LMFDB - Embedded newform 30.3.d.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,3,Mod(11,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, 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("30.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	30.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:	$0.817440793081$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.2
Root			$1.58114 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	30.11
Dual form			30.3.d.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(2.58114 + 1.52896i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(2.16228 - 3.65028i) q^{6} -7.48683 q^{7} +2.82843i q^{8} +(4.32456 + 7.89292i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(2.58114 + 1.52896i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(2.16228 - 3.65028i) q^{6} -7.48683 q^{7} +2.82843i q^{8} +(4.32456 + 7.89292i) q^{9} -3.16228 q^{10} +8.48528i q^{11} +(-5.16228 - 3.05792i) q^{12} -10.0000 q^{13} +10.5880i q^{14} +(3.41886 - 5.77160i) q^{15} +4.00000 q^{16} -30.3870i q^{17} +(11.1623 - 6.11584i) q^{18} +26.9737 q^{19} +4.47214i q^{20} +(-19.3246 - 11.4471i) q^{21} +12.0000 q^{22} +9.17377i q^{23} +(-4.32456 + 7.30056i) q^{24} -5.00000 q^{25} +14.1421i q^{26} +(-0.905694 + 26.9848i) q^{27} +14.9737 q^{28} -26.8328i q^{29} +(-8.16228 - 4.83500i) q^{30} +8.00000 q^{31} -5.65685i q^{32} +(-12.9737 + 21.9017i) q^{33} -42.9737 q^{34} +16.7411i q^{35} +(-8.64911 - 15.7858i) q^{36} +15.9473 q^{37} -38.1465i q^{38} +(-25.8114 - 15.2896i) q^{39} +6.32456 q^{40} +47.3575i q^{41} +(-16.1886 + 27.3290i) q^{42} -14.4605 q^{43} -16.9706i q^{44} +(17.6491 - 9.67000i) q^{45} +12.9737 q^{46} +45.8688i q^{47} +(10.3246 + 6.11584i) q^{48} +7.05267 q^{49} +7.07107i q^{50} +(46.4605 - 78.4330i) q^{51} +20.0000 q^{52} -30.3870i q^{53} +(38.1623 + 1.28084i) q^{54} +18.9737 q^{55} -21.1760i q^{56} +(69.6228 + 41.2417i) q^{57} -37.9473 q^{58} -24.0789i q^{59} +(-6.83772 + 11.5432i) q^{60} -53.9473 q^{61} -11.3137i q^{62} +(-32.3772 - 59.0930i) q^{63} -8.00000 q^{64} +22.3607i q^{65} +(30.9737 + 18.3475i) q^{66} -110.460 q^{67} +60.7739i q^{68} +(-14.0263 + 23.6788i) q^{69} +23.6754 q^{70} +15.5936i q^{71} +(-22.3246 + 12.2317i) q^{72} +87.9473 q^{73} -22.5529i q^{74} +(-12.9057 - 7.64481i) q^{75} -53.9473 q^{76} -63.5279i q^{77} +(-21.6228 + 36.5028i) q^{78} -46.9737 q^{79} -8.94427i q^{80} +(-43.5964 + 68.2668i) q^{81} +66.9737 q^{82} +26.1443i q^{83} +(38.6491 + 22.8942i) q^{84} -67.9473 q^{85} +20.4502i q^{86} +(41.0263 - 69.2592i) q^{87} -24.0000 q^{88} +60.7739i q^{89} +(-13.6754 - 24.9596i) q^{90} +74.8683 q^{91} -18.3475i q^{92} +(20.6491 + 12.2317i) q^{93} +64.8683 q^{94} -60.3150i q^{95} +(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} + 20 q^{15} + 16 q^{16} + 32 q^{18} + 32 q^{19} - 52 q^{21} + 48 q^{22} + 8 q^{24} - 20 q^{25} + 28 q^{27} - 16 q^{28} - 20 q^{30} + 32 q^{31} + 24 q^{33} - 96 q^{34} + 16 q^{36} - 88 q^{37} - 40 q^{39} - 128 q^{42} + 56 q^{43} + 20 q^{45} - 24 q^{46} + 16 q^{48} + 180 q^{49} + 72 q^{51} + 80 q^{52} + 140 q^{54} + 152 q^{57} - 40 q^{60} - 64 q^{61} - 256 q^{63} - 32 q^{64} + 48 q^{66} - 328 q^{67} - 132 q^{69} + 120 q^{70} - 64 q^{72} + 200 q^{73} - 20 q^{75} - 64 q^{76} + 40 q^{78} - 112 q^{79} + 28 q^{81} + 192 q^{82} + 104 q^{84} - 120 q^{85} + 240 q^{87} - 96 q^{88} - 80 q^{90} - 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 + 20 * q^15 + 16 * q^16 + 32 * q^18 + 32 * q^19 - 52 * q^21 + 48 * q^22 + 8 * q^24 - 20 * q^25 + 28 * q^27 - 16 * q^28 - 20 * q^30 + 32 * q^31 + 24 * q^33 - 96 * q^34 + 16 * q^36 - 88 * q^37 - 40 * q^39 - 128 * q^42 + 56 * q^43 + 20 * q^45 - 24 * q^46 + 16 * q^48 + 180 * q^49 + 72 * q^51 + 80 * q^52 + 140 * q^54 + 152 * q^57 - 40 * q^60 - 64 * q^61 - 256 * q^63 - 32 * q^64 + 48 * q^66 - 328 * q^67 - 132 * q^69 + 120 * q^70 - 64 * q^72 + 200 * q^73 - 20 * q^75 - 64 * q^76 + 40 * q^78 - 112 * q^79 + 28 * q^81 + 192 * q^82 + 104 * q^84 - 120 * q^85 + 240 * q^87 - 96 * q^88 - 80 * q^90 - 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 $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$1$	$-1$

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
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	2.16228	−	3.65028i	0.360380	−	0.608380i
$7$	−7.48683			−1.06955			−0.534774	−	0.844995i	$-0.679603\pi$
$7$	−7.48683			−1.06955			−0.534774	+	0.844995i	$0.679603\pi$
$8$			2.82843i			0.353553i
$9$	4.32456	+	7.89292i	0.480506	+	0.876991i
$10$	−3.16228			−0.316228
$11$			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	$-0.625666\pi$
$13$	−10.0000			−0.769231			−0.384615	+	0.923077i	$0.625666\pi$
$14$			10.5880i			0.756284i
$15$	3.41886	−	5.77160i	0.227924	−	0.384773i
$16$	4.00000			0.250000
$17$		−	30.3870i		−	1.78747i	−0.448596	−	0.893734i	$-0.648076\pi$
$17$		−	30.3870i		−	1.78747i	0.448596	−	0.893734i	$-0.351924\pi$
$18$	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	$0.248770\pi$
$20$			4.47214i			0.223607i
$21$	−19.3246	−	11.4471i	−0.920217	−	0.545099i
$22$	12.0000			0.545455
$23$			9.17377i			0.398859i	0.979912	+	0.199430i	$0.0639090\pi$
$23$			9.17377i			0.398859i	−0.979912	+	0.199430i	$0.936091\pi$
$24$	−4.32456	+	7.30056i	−0.180190	+	0.304190i
$25$	−5.00000			−0.200000
$26$			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	$-0.153096\pi$
$30$	−8.16228	−	4.83500i	−0.272076	−	0.161167i
$31$	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
$35$			16.7411i			0.478316i
$36$	−8.64911	−	15.7858i	−0.240253	−	0.438496i
$37$	15.9473			0.431009			0.215504	−	0.976503i	$-0.430860\pi$
$37$	15.9473			0.431009			0.215504	+	0.976503i	$0.430860\pi$
$38$		−	38.1465i		−	1.00386i
$39$	−25.8114	−	15.2896i	−0.661830	−	0.392041i
$40$	6.32456			0.158114
$41$			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	$-0.553778\pi$
$43$	−14.4605			−0.336291			−0.168145	+	0.985762i	$0.553778\pi$
$44$		−	16.9706i		−	0.385695i
$45$	17.6491	−	9.67000i	0.392202	−	0.214889i
$46$	12.9737			0.282036
$47$			45.8688i			0.975933i	0.872862	+	0.487966i	$0.162261\pi$
$47$			45.8688i			0.975933i	−0.872862	+	0.487966i	$0.837739\pi$
$48$	10.3246	+	6.11584i	0.215095	+	0.127413i
$49$	7.05267			0.143932
$50$			7.07107i			0.141421i
$51$	46.4605	−	78.4330i	0.910990	−	1.53790i
$52$	20.0000			0.384615
$53$		−	30.3870i		−	0.573339i	−0.958030	−	0.286670i	$-0.907452\pi$
$53$		−	30.3870i		−	0.573339i	0.958030	−	0.286670i	$-0.0925482\pi$
$54$	38.1623	+	1.28084i	0.706709	+	0.0237194i
$55$	18.9737			0.344976
$56$		−	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	$-0.0654132\pi$
$60$	−6.83772	+	11.5432i	−0.113962	+	0.192387i
$61$	−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
$65$			22.3607i			0.344010i
$66$	30.9737	+	18.3475i	0.469298	+	0.277993i
$67$	−110.460			−1.64866			−0.824332	−	0.566107i	$-0.808449\pi$
$67$	−110.460			−1.64866			−0.824332	+	0.566107i	$0.808449\pi$
$68$			60.7739i			0.893734i
$69$	−14.0263	+	23.6788i	−0.203280	+	0.343171i
$70$	23.6754			0.338221
$71$			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	$-0.294220\pi$
$73$	87.9473			1.20476			0.602379	+	0.798210i	$0.294220\pi$
$74$		−	22.5529i		−	0.304769i
$75$	−12.9057	−	7.64481i	−0.172076	−	0.101931i
$76$	−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	$0.596087\pi$
$80$		−	8.94427i		−	0.111803i
$81$	−43.5964	+	68.2668i	−0.538228	+	0.842799i
$82$	66.9737			0.816752
$83$			26.1443i			0.314992i	0.987520	+	0.157496i	$0.0503421\pi$
$83$			26.1443i			0.314992i	−0.987520	+	0.157496i	$0.949658\pi$
$84$	38.6491	+	22.8942i	0.460108	+	0.272549i
$85$	−67.9473			−0.799380
$86$			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	$0.889090\pi$
$90$	−13.6754	−	24.9596i	−0.151949	−	0.277329i
$91$	74.8683			0.822729
$92$		−	18.3475i		−	0.199430i
$93$	20.6491	+	12.2317i	0.222033	+	0.131524i
$94$	64.8683			0.690089
$95$		−	60.3150i		−	0.634894i
$96$	8.64911	−	14.6011i	0.0900949	−	0.152095i
$97$	36.0527			0.371677			0.185838	−	0.982580i	$-0.440500\pi$
$97$	36.0527			0.371677			0.185838	+	0.982580i	$0.440500\pi$
$98$		−	9.97398i		−	0.101775i
$99$	−66.9737	+	36.6951i	−0.676502	+	0.370657i
$100$	10.0000			0.100000
$101$		−	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	$-0.261288\pi$
$103$	140.408			1.36318			0.681591	+	0.731733i	$0.261288\pi$
$104$		−	28.2843i		−	0.271964i
$105$	−25.5964	+	43.2110i	−0.243776	+	0.411534i
$106$	−42.9737			−0.405412
$107$		−	43.1149i		−	0.402943i	−0.979494	−	0.201471i	$-0.935428\pi$
$107$		−	43.1149i		−	0.402943i	0.979494	−	0.201471i	$-0.0645723\pi$
$108$	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	$0.289578\pi$
$110$		−	26.8328i		−	0.243935i
$111$	41.1623	+	24.3829i	0.370831	+	0.219665i
$112$	−29.9473			−0.267387
$113$			7.90852i			0.0699869i	0.999388	+	0.0349935i	$0.0111410\pi$
$113$			7.90852i			0.0699869i	−0.999388	+	0.0349935i	$0.988859\pi$
$114$	58.3246	−	98.4615i	0.511619	−	0.863697i
$115$	20.5132			0.178375
$116$			53.6656i			0.462635i
$117$	−43.2456	−	78.9292i	−0.369620	−	0.674609i
$118$	−34.0527			−0.288582
$119$			227.502i			1.91178i
$120$	16.3246	+	9.67000i	0.136038	+	0.0805833i
$121$	49.0000			0.404959
$122$			76.2930i			0.625353i
$123$	−72.4078	+	122.236i	−0.588682	+	0.993792i
$124$	−16.0000			−0.129032
$125$			11.1803i			0.0894427i
$126$	−83.5701	+	45.7883i	−0.663255	+	0.363399i
$127$	−134.460			−1.05874			−0.529372	−	0.848390i	$-0.677572\pi$
$127$	−134.460			−1.05874			−0.529372	+	0.848390i	$0.677572\pi$
$128$			11.3137i			0.0883883i
$129$	−37.3246	−	22.1095i	−0.289338	−	0.171392i
$130$	31.6228			0.243252
$131$		−	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
$135$	60.3399	+	2.02519i	0.446962	+	0.0150014i
$136$	85.9473			0.631966
$137$			95.5153i			0.697192i	0.937273	+	0.348596i	$0.113341\pi$
$137$			95.5153i			0.697192i	−0.937273	+	0.348596i	$0.886659\pi$
$138$	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	$0.589113\pi$
$140$		−	33.4821i		−	0.239158i
$141$	−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
$145$	−60.0000			−0.413793
$146$		−	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	$-0.377595\pi$
$150$	−10.8114	+	18.2514i	−0.0720759	+	0.121676i
$151$	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
$155$		−	17.8885i		−	0.115410i
$156$	51.6228	+	30.5792i	0.330915	+	0.196021i
$157$	103.842			0.661414			0.330707	−	0.943733i	$-0.392713\pi$
$157$	103.842			0.661414			0.330707	+	0.943733i	$0.392713\pi$
$158$			66.4308i			0.420448i
$159$	46.4605	−	78.4330i	0.292204	−	0.493289i
$160$	−12.6491			−0.0790569
$161$		−	68.6825i		−	0.426599i
$162$	96.5438	+	61.6547i	0.595949	+	0.380584i
$163$	−11.3815			−0.0698251			−0.0349126	−	0.999390i	$-0.511115\pi$
$163$	−11.3815			−0.0698251			−0.0349126	+	0.999390i	$0.511115\pi$
$164$		−	94.7151i		−	0.577531i
$165$	48.9737	+	29.0100i	0.296810	+	0.175818i
$166$	36.9737			0.222733
$167$			252.270i			1.51060i	0.655382	+	0.755298i	$0.272508\pi$
$167$			252.270i			1.51060i	−0.655382	+	0.755298i	$0.727492\pi$
$168$	32.3772	−	54.6581i	0.192722	−	0.325346i
$169$	−69.0000			−0.408284
$170$			96.0920i			0.565247i
$171$	116.649	+	212.901i	0.682159	+	1.24504i
$172$	28.9210			0.168145
$173$			11.8160i			0.0683005i	0.999417	+	0.0341502i	$0.0108725\pi$
$173$			11.8160i			0.0683005i	−0.999417	+	0.0341502i	$0.989128\pi$
$174$	−97.9473	−	58.0200i	−0.562916	−	0.333448i
$175$	37.4342			0.213910
$176$			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	$-0.0617690\pi$
$180$	−35.2982	+	19.3400i	−0.196101	+	0.107444i
$181$	−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
$185$		−	35.6593i		−	0.192753i
$186$	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
$190$	−85.2982			−0.448938
$191$			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	$-0.643286\pi$
$193$	−167.947			−0.870193			−0.435097	+	0.900384i	$0.643286\pi$
$194$		−	50.9862i		−	0.262815i
$195$	−34.1886	+	57.7160i	−0.175326	+	0.295980i
$196$	−14.1053			−0.0719660
$197$			171.659i			0.871367i	0.900100	+	0.435684i	$0.143493\pi$
$197$			171.659i			0.871367i	−0.900100	+	0.435684i	$0.856507\pi$
$198$	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	$0.471908\pi$
$200$		−	14.1421i		−	0.0707107i
$201$	−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
$205$	105.895			0.516559
$206$		−	198.567i		−	0.963916i
$207$	−72.4078	+	39.6725i	−0.349796	+	0.191654i
$208$	−40.0000			−0.192308
$209$			228.879i			1.09512i
$210$	61.1096	+	36.1988i	0.290998	+	0.172375i
$211$	−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
$215$			32.3347i			0.150394i
$216$	−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
$220$	−37.9473			−0.172488
$221$			303.870i			1.37498i
$222$	34.4826	−	58.2123i	0.155327	−	0.262217i
$223$	99.3815			0.445657			0.222828	−	0.974858i	$-0.428471\pi$
$223$	99.3815			0.445657			0.222828	+	0.974858i	$0.428471\pi$
$224$			42.3519i			0.189071i
$225$	−21.6228	−	39.4646i	−0.0961012	−	0.175398i
$226$	11.1843			0.0494882
$227$		−	216.951i		−	0.955733i	−0.878432	−	0.477867i	$-0.841410\pi$
$227$		−	216.951i		−	0.955733i	0.878432	−	0.477867i	$-0.158590\pi$
$228$	−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	$0.248197\pi$
$230$		−	29.0100i		−	0.126130i
$231$	97.1317	−	163.974i	0.420483	−	0.709845i
$232$	75.8947			0.327132
$233$		−	51.7119i		−	0.221939i	−0.993824	−	0.110970i	$-0.964604\pi$
$233$		−	51.7119i		−	0.221939i	0.993824	−	0.110970i	$-0.0353957\pi$
$234$	−111.623	+	61.1584i	−0.477020	+	0.261361i
$235$	102.566			0.436450
$236$			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	$-0.328194\pi$
$240$	13.6754	−	23.0864i	0.0569810	−	0.0961934i
$241$	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
$245$		−	15.7702i		−	0.0643683i
$246$	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
$250$	15.8114			0.0632456
$251$		−	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
$255$	−175.381	−	103.889i	−0.687771	−	0.407407i
$256$	16.0000			0.0625000
$257$		−	318.887i		−	1.24080i	−0.784284	−	0.620402i	$-0.786970\pi$
$257$		−	318.887i		−	1.24080i	0.784284	−	0.620402i	$-0.213030\pi$
$258$	−31.2676	+	52.7849i	−0.121192	+	0.204593i
$259$	−119.395			−0.460985
$260$		−	44.7214i		−	0.172005i
$261$	211.789	−	116.040i	0.811453	−	0.444598i
$262$	−311.684			−1.18963
$263$		−	36.2300i		−	0.137757i	−0.997625	−	0.0688784i	$-0.978058\pi$
$263$		−	36.2300i		−	0.137757i	0.997625	−	0.0688784i	$-0.0219420\pi$
$264$	−61.9473	−	36.6951i	−0.234649	−	0.138996i
$265$	−67.9473			−0.256405
$266$			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	$0.561341\pi$
$270$	2.86406	−	85.3334i	0.0106076	−	0.316050i
$271$	−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
$275$		−	42.4264i		−	0.154278i
$276$	28.0527	−	47.3575i	0.101640	−	0.171585i
$277$	188.158			0.679271			0.339635	−	0.940557i	$-0.389696\pi$
$277$	188.158			0.679271			0.339635	+	0.940557i	$0.389696\pi$
$278$			108.634i			0.390769i
$279$	34.5964	+	63.1434i	0.124002	+	0.226320i
$280$	−47.3509			−0.169110
$281$		−	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	$-0.385965\pi$
$283$	198.460			0.701274			0.350637	+	0.936511i	$0.385965\pi$
$284$		−	31.1872i		−	0.109814i
$285$	92.2192	−	155.681i	0.323576	−	0.546250i
$286$	−120.000			−0.419580
$287$		−	354.558i		−	1.23539i
$288$	44.6491	−	24.4634i	0.155032	−	0.0849423i
$289$	−634.368			−2.19504
$290$			84.8528i			0.292596i
$291$	93.0569	+	55.1231i	0.319783	+	0.189427i
$292$	−175.895			−0.602379
$293$			513.825i			1.75367i	0.480794	+	0.876834i	$0.340349\pi$
$293$			513.825i			1.75367i	−0.480794	+	0.876834i	$0.659651\pi$
$294$	15.2498	−	25.7442i	0.0518702	−	0.0875654i
$295$	−53.8420			−0.182515
$296$			45.1059i			0.152385i
$297$	−228.974	−	7.68507i	−0.770955	−	0.0258757i
$298$	−390.658			−1.31093
$299$		−	91.7377i		−	0.306815i
$300$	25.8114	+	15.2896i	0.0860380	+	0.0509654i
$301$	108.263			0.359679
$302$		−	25.5303i		−	0.0845375i
$303$	73.6313	−	124.302i	0.243008	−	0.410237i
$304$	107.895			0.354917
$305$			120.630i			0.395508i
$306$	−185.842	−	339.188i	−0.607327	−	1.10846i
$307$	−11.3815			−0.0370733			−0.0185366	−	0.999828i	$-0.505901\pi$
$307$	−11.3815			−0.0370733			−0.0185366	+	0.999828i	$0.505901\pi$
$308$			127.056i			0.412519i
$309$	362.412	+	214.678i	1.17285	+	0.694751i
$310$	−25.2982			−0.0816072
$311$			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	$-0.523572\pi$
$313$	−46.3160			−0.147974			−0.0739872	+	0.997259i	$0.523572\pi$
$314$		−	146.855i		−	0.467690i
$315$	−132.136	+	72.3977i	−0.419479	+	0.229834i
$316$	93.9473			0.297302
$317$		−	39.0957i		−	0.123330i	−0.998097	−	0.0616651i	$-0.980359\pi$
$317$		−	39.0957i		−	0.123330i	0.998097	−	0.0616651i	$-0.0196411\pi$
$318$	−110.921	−	65.7051i	−0.348808	−	0.206620i
$319$	227.684			0.713743
$320$			17.8885i			0.0559017i
$321$	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
$325$	50.0000			0.153846
$326$			16.0959i			0.0493738i
$327$	345.465	+	204.639i	1.05647	+	0.625808i
$328$	−133.947			−0.408376
$329$		−	343.412i		−	1.04381i
$330$	41.0263	−	69.2592i	0.124322	−	0.209876i
$331$	−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
$335$			246.997i			0.737305i
$336$	−77.2982	−	45.7883i	−0.230054	−	0.136275i
$337$	325.684			0.966421			0.483211	−	0.875504i	$-0.339471\pi$
$337$	325.684			0.966421			0.483211	+	0.875504i	$0.339471\pi$
$338$			97.5807i			0.288700i
$339$	−12.0918	+	20.4130i	−0.0356691	+	0.0602153i
$340$	135.895			0.399690
$341$			67.8823i			0.199068i
$342$	301.088	−	164.967i	0.880373	−	0.482359i
$343$	314.053			0.915605
$344$		−	40.9005i		−	0.118897i
$345$	52.9473	+	31.3638i	0.153471	+	0.0909097i
$346$	16.7103			0.0482957
$347$			51.8236i			0.149348i	0.997208	+	0.0746738i	$0.0237916\pi$
$347$			51.8236i			0.149348i	−0.997208	+	0.0746738i	$0.976208\pi$
$348$	−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	$0.544645\pi$
$350$		−	52.9399i		−	0.151257i
$351$	9.05694	−	269.848i	0.0258033	−	0.768798i
$352$	48.0000			0.136364
$353$		−	569.797i		−	1.61416i	−0.590445	−	0.807078i	$-0.701048\pi$
$353$		−	569.797i		−	1.61416i	0.590445	−	0.807078i	$-0.298952\pi$
$354$	−87.8947	−	52.0652i	−0.248290	−	0.147077i
$355$	34.8683			0.0982206
$356$		−	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	$0.875232\pi$
$360$	27.3509	+	49.9192i	0.0759747	+	0.138665i
$361$	366.579			1.01545
$362$			268.254i			0.741032i
$363$	126.476	+	74.9191i	0.348418	+	0.206389i
$364$	−149.737			−0.411364
$365$		−	196.656i		−	0.538784i
$366$	−116.649	+	196.923i	−0.318713	+	0.538041i
$367$	461.828			1.25839			0.629194	−	0.777248i	$-0.283385\pi$
$367$	461.828			1.25839			0.629194	+	0.777248i	$0.283385\pi$
$368$			36.6951i			0.0997149i
$369$	−373.789	+	204.800i	−1.01298	+	0.555014i
$370$	−50.4299			−0.136297
$371$			227.502i			0.613213i
$372$	−41.2982	−	24.4634i	−0.111017	−	0.0657618i
$373$	−491.947			−1.31889			−0.659447	−	0.751751i	$-0.729209\pi$
$373$	−491.947			−1.31889			−0.659447	+	0.751751i	$0.729209\pi$
$374$		−	364.644i		−	0.974983i
$375$	−17.0943	+	28.8580i	−0.0455848	+	0.0769547i
$376$	−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	$0.610893\pi$
$380$			120.630i			0.317447i
$381$	−347.061	−	205.585i	−0.910922	−	0.539593i
$382$	153.737			0.402452
$383$			522.422i			1.36402i	0.731341	+	0.682012i	$0.238895\pi$
$383$			522.422i			1.36402i	−0.731341	+	0.682012i	$0.761105\pi$
$384$	−17.2982	+	29.2023i	−0.0450475	+	0.0760475i
$385$	−142.053			−0.368968
$386$			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	$-0.287414\pi$
$390$	81.6228	+	48.3500i	0.209289	+	0.123974i
$391$	278.763			0.712949
$392$			19.9480i			0.0508876i
$393$	336.974	−	568.867i	0.857439	−	1.44750i
$394$	242.763			0.616150
$395$			105.036i			0.265915i
$396$	133.947	−	73.3901i	0.338251	−	0.185329i
$397$	−214.000			−0.539043			−0.269521	−	0.962994i	$-0.586865\pi$
$397$	−214.000			−0.539043			−0.269521	+	0.962994i	$0.586865\pi$
$398$		−	49.6092i		−	0.124646i
$399$	−521.254	−	308.770i	−1.30640	−	0.773859i
$400$	−20.0000			−0.0500000
$401$		−	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
$405$	152.649	+	97.4846i	0.376911	+	0.240703i
$406$	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	$0.747494\pi$
$410$		−	149.758i		−	0.365263i
$411$	−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
$415$	58.4605			0.140869
$416$			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	$-0.0372780\pi$
$420$	51.1929	−	86.4220i	0.121888	−	0.205767i
$421$	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
$425$			151.935i			0.357494i
$426$	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
$430$	45.7281			0.106344
$431$		−	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	$-0.309661\pi$
$433$	487.526			1.12593			0.562963	+	0.826482i	$0.309661\pi$
$434$			84.7038i			0.195170i
$435$	−154.868	−	91.7377i	−0.356019	−	0.210891i
$436$	−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	$0.405353\pi$
$440$			53.6656i			0.121967i
$441$	30.4997	+	55.6662i	0.0691602	+	0.126227i
$442$	429.737			0.972255
$443$			293.096i			0.661615i	0.943698	+	0.330808i	$0.107321\pi$
$443$			293.096i			0.661615i	−0.943698	+	0.330808i	$0.892679\pi$
$444$	−82.3246	−	48.7657i	−0.185416	−	0.109833i
$445$	135.895			0.305381
$446$		−	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	$0.773875\pi$
$450$	−55.8114	+	30.5792i	−0.124025	+	0.0679538i
$451$	−401.842			−0.891002
$452$		−	15.8170i		−	0.0349935i
$453$	46.5964	+	27.6018i	0.102862	+	0.0609312i
$454$	−306.816			−0.675805
$455$		−	167.411i		−	0.367936i
$456$	−116.649	+	196.923i	−0.255809	+	0.431849i
$457$	−813.052			−1.77911			−0.889554	−	0.456831i	$-0.848984\pi$
$457$	−813.052			−1.77911			−0.889554	+	0.456831i	$0.848984\pi$
$458$		−	460.587i		−	1.00565i
$459$	819.986	+	27.5213i	1.78646	+	0.0599593i
$460$	−41.0263			−0.0891877
$461$		−	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	$-0.661421\pi$
$463$	−449.723			−0.971324			−0.485662	+	0.874147i	$0.661421\pi$
$464$		−	107.331i		−	0.231317i
$465$	27.3509	−	46.1728i	0.0588191	−	0.0992964i
$466$	−73.1317			−0.156935
$467$			30.7221i			0.0657862i	0.999459	+	0.0328931i	$0.0104721\pi$
$467$			30.7221i			0.0657862i	−0.999459	+	0.0328931i	$0.989528\pi$
$468$	86.4911	+	157.858i	0.184810	+	0.337304i
$469$	826.999			1.76332
$470$		−	145.050i		−	0.308617i
$471$	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
$475$	−134.868			−0.283933
$476$		−	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	$0.721512\pi$
$480$	−32.6491	−	19.3400i	−0.0680190	−	0.0402917i
$481$	−159.473			−0.331545
$482$		−	630.069i		−	1.30720i
$483$	105.013	−	177.279i	0.217418	−	0.367037i
$484$	−98.0000			−0.202479
$485$		−	80.6162i		−	0.166219i
$486$	154.925	+	306.751i	0.318776	+	0.631175i
$487$	−92.6185			−0.190182			−0.0950909	−	0.995469i	$-0.530314\pi$
$487$	−92.6185			−0.190182			−0.0950909	+	0.995469i	$0.530314\pi$
$488$		−	152.586i		−	0.312676i
$489$	−29.3772	−	17.4019i	−0.0600761	−	0.0355866i
$490$	−22.3025			−0.0455153
$491$			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
$495$	82.0527	+	149.758i	0.165763	+	0.302541i
$496$	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	$0.456191\pi$
$500$		−	22.3607i		−	0.0447214i
$501$	−385.710	+	651.143i	−0.769881	+	1.29969i
$502$	−335.684			−0.668693
$503$			443.077i			0.880868i	0.897785	+	0.440434i	$0.145175\pi$
$503$			443.077i			0.880868i	−0.897785	+	0.440434i	$0.854825\pi$
$504$	167.140	−	91.5766i	0.331627	−	0.181700i
$505$	−107.684			−0.213236
$506$			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	$-0.0671168\pi$
$510$	−146.921	+	248.027i	−0.288080	+	0.486327i
$511$	−658.447			−1.28855
$512$		−	22.6274i		−	0.0441942i
$513$	−24.4299	+	727.879i	−0.0476216	+	1.41887i
$514$	−450.974			−0.877381
$515$		−	313.961i		−	0.609634i
$516$	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
$520$	−63.2456			−0.121626
$521$		−	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	$-0.124788\pi$
$523$	966.644			1.84827			0.924134	+	0.382069i	$0.124788\pi$
$524$			440.788i			0.841198i
$525$	96.6228	+	57.2354i	0.184043	+	0.109020i
$526$	−51.2370			−0.0974088
$527$		−	243.096i		−	0.461282i
$528$	−51.8947	+	87.6068i	−0.0982853	+	0.165922i
$529$	444.842			0.840911
$530$			96.0920i			0.181306i
$531$	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
$535$	−96.4078			−0.180202
$536$		−	312.429i		−	0.582891i
$537$	105.553	−	178.191i	0.196561	−	0.331827i
$538$	746.763			1.38804
$539$			59.8439i			0.111028i
$540$	−120.680	−	4.05039i	−0.223481	−	0.00750072i
$541$	−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
$545$		−	299.280i		−	0.549137i
$546$	161.886	−	273.290i	0.296495	−	0.500532i
$547$	−309.434			−0.565693			−0.282847	−	0.959165i	$-0.591279\pi$
$547$	−309.434			−0.565693			−0.282847	+	0.959165i	$0.591279\pi$
$548$		−	191.031i		−	0.348596i
$549$	−233.298	−	425.802i	−0.424951	−	0.775596i
$550$	−60.0000			−0.109091
$551$		−	723.779i		−	1.31357i
$552$	−66.9737	−	39.6725i	−0.121329	−	0.0718704i
$553$	351.684			0.635957
$554$		−	266.096i		−	0.480317i
$555$	54.5217	−	92.0417i	0.0982373	−	0.165841i
$556$	153.631			0.276315
$557$		−	4.00106i		−	0.00718323i	−0.999994	−	0.00359161i	$-0.998857\pi$
$557$		−	4.00106i		−	0.00718323i	0.999994	−	0.00359161i	$-0.00114325\pi$
$558$	89.2982	−	48.9268i	0.160033	−	0.0876824i
$559$	144.605			0.258685
$560$			66.9643i			0.119579i
$561$	665.526	+	394.230i	1.18632	+	0.702728i
$562$	−34.5523			−0.0614810
$563$			166.970i			0.296572i	0.988945	+	0.148286i	$0.0473756\pi$
$563$			166.970i			0.296572i	−0.988945	+	0.148286i	$0.952624\pi$
$564$	140.263	−	236.788i	0.248694	−	0.419836i
$565$	17.6840			0.0312991
$566$		−	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	$0.956146\pi$
$570$	−220.167	−	130.418i	−0.386257	−	0.228803i
$571$	−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
$575$		−	45.8688i		−	0.0797719i
$576$	−34.5964	−	63.1434i	−0.0600633	−	0.109624i
$577$	532.947			0.923651			0.461826	−	0.886971i	$-0.347195\pi$
$577$	532.947			0.923651			0.461826	+	0.886971i	$0.347195\pi$
$578$			897.132i			1.55213i
$579$	−433.495	−	256.785i	−0.748697	−	0.443497i
$580$	120.000			0.206897
$581$		−	195.738i		−	0.336899i
$582$	77.9559	−	131.602i	0.133945	−	0.226121i
$583$	257.842			0.442268
$584$			248.753i			0.425946i
$585$	−176.491	+	96.7000i	−0.301694	+	0.165299i
$586$	726.658			1.24003
$587$			190.342i			0.324262i	0.986769	+	0.162131i	$0.0518368\pi$
$587$			190.342i			0.324262i	−0.986769	+	0.162131i	$0.948163\pi$
$588$	−36.4078	−	21.5665i	−0.0619181	−	0.0366777i
$589$	215.789			0.366366
$590$			76.1441i			0.129058i
$591$	−262.460	+	443.077i	−0.444096	+	0.749707i
$592$	63.7893			0.107752
$593$			345.719i			0.583001i	0.956571	+	0.291500i	$0.0941544\pi$
$593$			345.719i			0.583001i	−0.956571	+	0.291500i	$0.905846\pi$
$594$	−10.8683	+	323.818i	−0.0182969	+	0.545148i
$595$	508.710			0.854975
$596$			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	$-0.199963\pi$
$600$	21.6228	−	36.5028i	0.0360380	−	0.0608380i
$601$	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
$605$		−	109.567i		−	0.181103i
$606$	−175.789	−	104.130i	−0.290081	−	0.171832i
$607$	−816.513			−1.34516			−0.672581	−	0.740024i	$-0.734814\pi$
$607$	−816.513			−1.34516			−0.672581	+	0.740024i	$0.734814\pi$
$608$		−	152.586i		−	0.250964i
$609$	−307.157	+	518.532i	−0.504363	+	0.851449i
$610$	170.596			0.279666
$611$		−	458.688i		−	0.750717i
$612$	−479.684	+	262.820i	−0.783797	+	0.429445i
$613$	−229.263			−0.374001			−0.187001	−	0.982360i	$-0.559877\pi$
$613$	−229.263			−0.374001			−0.187001	+	0.982360i	$0.559877\pi$
$614$			16.0959i			0.0262148i
$615$	273.329	+	161.909i	0.444437	+	0.263266i
$616$	179.684			0.291695
$617$			1072.25i			1.73785i	0.494945	+	0.868924i	$0.335188\pi$
$617$			1072.25i			1.73785i	−0.494945	+	0.868924i	$0.664812\pi$
$618$	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	$0.520767\pi$
$620$			35.7771i			0.0577050i
$621$	−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
$625$	25.0000			0.0400000
$626$			65.5007i			0.104634i
$627$	−349.947	+	590.769i	−0.558130	+	0.942215i
$628$	−207.684			−0.330707
$629$		−	484.591i		−	0.770415i
$630$	102.386	+	186.868i	0.162517	+	0.296617i
$631$	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
$635$			300.663i			0.473485i
$636$	−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
$640$	25.2982			0.0395285
$641$		−	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	$-0.608161\pi$
$643$	−428.619			−0.666592			−0.333296	+	0.942822i	$0.608161\pi$
$644$			137.365i			0.213300i
$645$	−49.4384	+	83.4602i	−0.0766487	+	0.129396i
$646$	−1159.16			−1.79436
$647$			462.801i			0.715303i	0.933855	+	0.357652i	$0.116422\pi$
$647$			462.801i			0.715303i	−0.933855	+	0.357652i	$0.883578\pi$
$648$	−193.088	−	123.309i	−0.297975	−	0.190292i
$649$	204.316			0.314817
$650$		−	70.7107i		−	0.108786i
$651$	−154.596	−	91.5766i	−0.237475	−	0.140671i
$652$	22.7630			0.0349126
$653$			425.064i			0.650941i	0.945552	+	0.325470i	$0.105523\pi$
$653$			425.064i			0.650941i	−0.945552	+	0.325470i	$0.894477\pi$
$654$	289.404	−	488.561i	0.442513	−	0.747035i
$655$	−492.816			−0.752390
$656$			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	$-0.0442831\pi$
$660$	−97.9473	−	58.0200i	−0.148405	−	0.0879091i
$661$	−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
$665$			451.568i			0.679050i
$666$	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
$670$	349.307			0.521353
$671$		−	457.758i		−	0.682203i
$672$	−64.7544	+	109.316i	−0.0963608	+	0.162673i
$673$	184.579			0.274264			0.137132	−	0.990553i	$-0.456212\pi$
$673$	184.579			0.274264			0.137132	+	0.990553i	$0.456212\pi$
$674$		−	460.587i		−	0.683363i
$675$	4.52847	−	134.924i	0.00670885	−	0.199887i
$676$	138.000			0.204142
$677$		−	1065.85i		−	1.57437i	−0.616715	−	0.787187i	$-0.711537\pi$
$677$		−	1065.85i		−	1.57437i	0.616715	−	0.787187i	$-0.288463\pi$
$678$	28.8683	+	17.1004i	0.0425787	+	0.0252219i
$679$	−269.920			−0.397526
$680$		−	192.184i		−	0.282624i
$681$	331.710	−	559.982i	0.487093	−	0.822293i
$682$	96.0000			0.140762
$683$		−	788.926i		−	1.15509i	−0.816359	−	0.577545i	$-0.804011\pi$
$683$		−	788.926i		−	1.15509i	0.816359	−	0.577545i	$-0.195989\pi$
$684$	−233.298	−	425.802i	−0.341079	−	0.622518i
$685$	213.579			0.311794
$686$		−	444.138i		−	0.647431i
$687$	840.636	+	497.958i	1.22363	+	0.724830i
$688$	−57.8420			−0.0840727
$689$			303.870i			0.441030i
$690$	44.3552	−	74.8788i	0.0642828	−	0.108520i
$691$	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
$695$			171.765i			0.247144i
$696$	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
$700$	−74.8683			−0.106955
$701$			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
$705$	264.737	+	156.819i	0.375513	+	0.222439i
$706$	−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	$0.560861\pi$
$710$		−	49.3113i		−	0.0694525i
$711$	−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
$715$	−189.737			−0.265366
$716$			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	$-0.121845\pi$
$720$	70.5964	−	38.6800i	0.0980506	−	0.0537222i
$721$	−1051.21			−1.45799
$722$		−	518.421i		−	0.718034i
$723$	1149.96	+	681.192i	1.59055	+	0.942174i
$724$	379.368			0.523989
$725$			134.164i			0.185054i
$726$	105.952	−	178.864i	0.145939	−	0.246369i
$727$	−1117.83			−1.53759			−0.768795	−	0.639495i	$-0.779144\pi$
$727$	−1117.83			−1.53759			−0.768795	+	0.639495i	$0.779144\pi$
$728$			211.760i			0.290879i
$729$	−727.359	−	48.8800i	−0.997750	−	0.0670507i
$730$	−278.114			−0.380978
$731$			439.411i			0.601109i
$732$	278.491	+	164.967i	0.380452	+	0.225364i
$733$	7.52599			0.0102674			0.00513369	−	0.999987i	$-0.498366\pi$
$733$	7.52599			0.0102674			0.00513369	+	0.999987i	$0.498366\pi$
$734$		−	653.124i		−	0.889815i
$735$	24.1121	−	40.7052i	0.0328056	−	0.0553812i
$736$	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	$0.688004\pi$
$740$			71.3186i			0.0963765i
$741$	−696.228	−	412.417i	−0.939579	−	0.556568i
$742$	321.737			0.433607
$743$		−	3.21898i		−	0.00433241i	−0.999998	−	0.00216620i	$-0.999310\pi$
$743$		−	3.21898i		−	0.00433241i	0.999998	−	0.00216620i	$-0.000689524\pi$
$744$	−34.5964	+	58.4045i	−0.0465006	+	0.0785007i
$745$	−617.684			−0.829106
$746$			695.719i			0.932599i
$747$	−206.355	+	113.063i	−0.276245	+	0.151356i
$748$	−515.684			−0.689417
$749$			322.794i			0.430967i
$750$	40.8114	+	24.1750i	0.0544152	+	0.0322333i
$751$	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
$755$		−	40.3670i		−	0.0534662i
$756$	−13.5616	+	404.061i	−0.0179386	+	0.534473i
$757$	−863.315			−1.14044			−0.570221	−	0.821491i	$-0.693143\pi$
$757$	−863.315			−1.14044			−0.570221	+	0.821491i	$0.693143\pi$
$758$			365.946i			0.482779i
$759$	−200.921	−	119.017i	−0.264718	−	0.156808i
$760$	170.596			0.224469
$761$			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
$765$	−293.842	−	536.303i	−0.384107	−	0.701050i
$766$	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	$0.660176\pi$
$770$			200.893i			0.260900i
$771$	487.565	−	823.090i	0.632380	−	1.06756i
$772$	335.895			0.435097
$773$		−	623.203i		−	0.806214i	−0.915153	−	0.403107i	$-0.867930\pi$
$773$		−	623.203i		−	0.806214i	0.915153	−	0.403107i	$-0.132070\pi$
$774$	−161.412	+	88.4382i	−0.208543	+	0.114261i
$775$	−40.0000			−0.0516129
$776$			101.972i			0.131408i
$777$	−308.175	−	182.550i	−0.396622	−	0.234943i
$778$	−863.868			−1.11037
$779$			1277.41i			1.63980i
$780$	68.3772	−	115.432i	0.0876631	−	0.147990i
$781$	−132.316			−0.169419
$782$		−	394.230i		−	0.504131i
$783$	724.078	+	24.3023i	0.924749	+	0.0310375i
$784$	28.2107			0.0359830
$785$		−	232.198i		−	0.295793i
$786$	−804.500	−	476.553i	−1.02354	−	0.606301i
$787$	335.303			0.426052			0.213026	−	0.977046i	$-0.431668\pi$
$787$	335.303			0.426052			0.213026	+	0.977046i	$0.431668\pi$
$788$		−	343.319i		−	0.435684i
$789$	55.3943	−	93.5147i	0.0702083	−	0.118523i
$790$	148.544			0.188030
$791$		−	59.2098i		−	0.0748543i
$792$	−103.789	−	189.430i	−0.131047	−	0.239179i
$793$	539.473			0.680294
$794$			302.642i			0.381161i
$795$	−175.381	−	103.889i	−0.220606	−	0.130678i
$796$	−70.1580			−0.0881382
$797$		−	550.520i		−	0.690740i	−0.938467	−	0.345370i	$-0.887753\pi$
$797$		−	550.520i		−	0.690740i	0.938467	−	0.345370i	$-0.112247\pi$
$798$	−436.666	+	737.165i	−0.547201	+	0.923765i
$799$	1393.81			1.74445
$800$			28.2843i			0.0353553i
$801$	−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
$805$	−153.579			−0.190781
$806$			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	$0.887443\pi$
$810$	137.864	−	215.878i	0.170203	−	0.266517i
$811$	−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
$815$			25.4498i			0.0312267i
$816$	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
$820$	−211.789			−0.258280
$821$		−	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	$-0.397379\pi$
$823$	521.512			0.633673			0.316836	+	0.948480i	$0.397379\pi$
$824$			397.133i			0.481958i
$825$	64.8683	−	109.508i	0.0786283	−	0.132738i
$826$	254.947			0.308652
$827$		−	987.512i		−	1.19409i	−0.802208	−	0.597045i	$-0.796342\pi$
$827$		−	987.512i		−	1.19409i	0.802208	−	0.597045i	$-0.203658\pi$
$828$	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	$0.435508\pi$
$830$		−	82.6756i		−	0.0996092i
$831$	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
$835$	564.092			0.675559
$836$		−	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	$0.975436\pi$
$840$	−122.219	−	72.3977i	−0.145499	−	0.0861877i
$841$	121.000			0.143876
$842$		−	1014.44i		−	1.20479i
$843$	37.3559	−	63.0629i	0.0443130	−	0.0748077i
$844$	116.316			0.137815
$845$			154.289i			0.182590i
$846$	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
$850$	214.868			0.252786
$851$			146.297i			0.171912i
$852$	47.6840	−	80.4984i	0.0559671	−	0.0944817i
$853$	1080.42			1.26661			0.633306	−	0.773902i	$-0.281697\pi$
$853$	1080.42			1.26661			0.633306	+	0.773902i	$0.281697\pi$
$854$		−	571.193i		−	0.668845i
$855$	476.061	−	260.835i	0.556797	−	0.305071i
$856$	121.947			0.142462
$857$		−	702.548i		−	0.819776i	−0.912136	−	0.409888i	$-0.865568\pi$
$857$		−	702.548i		−	0.819776i	0.912136	−	0.409888i	$-0.134432\pi$
$858$	−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	$0.552323\pi$
$860$		−	64.6693i		−	0.0751969i
$861$	542.105	−	915.163i	0.629623	−	1.06291i
$862$	−414.474			−0.480828
$863$		−	419.221i		−	0.485772i	−0.970055	−	0.242886i	$-0.921906\pi$
$863$		−	419.221i		−	0.485772i	0.970055	−	0.242886i	$-0.0780941\pi$
$864$	152.649	+	5.12338i	0.176677	+	0.00592984i
$865$	26.4213			0.0305449
$866$		−	689.466i		−	0.796150i
$867$	−1637.39	−	969.924i	−1.88857	−	1.11871i
$868$	119.789			0.138006
$869$		−	398.585i		−	0.458671i
$870$	−129.737	+	219.017i	−0.149123	+	0.251744i
$871$	1104.60			1.26820
$872$			378.562i			0.434131i
$873$	155.912	+	284.561i	0.178593	+	0.325958i
$874$	349.947			0.400397
$875$		−	83.7053i		−	0.0956632i
$876$	−454.009	−	268.936i	−0.518275	−	0.307005i
$877$	1079.42			1.23081			0.615405	−	0.788211i	$-0.288992\pi$
$877$	1079.42			1.23081			0.615405	+	0.788211i	$0.288992\pi$
$878$		−	363.788i		−	0.414337i
$879$	−785.618	+	1326.25i	−0.893763	+	1.50882i
$880$	75.8947			0.0862439
$881$			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	$-0.665160\pi$
$883$	−875.749			−0.991788			−0.495894	+	0.868383i	$0.665160\pi$
$884$		−	607.739i		−	0.687488i
$885$	−138.974	−	82.3223i	−0.157032	−	0.0930196i
$886$	414.500			0.467833
$887$		−	1015.05i		−	1.14436i	−0.820127	−	0.572182i	$-0.806097\pi$
$887$		−	1015.05i		−	1.14436i	0.820127	−	0.572182i	$-0.193903\pi$
$888$	−68.9651	+	116.425i	−0.0776634	+	0.131109i
$889$	1006.68			1.13238
$890$		−	192.184i		−	0.215937i
$891$	−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
$895$	−154.369			−0.172479
$896$		−	84.7038i		−	0.0945355i
$897$	140.263	−	236.788i	0.156369	−	0.263977i
$898$	828.184			0.922254
$899$		−	214.663i		−	0.238779i
$900$	43.2456	+	78.9292i	0.0480506	+	0.0876991i
$901$	−923.368			−1.02483
$902$			568.290i			0.630034i
$903$	279.443	+	165.530i	0.309460	+	0.183312i
$904$	−22.3687			−0.0247441
$905$			424.146i			0.468670i
$906$	39.0349	−	65.8973i	0.0430849	−	0.0727343i
$907$	1504.70			1.65898			0.829491	−	0.558520i	$-0.188631\pi$
$907$	1504.70			1.65898			0.829491	+	0.558520i	$0.188631\pi$
$908$			433.903i			0.477867i
$909$	380.105	−	208.261i	0.418158	−	0.229110i
$910$	−236.754			−0.260170
$911$			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
$915$	−184.438	+	311.363i	−0.201572	+	0.340287i
$916$	−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	$0.639561\pi$
$920$			58.0200i			0.0630652i
$921$	−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
$925$	−79.7367			−0.0862018
$926$			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	$-0.200367\pi$
$930$	−65.2982	−	38.6800i	−0.0702131	−	0.0415914i
$931$	190.236			0.204335
$932$			103.424i			0.110970i
$933$	−793.157	+	1338.98i	−0.850115	+	1.43513i
$934$	43.4477			0.0465179
$935$		−	576.552i		−	0.616633i
$936$	223.246	−	122.317i	0.238510	−	0.130680i
$937$	−407.947			−0.435376			−0.217688	−	0.976018i	$-0.569852\pi$
$937$	−407.947			−0.435376			−0.217688	+	0.976018i	$0.569852\pi$
$938$		−	1169.55i		−	1.24686i
$939$	−119.548	−	70.8154i	−0.127314	−	0.0754157i
$940$	−205.132			−0.218225
$941$		−	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
$945$	−451.754	−	15.1623i	−0.478047	−	0.0160447i
$946$	−173.526			−0.183431
$947$			1608.13i			1.69813i	0.528290	+	0.849064i	$0.322833\pi$
$947$			1608.13i			1.69813i	−0.528290	+	0.849064i	$0.677167\pi$
$948$	242.491	+	143.642i	0.255792	+	0.151521i
$949$	−879.473			−0.926737
$950$			190.733i			0.200771i
$951$	59.7758	−	100.911i	0.0628557	−	0.106111i
$952$	−643.473			−0.675917
$953$			695.440i			0.729737i	0.931059	+	0.364869i	$0.118886\pi$
$953$			695.440i			0.729737i	−0.931059	+	0.364869i	$0.881114\pi$
$954$	−185.842	−	339.188i	−0.194803	−	0.355543i
$955$	243.079			0.254533
$956$			820.095i			0.857840i
$957$	587.684	+	348.120i	0.614090	+	0.363762i
$958$	1039.79			1.08538
$959$		−	715.107i		−	0.745680i
$960$	−27.3509	+	46.1728i	−0.0284905	+	0.0480967i
$961$	−897.000			−0.933403
$962$			225.529i			0.234438i
$963$	340.302	−	186.453i	0.353377	−	0.193617i
$964$	−891.052			−0.924328
$965$			375.542i			0.389162i
$966$	−250.710	−	148.511i	−0.259534	−	0.153738i
$967$	−1030.07			−1.06522			−0.532609	−	0.846361i	$-0.678788\pi$
$967$	−1030.07			−1.06522			−0.532609	+	0.846361i	$0.678788\pi$
$968$			138.593i			0.143175i
$969$	1253.21	−	2115.63i	1.29330	−	2.18331i
$970$	−114.009			−0.117535
$971$		−	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
$975$	129.057	+	76.4481i	0.132366	+	0.0784083i
$976$	−215.789			−0.221096
$977$		−	726.440i		−	0.743541i	−0.928325	−	0.371771i	$-0.878751\pi$
$977$		−	726.440i		−	0.743541i	0.928325	−	0.371771i	$-0.121249\pi$
$978$	−24.6100	+	41.5457i	−0.0251636	+	0.0424802i
$979$	−515.684			−0.526746
$980$			31.5405i			0.0321842i
$981$	578.807	+	1056.40i	0.590017	+	1.07686i
$982$	1270.42			1.29371
$983$		−	1024.21i		−	1.04192i	−0.853581	−	0.520960i	$-0.825574\pi$
$983$		−	1024.21i		−	1.04192i	0.853581	−	0.520960i	$-0.174426\pi$
$984$	−345.737	−	204.800i	−0.351358	−	0.208130i
$985$	383.842			0.389687
$986$			1153.10i			1.16948i
$987$	525.064	−	886.395i	0.531980	−	0.898070i
$988$	539.473			0.546026
$989$		−	132.657i		−	0.134133i
$990$	211.789	−	116.040i	0.213929	−	0.117212i
$991$	−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
$995$		−	78.4390i		−	0.0788332i
$996$	79.9473	−	134.964i	0.0802684	−	0.135506i
$997$	901.368			0.904080			0.452040	−	0.891998i	$-0.350696\pi$
$997$	901.368			0.904080			0.452040	+	0.891998i	$0.350696\pi$
$998$		−	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	30.3.d.a.11.2	✓	4
3.2	odd	2	inner	30.3.d.a.11.4	yes	4
4.3	odd	2		240.3.l.c.161.1		4
5.2	odd	4		150.3.b.b.149.7		8
5.3	odd	4		150.3.b.b.149.2		8
5.4	even	2		150.3.d.c.101.3		4
8.3	odd	2		960.3.l.f.641.4		4
8.5	even	2		960.3.l.e.641.1		4
9.2	odd	6		810.3.h.a.701.3		8
9.4	even	3		810.3.h.a.431.3		8
9.5	odd	6		810.3.h.a.431.2		8
9.7	even	3		810.3.h.a.701.2		8
12.11	even	2		240.3.l.c.161.2		4
15.2	even	4		150.3.b.b.149.1		8
15.8	even	4		150.3.b.b.149.8		8
15.14	odd	2		150.3.d.c.101.1		4
20.3	even	4		1200.3.c.k.449.5		8
20.7	even	4		1200.3.c.k.449.4		8
20.19	odd	2		1200.3.l.u.401.4		4
24.5	odd	2		960.3.l.e.641.2		4
24.11	even	2		960.3.l.f.641.3		4
60.23	odd	4		1200.3.c.k.449.3		8
60.47	odd	4		1200.3.c.k.449.6		8
60.59	even	2		1200.3.l.u.401.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.d.a.11.2	✓	4	1.1	even	1	trivial
30.3.d.a.11.4	yes	4	3.2	odd	2	inner
150.3.b.b.149.1		8	15.2	even	4
150.3.b.b.149.2		8	5.3	odd	4
150.3.b.b.149.7		8	5.2	odd	4
150.3.b.b.149.8		8	15.8	even	4
150.3.d.c.101.1		4	15.14	odd	2
150.3.d.c.101.3		4	5.4	even	2
240.3.l.c.161.1		4	4.3	odd	2
240.3.l.c.161.2		4	12.11	even	2
810.3.h.a.431.2		8	9.5	odd	6
810.3.h.a.431.3		8	9.4	even	3
810.3.h.a.701.2		8	9.7	even	3
810.3.h.a.701.3		8	9.2	odd	6
960.3.l.e.641.1		4	8.5	even	2
960.3.l.e.641.2		4	24.5	odd	2
960.3.l.f.641.3		4	24.11	even	2
960.3.l.f.641.4		4	8.3	odd	2
1200.3.c.k.449.3		8	60.23	odd	4
1200.3.c.k.449.4		8	20.7	even	4
1200.3.c.k.449.5		8	20.3	even	4
1200.3.c.k.449.6		8	60.47	odd	4
1200.3.l.u.401.3		4	60.59	even	2
1200.3.l.u.401.4		4	20.19	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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	30.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(2.58114 + 1.52896i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(2.16228 - 3.65028i) q^{6} -7.48683 q^{7} +2.82843i q^{8} +(4.32456 + 7.89292i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(2.58114 + 1.52896i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(2.16228 - 3.65028i) q^{6} -7.48683 q^{7} +2.82843i q^{8} +(4.32456 + 7.89292i) q^{9} -3.16228 q^{10} +8.48528i q^{11} +(-5.16228 - 3.05792i) q^{12} -10.0000 q^{13} +10.5880i q^{14} +(3.41886 - 5.77160i) q^{15} +4.00000 q^{16} -30.3870i q^{17} +(11.1623 - 6.11584i) q^{18} +26.9737 q^{19} +4.47214i q^{20} +(-19.3246 - 11.4471i) q^{21} +12.0000 q^{22} +9.17377i q^{23} +(-4.32456 + 7.30056i) q^{24} -5.00000 q^{25} +14.1421i q^{26} +(-0.905694 + 26.9848i) q^{27} +14.9737 q^{28} -26.8328i q^{29} +(-8.16228 - 4.83500i) q^{30} +8.00000 q^{31} -5.65685i q^{32} +(-12.9737 + 21.9017i) q^{33} -42.9737 q^{34} +16.7411i q^{35} +(-8.64911 - 15.7858i) q^{36} +15.9473 q^{37} -38.1465i q^{38} +(-25.8114 - 15.2896i) q^{39} +6.32456 q^{40} +47.3575i q^{41} +(-16.1886 + 27.3290i) q^{42} -14.4605 q^{43} -16.9706i q^{44} +(17.6491 - 9.67000i) q^{45} +12.9737 q^{46} +45.8688i q^{47} +(10.3246 + 6.11584i) q^{48} +7.05267 q^{49} +7.07107i q^{50} +(46.4605 - 78.4330i) q^{51} +20.0000 q^{52} -30.3870i q^{53} +(38.1623 + 1.28084i) q^{54} +18.9737 q^{55} -21.1760i q^{56} +(69.6228 + 41.2417i) q^{57} -37.9473 q^{58} -24.0789i q^{59} +(-6.83772 + 11.5432i) q^{60} -53.9473 q^{61} -11.3137i q^{62} +(-32.3772 - 59.0930i) q^{63} -8.00000 q^{64} +22.3607i q^{65} +(30.9737 + 18.3475i) q^{66} -110.460 q^{67} +60.7739i q^{68} +(-14.0263 + 23.6788i) q^{69} +23.6754 q^{70} +15.5936i q^{71} +(-22.3246 + 12.2317i) q^{72} +87.9473 q^{73} -22.5529i q^{74} +(-12.9057 - 7.64481i) q^{75} -53.9473 q^{76} -63.5279i q^{77} +(-21.6228 + 36.5028i) q^{78} -46.9737 q^{79} -8.94427i q^{80} +(-43.5964 + 68.2668i) q^{81} +66.9737 q^{82} +26.1443i q^{83} +(38.6491 + 22.8942i) q^{84} -67.9473 q^{85} +20.4502i q^{86} +(41.0263 - 69.2592i) q^{87} -24.0000 q^{88} +60.7739i q^{89} +(-13.6754 - 24.9596i) q^{90} +74.8683 q^{91} -18.3475i q^{92} +(20.6491 + 12.2317i) q^{93} +64.8683 q^{94} -60.3150i q^{95} +(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	\( 4 q + 4 q^{3} - 8 q^{4} - 4 q^{6} + 8 q^{7} - 8 q^{9} - 8 q^{12} - 40 q^{13} + 20 q^{15} + 16 q^{16} + 32 q^{18} + 32 q^{19} - 52 q^{21} + 48 q^{22} + 8 q^{24} - 20 q^{25} + 28 q^{27} - 16 q^{28} - 20 q^{30} + 32 q^{31} + 24 q^{33} - 96 q^{34} + 16 q^{36} - 88 q^{37} - 40 q^{39} - 128 q^{42} + 56 q^{43} + 20 q^{45} - 24 q^{46} + 16 q^{48} + 180 q^{49} + 72 q^{51} + 80 q^{52} + 140 q^{54} + 152 q^{57} - 40 q^{60} - 64 q^{61} - 256 q^{63} - 32 q^{64} + 48 q^{66} - 328 q^{67} - 132 q^{69} + 120 q^{70} - 64 q^{72} + 200 q^{73} - 20 q^{75} - 64 q^{76} + 40 q^{78} - 112 q^{79} + 28 q^{81} + 192 q^{82} + 104 q^{84} - 120 q^{85} + 240 q^{87} - 96 q^{88} - 80 q^{90} - 80 q^{91} + 32 q^{93} - 120 q^{94} - 16 q^{96} + 296 q^{97} - 192 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 8 * q^4 - 4 * q^6 + 8 * q^7 - 8 * q^9 - 8 * q^12 - 40 * q^13 + 20 * q^15 + 16 * q^16 + 32 * q^18 + 32 * q^19 - 52 * q^21 + 48 * q^22 + 8 * q^24 - 20 * q^25 + 28 * q^27 - 16 * q^28 - 20 * q^30 + 32 * q^31 + 24 * q^33 - 96 * q^34 + 16 * q^36 - 88 * q^37 - 40 * q^39 - 128 * q^42 + 56 * q^43 + 20 * q^45 - 24 * q^46 + 16 * q^48 + 180 * q^49 + 72 * q^51 + 80 * q^52 + 140 * q^54 + 152 * q^57 - 40 * q^60 - 64 * q^61 - 256 * q^63 - 32 * q^64 + 48 * q^66 - 328 * q^67 - 132 * q^69 + 120 * q^70 - 64 * q^72 + 200 * q^73 - 20 * q^75 - 64 * q^76 + 40 * q^78 - 112 * q^79 + 28 * q^81 + 192 * q^82 + 104 * q^84 - 120 * q^85 + 240 * q^87 - 96 * q^88 - 80 * q^90 - 80 * q^91 + 32 * q^93 - 120 * q^94 - 16 * q^96 + 296 * q^97 - 192 * q^99

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