.0000			0.0645161
$497$			116.747i			0.234903i
$498$	−95.4342	−	56.5313i	−0.191635	−	0.113517i
$499$	136.921			0.274391			0.137195	−	0.990544i	$-0.456191\pi$
$499$	136.921			0.274391			0.137195	+	0.990544i	$0.456191\pi$
$500$		0			0
$501$	−385.710	+	651.143i	−0.769881	+	1.29969i
$502$	335.684			0.668693
$503$		−	443.077i		−	0.880868i	−0.897785	−	0.440434i	$-0.854825\pi$
$503$		−	443.077i		−	0.880868i	0.897785	−	0.440434i	$-0.145175\pi$
$504$	167.140	−	91.5766i	0.331627	−	0.181700i
$505$		0			0
$506$			110.085i			0.217560i
$507$	178.099	+	105.498i	0.351279	+	0.208083i
$508$	−268.921			−0.529372
$509$		−	213.062i		−	0.418590i	−0.977853	−	0.209295i	$-0.932883\pi$
$509$		−	213.062i		−	0.418590i	0.977853	−	0.209295i	$-0.0671168\pi$
$510$		0			0
$511$	−658.447			−1.28855
$512$			22.6274i			0.0441942i
$513$	24.4299	−	727.879i	0.0476216	−	1.41887i
$514$	−450.974			−0.877381
$515$		0			0
$516$	74.6491	+	44.2191i	0.144669	+	0.0856959i
$517$	389.210			0.752824
$518$		−	168.850i		−	0.325965i
$519$	−18.0662	+	30.4987i	−0.0348096	+	0.0587643i
$520$		0			0
$521$		−	3.20085i		−	0.00614366i	−0.999995	−	0.00307183i	$-0.999022\pi$
$521$		−	3.20085i		−	0.00614366i	0.999995	−	0.00307183i	$-0.000977795\pi$
$522$	164.105	+	299.515i	0.314378	+	0.573784i
$523$	−966.644			−1.84827			−0.924134	−	0.382069i	$-0.875212\pi$
$523$	−966.644			−1.84827			−0.924134	+	0.382069i	$0.875212\pi$
$524$			440.788i			0.841198i
$525$		0			0
$526$	−51.2370			−0.0974088
$527$			243.096i			0.461282i
$528$	51.8947	−	87.6068i	0.0982853	−	0.165922i
$529$	444.842			0.840911
$530$		0			0
$531$	190.053	−	104.130i	0.357915	−	0.196102i
$532$	−403.895			−0.759200
$533$			473.575i			0.888509i
$534$	221.842	+	131.410i	0.415434	+	0.246086i
$535$		0			0
$536$		−	312.429i		−	0.582891i
$537$	−105.553	+	178.191i	−0.196561	+	0.331827i
$538$	−746.763			−1.38804
$539$			59.8439i			0.111028i
$540$		0			0
$541$	−186.105			−0.344002			−0.172001	−	0.985097i	$-0.555023\pi$
$541$	−186.105			−0.344002			−0.172001	+	0.985097i	$0.555023\pi$
$542$		−	673.017i		−	1.24173i
$543$	489.601	+	290.019i	0.901659	+	0.534106i
$544$	−171.895			−0.315983
$545$		0			0
$546$	161.886	−	273.290i	0.296495	−	0.500532i
$547$	309.434			0.565693			0.282847	−	0.959165i	$-0.408721\pi$
$547$	309.434			0.565693			0.282847	+	0.959165i	$0.408721\pi$
$548$			191.031i			0.348596i
$549$	−233.298	−	425.802i	−0.424951	−	0.775596i
$550$		0			0
$551$		−	723.779i		−	1.31357i
$552$	66.9737	+	39.6725i	0.121329	+	0.0718704i
$553$	−351.684			−0.635957
$554$		−	266.096i		−	0.480317i
$555$		0			0
$556$	153.631			0.276315
$557$			4.00106i			0.00718323i	0.999994	+	0.00359161i	$0.00114325\pi$
$557$			4.00106i			0.00718323i	−0.999994	+	0.00359161i	$0.998857\pi$
$558$	−89.2982	+	48.9268i	−0.160033	+	0.0876824i
$559$	144.605			0.258685
$560$		0			0
$561$	665.526	+	394.230i	1.18632	+	0.702728i
$562$	34.5523			0.0614810
$563$		−	166.970i		−	0.296572i	−0.988945	−	0.148286i	$-0.952624\pi$
$563$		−	166.970i		−	0.296572i	0.988945	−	0.148286i	$-0.0473756\pi$
$564$	140.263	−	236.788i	0.248694	−	0.419836i
$565$		0			0
$566$		−	280.666i		−	0.495875i
$567$	−326.399	+	511.102i	−0.575660	+	0.901414i
$568$	44.1053			0.0776502
$569$			156.289i			0.274673i	0.990524	+	0.137337i	$0.0438542\pi$
$569$			156.289i			0.274673i	−0.990524	+	0.137337i	$0.956146\pi$
$570$		0			0
$571$	−144.105			−0.252374			−0.126187	−	0.992006i	$-0.540274\pi$
$571$	−144.105			−0.252374			−0.126187	+	0.992006i	$0.540274\pi$
$572$		−	169.706i		−	0.296688i
$573$	166.211	−	280.591i	0.290071	−	0.489688i
$574$	−501.421			−0.873555
$575$		0			0
$576$	−34.5964	−	63.1434i	−0.0600633	−	0.109624i
$577$	−532.947			−0.923651			−0.461826	−	0.886971i	$-0.652805\pi$
$577$	−532.947			−0.923651			−0.461826	+	0.886971i	$0.652805\pi$
$578$		−	897.132i		−	1.55213i
$579$	−433.495	−	256.785i	−0.748697	−	0.443497i
$580$		0			0
$581$		−	195.738i		−	0.336899i
$582$	−77.9559	+	131.602i	−0.133945	+	0.226121i
$583$	−257.842			−0.442268
$584$			248.753i			0.425946i
$585$		0			0
$586$	726.658			1.24003
$587$		−	190.342i		−	0.324262i	−0.986769	−	0.162131i	$-0.948163\pi$
$587$		−	190.342i		−	0.324262i	0.986769	−	0.162131i	$-0.0518368\pi$
$588$	36.4078	+	21.5665i	0.0619181	+	0.0366777i
$589$	215.789			0.366366
$590$		0			0
$591$	−262.460	+	443.077i	−0.444096	+	0.749707i
$592$	−63.7893			−0.107752
$593$		−	345.719i		−	0.583001i	−0.956571	−	0.291500i	$-0.905846\pi$
$593$		−	345.719i		−	0.583001i	0.956571	−	0.291500i	$-0.0941544\pi$
$594$	−10.8683	+	323.818i	−0.0182969	+	0.545148i
$595$		0			0
$596$			552.473i			0.926969i
$597$	−90.5438	−	53.6344i	−0.151665	−	0.0898399i
$598$	129.737			0.216951
$599$		−	704.055i		−	1.17538i	−0.809085	−	0.587692i	$-0.800037\pi$
$599$		−	704.055i		−	1.17538i	0.809085	−	0.587692i	$-0.199963\pi$
$600$		0			0
$601$	338.474			0.563185			0.281592	−	0.959534i	$-0.409137\pi$
$601$	338.474			0.563185			0.281592	+	0.959534i	$0.409137\pi$
$602$			153.107i			0.254331i
$603$	477.693	+	871.856i	0.792193	+	1.44586i
$604$	−36.1053			−0.0597770
$605$		0			0
$606$	−175.789	−	104.130i	−0.290081	−	0.171832i
$607$	816.513			1.34516			0.672581	−	0.740024i	$-0.265186\pi$
$607$	816.513			1.34516			0.672581	+	0.740024i	$0.265186\pi$
$608$			152.586i			0.250964i
$609$	−307.157	+	518.532i	−0.504363	+	0.851449i
$610$		0			0
$611$		−	458.688i		−	0.750717i
$612$	479.684	−	262.820i	0.783797	−	0.429445i
$613$	229.263			0.374001			0.187001	−	0.982360i	$-0.440123\pi$
$613$	229.263			0.374001			0.187001	+	0.982360i	$0.440123\pi$
$614$			16.0959i			0.0262148i
$615$		0			0
$616$	179.684			0.291695
$617$		−	1072.25i		−	1.73785i	−0.494945	−	0.868924i	$-0.664812\pi$
$617$		−	1072.25i		−	1.73785i	0.494945	−	0.868924i	$-0.335188\pi$
$618$	−303.601	+	512.528i	−0.491263	+	0.829334i
$619$	−80.7103			−0.130388			−0.0651941	−	0.997873i	$-0.520767\pi$
$619$	−80.7103			−0.130388			−0.0651941	+	0.997873i	$0.520767\pi$
$620$		0			0
$621$	−247.552	−	8.30863i	−0.398635	−	0.0133794i
$622$	−733.631			−1.17947
$623$			455.004i			0.730344i
$624$	−103.246	−	61.1584i	−0.165458	−	0.0980103i
$625$		0			0
$626$			65.5007i			0.104634i
$627$	349.947	−	590.769i	0.558130	−	0.942215i
$628$	207.684			0.330707
$629$		−	484.591i		−	0.770415i
$630$		0			0
$631$	492.894			0.781131			0.390566	−	0.920575i	$-0.372279\pi$
$631$	492.894			0.781131			0.390566	+	0.920575i	$0.372279\pi$
$632$			132.862i			0.210224i
$633$	150.114	+	88.9213i	0.237147	+	0.140476i
$634$	−55.2897			−0.0872077
$635$		0			0
$636$	−92.9210	+	156.866i	−0.146102	+	0.246645i
$637$	70.5267			0.110717
$638$			321.994i			0.504692i
$639$	−123.079	+	67.4353i	−0.192612	+	0.105533i
$640$		0			0
$641$		−	65.4816i		−	0.102155i	−0.998695	−	0.0510777i	$-0.983734\pi$
$641$		−	65.4816i		−	0.102155i	0.998695	−	0.0510777i	$-0.0162656\pi$
$642$	157.381	+	93.2264i	0.245143	+	0.145212i
$643$	428.619			0.666592			0.333296	−	0.942822i	$-0.391839\pi$
$643$	428.619			0.666592			0.333296	+	0.942822i	$0.391839\pi$
$644$			137.365i			0.213300i
$645$		0			0
$646$	−1159.16			−1.79436
$647$		−	462.801i		−	0.715303i	−0.933855	−	0.357652i	$-0.883578\pi$
$647$		−	462.801i		−	0.715303i	0.933855	−	0.357652i	$-0.116422\pi$
$648$	193.088	+	123.309i	0.297975	+	0.190292i
$649$	204.316			0.314817
$650$		0			0
$651$	−154.596	−	91.5766i	−0.237475	−	0.140671i
$652$	−22.7630			−0.0349126
$653$		−	425.064i		−	0.650941i	−0.945552	−	0.325470i	$-0.894477\pi$
$653$		−	425.064i		−	0.650941i	0.945552	−	0.325470i	$-0.105523\pi$
$654$	289.404	−	488.561i	0.442513	−	0.747035i
$655$		0			0
$656$			189.430i			0.288765i
$657$	−380.333	−	694.161i	−0.578894	−	1.05656i
$658$	485.658			0.738083
$659$		−	182.769i		−	0.277343i	−0.990338	−	0.138671i	$-0.955717\pi$
$659$		−	182.769i		−	0.277343i	0.990338	−	0.138671i	$-0.0442831\pi$
$660$		0			0
$661$	−482.053			−0.729278			−0.364639	−	0.931149i	$-0.618808\pi$
$661$	−482.053			−0.729278			−0.364639	+	0.931149i	$0.618808\pi$
$662$		−	629.920i		−	0.951541i
$663$	464.605	−	784.330i	0.700762	−	1.18300i
$664$	−73.9473			−0.111366
$665$		0			0
$666$	178.009	−	97.5314i	0.267280	−	0.146444i
$667$	−246.158			−0.369052
$668$			504.539i			0.755298i
$669$	256.517	+	151.950i	0.383434	+	0.227131i
$670$		0			0
$671$		−	457.758i		−	0.682203i
$672$	64.7544	−	109.316i	0.0963608	−	0.162673i
$673$	−184.579			−0.274264			−0.137132	−	0.990553i	$-0.543788\pi$
$673$	−184.579			−0.274264			−0.137132	+	0.990553i	$0.543788\pi$
$674$		−	460.587i		−	0.683363i
$675$		0			0
$676$	138.000			0.204142
$677$			1065.85i			1.57437i	0.616715	+	0.787187i	$0.288463\pi$
$677$			1065.85i			1.57437i	−0.616715	+	0.787187i	$0.711537\pi$
$678$	−28.8683	−	17.1004i	−0.0425787	−	0.0252219i
$679$	−269.920			−0.397526
$680$		0			0
$681$	331.710	−	559.982i	0.487093	−	0.822293i
$682$	−96.0000			−0.140762
$683$			788.926i			1.15509i	0.816359	+	0.577545i	$0.195989\pi$
$683$			788.926i			1.15509i	−0.816359	+	0.577545i	$0.804011\pi$
$684$	−233.298	−	425.802i	−0.341079	−	0.622518i
$685$		0			0
$686$		−	444.138i		−	0.647431i
$687$	−840.636	−	497.958i	−1.22363	−	0.724830i
$688$	57.8420			0.0840727
$689$			303.870i			0.441030i
$690$		0			0
$691$	932.000			1.34877			0.674385	−	0.738380i	$-0.264409\pi$
$691$	932.000			1.34877			0.674385	+	0.738380i	$0.264409\pi$
$692$			23.6320i			0.0341502i
$693$	−501.421	+	274.730i	−0.723551	+	0.396436i
$694$	73.2897			0.105605
$695$		0			0
$696$	195.895	+	116.040i	0.281458	+	0.166724i
$697$	−1439.05			−2.06464
$698$		−	137.997i		−	0.197704i
$699$	79.0655	−	133.476i	0.113112	−	0.190952i
$700$		0			0
$701$			1352.75i			1.92974i	0.262721	+	0.964872i	$0.415380\pi$
$701$			1352.75i			1.92974i	−0.262721	+	0.964872i	$0.584620\pi$
$702$	381.623	+	12.8084i	0.543622	+	0.0182457i
$703$	−430.158			−0.611889
$704$		−	67.8823i		−	0.0964237i
$705$		0			0
$706$	−805.815			−1.14138
$707$		−	360.549i		−	0.509970i
$708$	73.6313	−	124.302i	0.103999	−	0.175568i
$709$	−269.473			−0.380075			−0.190038	−	0.981777i	$-0.560861\pi$
$709$	−269.473			−0.380075			−0.190038	+	0.981777i	$0.560861\pi$
$710$		0			0
$711$	−203.140	−	370.759i	−0.285711	−	0.521462i
$712$	171.895			0.241425
$713$		−	73.3901i		−	0.102931i
$714$	830.447	+	491.923i	1.16309	+	0.688968i
$715$		0			0
$716$			138.072i			0.192837i
$717$	−626.947	+	1058.39i	−0.874403	+	1.47614i
$718$	−387.895			−0.540243
$719$		−	537.103i		−	0.747014i	−0.927627	−	0.373507i	$-0.878155\pi$
$719$		−	537.103i		−	0.747014i	0.927627	−	0.373507i	$-0.121845\pi$
$720$		0			0
$721$	−1051.21			−1.45799
$722$			518.421i			0.718034i
$723$	−1149.96	−	681.192i	−1.59055	−	0.942174i
$724$	379.368			0.523989
$725$		0			0
$726$	105.952	−	178.864i	0.145939	−	0.246369i
$727$	1117.83			1.53759			0.768795	−	0.639495i	$-0.220856\pi$
$727$	1117.83			1.53759			0.768795	+	0.639495i	$0.220856\pi$
$728$		−	211.760i		−	0.290879i
$729$	−727.359	−	48.8800i	−0.997750	−	0.0670507i
$730$		0			0
$731$			439.411i			0.601109i
$732$	−278.491	−	164.967i	−0.380452	−	0.225364i
$733$	−7.52599			−0.0102674			−0.00513369	−	0.999987i	$-0.501634\pi$
$733$	−7.52599			−0.0102674			−0.00513369	+	0.999987i	$0.501634\pi$
$734$		−	653.124i		−	0.889815i
$735$		0			0
$736$	51.8947			0.0705091
$737$			937.288i			1.27176i
$738$	−289.631	−	528.618i	−0.392454	−	0.716284i
$739$	−823.079			−1.11377			−0.556887	−	0.830588i	$-0.688004\pi$
$739$	−823.079			−1.11377			−0.556887	+	0.830588i	$0.688004\pi$
$740$		0			0
$741$	−696.228	−	412.417i	−0.939579	−	0.556568i
$742$	−321.737			−0.433607
$743$			3.21898i			0.00433241i	0.999998	+	0.00216620i	$0.000689524\pi$
$743$			3.21898i			0.00433241i	−0.999998	+	0.00216620i	$0.999310\pi$
$744$	−34.5964	+	58.4045i	−0.0465006	+	0.0785007i
$745$		0			0
$746$			695.719i			0.932599i
$747$	206.355	−	113.063i	0.276245	−	0.151356i
$748$	515.684			0.689417
$749$			322.794i			0.430967i
$750$		0			0
$751$	1185.63			1.57874			0.789368	−	0.613920i	$-0.210408\pi$
$751$	1185.63			1.57874			0.789368	+	0.613920i	$0.210408\pi$
$752$		−	183.475i		−	0.243983i
$753$	−362.921	+	612.671i	−0.481967	+	0.813639i
$754$	379.473			0.503280
$755$		0			0
$756$	−13.5616	+	404.061i	−0.0179386	+	0.534473i
$757$	863.315			1.14044			0.570221	−	0.821491i	$-0.306857\pi$
$757$	863.315			1.14044			0.570221	+	0.821491i	$0.306857\pi$
$758$		−	365.946i		−	0.482779i
$759$	−200.921	−	119.017i	−0.264718	−	0.156808i
$760$		0			0
$761$			570.597i			0.749800i	0.927065	+	0.374900i	$0.122323\pi$
$761$			570.597i			0.749800i	−0.927065	+	0.374900i	$0.877677\pi$
$762$	290.741	−	490.819i	0.381550	−	0.644119i
$763$	1002.05			1.31331
$764$		−	217.416i		−	0.284577i
$765$		0			0
$766$	738.816			0.964511
$767$		−	240.789i		−	0.313936i
$768$	−41.2982	−	24.4634i	−0.0537737	−	0.0318534i
$769$	−741.684			−0.964479			−0.482239	−	0.876040i	$-0.660176\pi$
$769$	−741.684			−0.964479			−0.482239	+	0.876040i	$0.660176\pi$
$770$		0			0
$771$	487.565	−	823.090i	0.632380	−	1.06756i
$772$	−335.895			−0.435097
$773$			623.203i			0.806214i	0.915153	+	0.403107i	$0.132070\pi$
$773$			623.203i			0.806214i	−0.915153	+	0.403107i	$0.867930\pi$
$774$	−161.412	+	88.4382i	−0.208543	+	0.114261i
$775$		0			0
$776$			101.972i			0.131408i
$777$	308.175	+	182.550i	0.396622	+	0.234943i
$778$	863.868			1.11037
$779$			1277.41i			1.63980i
$780$		0			0
$781$	−132.316			−0.169419
$782$			394.230i			0.504131i
$783$	−724.078	−	24.3023i	−0.924749	−	0.0310375i
$784$	28.2107			0.0359830
$785$		0			0
$786$	−804.500	−	476.553i	−1.02354	−	0.606301i
$787$	−335.303			−0.426052			−0.213026	−	0.977046i	$-0.568332\pi$
$787$	−335.303			−0.426052			−0.213026	+	0.977046i	$0.568332\pi$
$788$			343.319i			0.435684i
$789$	55.3943	−	93.5147i	0.0702083	−	0.118523i
$790$		0			0
$791$		−	59.2098i		−	0.0748543i
$792$	103.789	+	189.430i	0.131047	+	0.239179i
$793$	−539.473			−0.680294
$794$			302.642i			0.381161i
$795$		0			0
$796$	−70.1580			−0.0881382
$797$			550.520i			0.690740i	0.938467	+	0.345370i	$0.112247\pi$
$797$			550.520i			0.690740i	−0.938467	+	0.345370i	$0.887753\pi$
$798$	436.666	−	737.165i	0.547201	−	0.923765i
$799$	1393.81			1.74445
$800$		0			0
$801$	−479.684	+	262.820i	−0.598856	+	0.328115i
$802$	642.841			0.801548
$803$		−	746.258i		−	0.929337i
$804$	570.228	+	337.780i	0.709239	+	0.420124i
$805$		0			0
$806$			113.137i			0.140369i
$807$	807.354	−	1362.95i	1.00044	−	1.68891i
$808$	−136.211			−0.168578
$809$			560.288i			0.692569i	0.938130	+	0.346284i	$0.112557\pi$
$809$			560.288i			0.692569i	−0.938130	+	0.346284i	$0.887443\pi$
$810$		0			0
$811$	−237.842			−0.293270			−0.146635	−	0.989191i	$-0.546844\pi$
$811$	−237.842			−0.293270			−0.146635	+	0.989191i	$0.546844\pi$
$812$			401.786i			0.494810i
$813$	1228.35	+	727.624i	1.51089	+	0.894987i
$814$	191.368			0.235096
$815$		0			0
$816$	185.842	−	313.732i	0.227748	−	0.384475i
$817$	390.053			0.477421
$818$		−	811.535i		−	0.992097i
$819$	323.772	+	590.930i	0.395326	+	0.721526i
$820$		0			0
$821$		−	65.4816i		−	0.0797584i	−0.999205	−	0.0398792i	$-0.987303\pi$
$821$		−	65.4816i		−	0.0797584i	0.999205	−	0.0398792i	$-0.0126973\pi$
$822$	−348.658	−	206.531i	−0.424158	−	0.251254i
$823$	−521.512			−0.633673			−0.316836	−	0.948480i	$-0.602621\pi$
$823$	−521.512			−0.633673			−0.316836	+	0.948480i	$0.602621\pi$
$824$			397.133i			0.481958i
$825$		0			0
$826$	254.947			0.308652
$827$			987.512i			1.19409i	0.802208	+	0.597045i	$0.203658\pi$
$827$			987.512i			1.19409i	−0.802208	+	0.597045i	$0.796342\pi$
$828$	−144.816	+	79.3449i	−0.174898	+	0.0958272i
$829$	333.631			0.402450			0.201225	−	0.979545i	$-0.435508\pi$
$829$	333.631			0.402450			0.201225	+	0.979545i	$0.435508\pi$
$830$		0			0
$831$	485.662	+	287.686i	0.584431	+	0.346193i
$832$	−80.0000			−0.0961538
$833$			214.309i			0.257274i
$834$	−166.097	+	280.399i	−0.199157	+	0.336210i
$835$		0			0
$836$		−	457.758i		−	0.547558i
$837$	7.24555	−	215.878i	0.00865657	−	0.257919i
$838$	138.474			0.165243
$839$			129.363i			0.154187i	0.997024	+	0.0770934i	$0.0245640\pi$
$839$			129.363i			0.154187i	−0.997024	+	0.0770934i	$0.975436\pi$
$840$		0			0
$841$	121.000			0.143876
$842$			1014.44i			1.20479i
$843$	−37.3559	+	63.0629i	−0.0443130	+	0.0748077i
$844$	116.316			0.137815
$845$		0			0
$846$	280.527	+	512.001i	0.331592	+	0.605202i
$847$	366.855			0.433123
$848$			121.548i			0.143335i
$849$	512.254	+	303.438i	0.603362	+	0.357407i
$850$		0			0
$851$			146.297i			0.171912i
$852$	−47.6840	+	80.4984i	−0.0559671	+	0.0944817i
$853$	−1080.42			−1.26661			−0.633306	−	0.773902i	$-0.718303\pi$
$853$	−1080.42			−1.26661			−0.633306	+	0.773902i	$0.718303\pi$
$854$		−	571.193i		−	0.668845i
$855$		0			0
$856$	121.947			0.142462
$857$			702.548i			0.819776i	0.912136	+	0.409888i	$0.134432\pi$
$857$			702.548i			0.819776i	−0.912136	+	0.409888i	$0.865568\pi$
$858$	309.737	+	183.475i	0.360998	+	0.213841i
$859$	−281.132			−0.327278			−0.163639	−	0.986520i	$-0.552323\pi$
$859$	−281.132			−0.327278			−0.163639	+	0.986520i	$0.552323\pi$
$860$		0			0
$861$	542.105	−	915.163i	0.629623	−	1.06291i
$862$	414.474			0.480828
$863$			419.221i			0.485772i	0.970055	+	0.242886i	$0.0780941\pi$
$863$			419.221i			0.485772i	−0.970055	+	0.242886i	$0.921906\pi$
$864$	152.649	+	5.12338i	0.176677	+	0.00592984i
$865$		0			0
$866$		−	689.466i		−	0.796150i
$867$	1637.39	+	969.924i	1.88857	+	1.11871i
$868$	−119.789			−0.138006
$869$		−	398.585i		−	0.458671i
$870$		0			0
$871$	1104.60			1.26820
$872$		−	378.562i		−	0.434131i
$873$	−155.912	−	284.561i	−0.178593	−	0.325958i
$874$	349.947			0.400397
$875$		0			0
$876$	−454.009	−	268.936i	−0.518275	−	0.307005i
$877$	−1079.42			−1.23081			−0.615405	−	0.788211i	$-0.711008\pi$
$877$	−1079.42			−1.23081			−0.615405	+	0.788211i	$0.711008\pi$
$878$			363.788i			0.414337i
$879$	−785.618	+	1326.25i	−0.893763	+	1.50882i
$880$		0			0
$881$			748.212i			0.849275i	0.905363	+	0.424638i	$0.139599\pi$
$881$			748.212i			0.849275i	−0.905363	+	0.424638i	$0.860401\pi$
$882$	−78.7238	+	43.1330i	−0.0892561	+	0.0489037i
$883$	875.749			0.991788			0.495894	−	0.868383i	$-0.334840\pi$
$883$	875.749			0.991788			0.495894	+	0.868383i	$0.334840\pi$
$884$		−	607.739i		−	0.687488i
$885$		0			0
$886$	414.500			0.467833
$887$			1015.05i			1.14436i	0.820127	+	0.572182i	$0.193903\pi$
$887$			1015.05i			1.14436i	−0.820127	+	0.572182i	$0.806097\pi$
$888$	68.9651	−	116.425i	0.0776634	−	0.131109i
$889$	1006.68			1.13238
$890$		0			0
$891$	−579.263	−	369.928i	−0.650126	−	0.415183i
$892$	198.763			0.222828
$893$		−	1237.25i		−	1.38550i
$894$	−1008.34	−	597.300i	−1.12790	−	0.668121i
$895$		0			0
$896$		−	84.7038i		−	0.0945355i
$897$	−140.263	+	236.788i	−0.156369	+	0.263977i
$898$	−828.184			−0.922254
$899$		−	214.663i		−	0.238779i
$900$		0			0
$901$	−923.368			−1.02483
$902$		−	568.290i		−	0.630034i
$903$	−279.443	−	165.530i	−0.309460	−	0.183312i
$904$	−22.3687			−0.0247441
$905$		0			0
$906$	39.0349	−	65.8973i	0.0430849	−	0.0727343i
$907$	−1504.70			−1.65898			−0.829491	−	0.558520i	$-0.811369\pi$
$907$	−1504.70			−1.65898			−0.829491	+	0.558520i	$0.811369\pi$
$908$		−	433.903i		−	0.477867i
$909$	380.105	−	208.261i	0.418158	−	0.229110i
$910$		0			0
$911$			1002.19i			1.10010i	0.835131	+	0.550051i	$0.185392\pi$
$911$			1002.19i			1.10010i	−0.835131	+	0.550051i	$0.814608\pi$
$912$	−278.491	−	164.967i	−0.305363	−	0.180885i
$913$	221.842			0.242981
$914$			1149.83i			1.25802i
$915$		0			0
$916$	−651.368			−0.711100
$917$		−	1650.05i		−	1.79940i
$918$	−38.9210	+	1159.64i	−0.0423976	+	1.26322i
$919$	−780.289			−0.849063			−0.424532	−	0.905413i	$-0.639561\pi$
$919$	−780.289			−0.849063			−0.424532	+	0.905413i	$0.639561\pi$
$920$		0			0
$921$	−29.3772	−	17.4019i	−0.0318971	−	0.0188945i
$922$	783.579			0.849868
$923$			155.936i			0.168945i
$924$	−194.263	+	327.949i	−0.210242	+	0.354923i
$925$		0			0
$926$			636.005i			0.686830i
$927$	−607.201	−	1108.23i	−0.655018	−	1.19550i
$928$	151.789			0.163566
$929$		−	1093.84i		−	1.17744i	−0.808339	−	0.588718i	$-0.799633\pi$
$929$		−	1093.84i		−	1.17744i	0.808339	−	0.588718i	$-0.200367\pi$
$930$		0			0
$931$	190.236			0.204335
$932$		−	103.424i		−	0.110970i
$933$	793.157	−	1338.98i	0.850115	−	1.43513i
$934$	43.4477			0.0465179
$935$		0			0
$936$	223.246	−	122.317i	0.238510	−	0.130680i
$937$	407.947			0.435376			0.217688	−	0.976018i	$-0.430148\pi$
$937$	407.947			0.435376			0.217688	+	0.976018i	$0.430148\pi$
$938$			1169.55i			1.24686i
$939$	−119.548	−	70.8154i	−0.127314	−	0.0754157i
$940$		0			0
$941$		−	671.008i		−	0.713079i	−0.934280	−	0.356540i	$-0.883956\pi$
$941$		−	671.008i		−	0.713079i	0.934280	−	0.356540i	$-0.116044\pi$
$942$	−224.535	+	379.053i	−0.238360	+	0.402391i
$943$	434.447			0.460707
$944$		−	96.3155i		−	0.102029i
$945$		0			0
$946$	−173.526			−0.183431
$947$		−	1608.13i		−	1.69813i	−0.528290	−	0.849064i	$-0.677167\pi$
$947$		−	1608.13i		−	1.69813i	0.528290	−	0.849064i	$-0.322833\pi$
$948$	−242.491	−	143.642i	−0.255792	−	0.151521i
$949$	−879.473			−0.926737
$950$		0			0
$951$	59.7758	−	100.911i	0.0628557	−	0.106111i
$952$	643.473			0.675917
$953$		−	695.440i		−	0.729737i	−0.931059	−	0.364869i	$-0.881114\pi$
$953$		−	695.440i		−	0.729737i	0.931059	−	0.364869i	$-0.118886\pi$
$954$	−185.842	−	339.188i	−0.194803	−	0.355543i
$955$		0			0
$956$			820.095i			0.857840i
$957$	−587.684	−	348.120i	−0.614090	−	0.363762i
$958$	−1039.79			−1.08538
$959$		−	715.107i		−	0.745680i
$960$		0			0
$961$	−897.000			−0.933403
$962$		−	225.529i		−	0.234438i
$963$	−340.302	+	186.453i	−0.353377	+	0.193617i
$964$	−891.052			−0.924328
$965$		0			0
$966$	−250.710	−	148.511i	−0.259534	−	0.153738i
$967$	1030.07			1.06522			0.532609	−	0.846361i	$-0.321212\pi$
$967$	1030.07			1.06522			0.532609	+	0.846361i	$0.321212\pi$
$968$		−	138.593i		−	0.143175i
$969$	1253.21	−	2115.63i	1.29330	−	2.18331i
$970$		0			0
$971$		−	1165.24i		−	1.20004i	−0.799986	−	0.600019i	$-0.795160\pi$
$971$		−	1165.24i		−	1.20004i	0.799986	−	0.600019i	$-0.204840\pi$
$972$	−433.811	+	219.097i	−0.446308	+	0.225409i
$973$	−575.106			−0.591065
$974$			130.982i			0.134479i
$975$		0			0
$976$	−215.789			−0.221096
$977$			726.440i			0.743541i	0.928325	+	0.371771i	$0.121249\pi$
$977$			726.440i			0.743541i	−0.928325	+	0.371771i	$0.878751\pi$
$978$	24.6100	−	41.5457i	0.0251636	−	0.0424802i
$979$	−515.684			−0.526746
$980$		0			0
$981$	578.807	+	1056.40i	0.590017	+	1.07686i
$982$	−1270.42			−1.29371
$983$			1024.21i			1.04192i	0.853581	+	0.520960i	$0.174426\pi$
$983$			1024.21i			1.04192i	−0.853581	+	0.520960i	$0.825574\pi$
$984$	−345.737	−	204.800i	−0.351358	−	0.208130i
$985$		0			0
$986$			1153.10i			1.16948i
$987$	−525.064	+	886.395i	−0.531980	+	0.898070i
$988$	−539.473			−0.546026
$989$		−	132.657i		−	0.134133i
$990$		0			0
$991$	−1797.89			−1.81422			−0.907111	−	0.420892i	$-0.861717\pi$
$991$	−1797.89			−1.81422			−0.907111	+	0.420892i	$0.861717\pi$
$992$			45.2548i			0.0456198i
$993$	1149.69	+	681.031i	1.15780	+	0.685832i
$994$	−165.105			−0.166101
$995$		0			0
$996$	79.9473	−	134.964i	0.0802684	−	0.135506i
$997$	−901.368			−0.904080			−0.452040	−	0.891998i	$-0.649304\pi$
$997$	−901.368			−0.904080			−0.452040	+	0.891998i	$0.649304\pi$
$998$			193.636i			0.194024i
$999$	−14.4434	+	430.336i	−0.0144579	+	0.430766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.3.d.c.101.3		4
3.2	odd	2	inner	150.3.d.c.101.1		4
4.3	odd	2		1200.3.l.u.401.4		4
5.2	odd	4		150.3.b.b.149.2		8
5.3	odd	4		150.3.b.b.149.7		8
5.4	even	2		30.3.d.a.11.2	✓	4
12.11	even	2		1200.3.l.u.401.3		4
15.2	even	4		150.3.b.b.149.8		8
15.8	even	4		150.3.b.b.149.1		8
15.14	odd	2		30.3.d.a.11.4	yes	4
20.3	even	4		1200.3.c.k.449.4		8
20.7	even	4		1200.3.c.k.449.5		8
20.19	odd	2		240.3.l.c.161.1		4
40.19	odd	2		960.3.l.f.641.4		4
40.29	even	2		960.3.l.e.641.1		4
45.4	even	6		810.3.h.a.431.3		8
45.14	odd	6		810.3.h.a.431.2		8
45.29	odd	6		810.3.h.a.701.3		8
45.34	even	6		810.3.h.a.701.2		8
60.23	odd	4		1200.3.c.k.449.6		8
60.47	odd	4		1200.3.c.k.449.3		8
60.59	even	2		240.3.l.c.161.2		4
120.29	odd	2		960.3.l.e.641.2		4
120.59	even	2		960.3.l.f.641.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.d.a.11.2	✓	4	5.4	even	2
30.3.d.a.11.4	yes	4	15.14	odd	2
150.3.b.b.149.1		8	15.8	even	4
150.3.b.b.149.2		8	5.2	odd	4
150.3.b.b.149.7		8	5.3	odd	4
150.3.b.b.149.8		8	15.2	even	4
150.3.d.c.101.1		4	3.2	odd	2	inner
150.3.d.c.101.3		4	1.1	even	1	trivial
240.3.l.c.161.1		4	20.19	odd	2
240.3.l.c.161.2		4	60.59	even	2
810.3.h.a.431.2		8	45.14	odd	6
810.3.h.a.431.3		8	45.4	even	6
810.3.h.a.701.2		8	45.34	even	6
810.3.h.a.701.3		8	45.29	odd	6
960.3.l.e.641.1		4	40.29	even	2
960.3.l.e.641.2		4	120.29	odd	2
960.3.l.f.641.3		4	120.59	even	2
960.3.l.f.641.4		4	40.19	odd	2
1200.3.c.k.449.3		8	60.47	odd	4
1200.3.c.k.449.4		8	20.3	even	4
1200.3.c.k.449.5		8	20.7	even	4
1200.3.c.k.449.6		8	60.23	odd	4
1200.3.l.u.401.3		4	12.11	even	2
1200.3.l.u.401.4		4	4.3	odd	2

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	150.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(-2.58114 - 1.52896i) q^{3} -2.00000 q^{4} +(2.16228 - 3.65028i) q^{6} +7.48683 q^{7} -2.82843i q^{8} +(4.32456 + 7.89292i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(-2.58114 - 1.52896i) q^{3} -2.00000 q^{4} +(2.16228 - 3.65028i) q^{6} +7.48683 q^{7} -2.82843i q^{8} +(4.32456 + 7.89292i) q^{9} +8.48528i q^{11} +(5.16228 + 3.05792i) q^{12} +10.0000 q^{13} +10.5880i q^{14} +4.00000 q^{16} +30.3870i q^{17} +(-11.1623 + 6.11584i) q^{18} +26.9737 q^{19} +(-19.3246 - 11.4471i) q^{21} -12.0000 q^{22} -9.17377i q^{23} +(-4.32456 + 7.30056i) q^{24} +14.1421i q^{26} +(0.905694 - 26.9848i) q^{27} -14.9737 q^{28} -26.8328i q^{29} +8.00000 q^{31} +5.65685i q^{32} +(12.9737 - 21.9017i) q^{33} -42.9737 q^{34} +(-8.64911 - 15.7858i) q^{36} -15.9473 q^{37} +38.1465i q^{38} +(-25.8114 - 15.2896i) q^{39} +47.3575i q^{41} +(16.1886 - 27.3290i) q^{42} +14.4605 q^{43} -16.9706i q^{44} +12.9737 q^{46} -45.8688i q^{47} +(-10.3246 - 6.11584i) q^{48} +7.05267 q^{49} +(46.4605 - 78.4330i) q^{51} -20.0000 q^{52} +30.3870i q^{53} +(38.1623 + 1.28084i) q^{54} -21.1760i q^{56} +(-69.6228 - 41.2417i) q^{57} +37.9473 q^{58} -24.0789i q^{59} -53.9473 q^{61} +11.3137i q^{62} +(32.3772 + 59.0930i) q^{63} -8.00000 q^{64} +(30.9737 + 18.3475i) q^{66} +110.460 q^{67} -60.7739i q^{68} +(-14.0263 + 23.6788i) q^{69} +15.5936i q^{71} +(22.3246 - 12.2317i) q^{72} -87.9473 q^{73} -22.5529i q^{74} -53.9473 q^{76} +63.5279i q^{77} +(21.6228 - 36.5028i) q^{78} -46.9737 q^{79} +(-43.5964 + 68.2668i) q^{81} -66.9737 q^{82} -26.1443i q^{83} +(38.6491 + 22.8942i) q^{84} +20.4502i q^{86} +(-41.0263 + 69.2592i) q^{87} +24.0000 q^{88} +60.7739i q^{89} +74.8683 q^{91} +18.3475i q^{92} +(-20.6491 - 12.2317i) q^{93} +64.8683 q^{94} +(8.64911 - 14.6011i) q^{96} -36.0527 q^{97} +9.97398i q^{98} +(-66.9737 + 36.6951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 8 * q^9	\( 4 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 8 q^{9} + 8 q^{12} + 40 q^{13} + 16 q^{16} - 32 q^{18} + 32 q^{19} - 52 q^{21} - 48 q^{22} + 8 q^{24} - 28 q^{27} + 16 q^{28} + 32 q^{31} - 24 q^{33} - 96 q^{34} + 16 q^{36} + 88 q^{37} - 40 q^{39} + 128 q^{42} - 56 q^{43} - 24 q^{46} - 16 q^{48} + 180 q^{49} + 72 q^{51} - 80 q^{52} + 140 q^{54} - 152 q^{57} - 64 q^{61} + 256 q^{63} - 32 q^{64} + 48 q^{66} + 328 q^{67} - 132 q^{69} + 64 q^{72} - 200 q^{73} - 64 q^{76} - 40 q^{78} - 112 q^{79} + 28 q^{81} - 192 q^{82} + 104 q^{84} - 240 q^{87} + 96 q^{88} - 80 q^{91} - 32 q^{93} - 120 q^{94} - 16 q^{96} - 296 q^{97} - 192 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 8 * q^9 + 8 * q^12 + 40 * q^13 + 16 * q^16 - 32 * q^18 + 32 * q^19 - 52 * q^21 - 48 * q^22 + 8 * q^24 - 28 * q^27 + 16 * q^28 + 32 * q^31 - 24 * q^33 - 96 * q^34 + 16 * q^36 + 88 * q^37 - 40 * q^39 + 128 * q^42 - 56 * q^43 - 24 * q^46 - 16 * q^48 + 180 * q^49 + 72 * q^51 - 80 * q^52 + 140 * q^54 - 152 * q^57 - 64 * q^61 + 256 * q^63 - 32 * q^64 + 48 * q^66 + 328 * q^67 - 132 * q^69 + 64 * q^72 - 200 * q^73 - 64 * q^76 - 40 * q^78 - 112 * q^79 + 28 * q^81 - 192 * q^82 + 104 * q^84 - 240 * q^87 + 96 * q^88 - 80 * q^91 - 32 * q^93 - 120 * q^94 - 16 * q^96 - 296 * q^97 - 192 * q^99

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