LMFDB - Embedded newform 30.3.d.a.11.4

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

$q$-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} -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} - 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}+ \cdots - 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

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	$-0.873962\pi$
$11$		−	8.48528i		−	0.771389i	0.922627	−	0.385695i	$-0.126038\pi$
$12$	−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	$0.351924\pi$
$17$			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	$0.248770\pi$
$20$		−	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	$-0.936091\pi$
$23$		−	9.17377i		−	0.398859i	0.979912	−	0.199430i	$-0.0639090\pi$
$24$	−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	$0.153096\pi$
$29$			26.8328i			0.925270i	−0.886549	+	0.462635i	$0.846904\pi$
$30$	−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	$-0.804016\pi$
$41$		−	47.3575i		−	1.15506i	0.816369	−	0.577531i	$-0.195984\pi$
$42$	−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	$-0.837739\pi$
$47$		−	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
$50$		−	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	$0.0925482\pi$
$53$			30.3870i			0.573339i	−0.958030	+	0.286670i	$0.907452\pi$
$54$	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	$0.0654132\pi$
$59$			24.0789i			0.408116i	−0.978959	+	0.204058i	$0.934587\pi$
$60$	−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	$-0.964974\pi$
$71$		−	15.5936i		−	0.219628i	0.993952	−	0.109814i	$-0.0350255\pi$
$72$	−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	$-0.949658\pi$
$83$		−	26.1443i		−	0.314992i	0.987520	−	0.157496i	$-0.0503421\pi$
$84$	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	$-0.889090\pi$
$89$		−	60.7739i		−	0.682853i	0.939908	−	0.341427i	$-0.110910\pi$
$90$	−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	$0.0766245\pi$
$101$			48.1577i			0.476809i	−0.971166	+	0.238405i	$0.923376\pi$
$102$	−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	$0.0645723\pi$
$107$			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	$0.289578\pi$
$110$			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	$-0.988859\pi$
$113$		−	7.90852i		−	0.0699869i	0.999388	−	0.0349935i	$-0.0111410\pi$
$114$	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	$0.318149\pi$
$131$			220.394i			1.68240i	−0.540727	+	0.841198i	$0.681851\pi$
$132$	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	$-0.886659\pi$
$137$		−	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	$0.589113\pi$
$140$			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	$0.377595\pi$
$149$			276.237i			1.85394i	−0.375139	+	0.926969i	$0.622405\pi$
$150$	−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	$-0.727492\pi$
$167$		−	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
$170$		−	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	$-0.989128\pi$
$173$		−	11.8160i		−	0.0683005i	0.999417	−	0.0341502i	$-0.0108725\pi$
$174$	−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	$0.0617690\pi$
$179$			69.0358i			0.385675i	−0.981231	+	0.192837i	$0.938231\pi$
$180$	−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	$-0.908147\pi$
$191$		−	108.708i		−	0.569153i	0.958653	−	0.284577i	$-0.0918530\pi$
$192$	−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	$-0.856507\pi$
$197$		−	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	$0.471908\pi$
$200$			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	$0.158590\pi$
$227$			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	$0.248197\pi$
$230$			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	$0.0353957\pi$
$233$			51.7119i			0.221939i	−0.993824	+	0.110970i	$0.964604\pi$
$234$	−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	$0.328194\pi$
$239$			410.047i			1.71568i	−0.513917	+	0.857840i	$0.671806\pi$
$240$	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	$0.156770\pi$
$251$			237.364i			0.945675i	−0.881150	+	0.472838i	$0.843230\pi$
$252$	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	$0.213030\pi$
$257$			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
$260$			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	$0.0219420\pi$
$263$			36.2300i			0.137757i	−0.997625	+	0.0688784i	$0.978058\pi$
$264$	−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	$-0.561341\pi$
$269$		−	528.041i		−	1.96298i	0.191518	−	0.981489i	$-0.438659\pi$
$270$	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	$0.0138424\pi$
$281$			24.4322i			0.0869473i	−0.999055	+	0.0434736i	$0.986158\pi$
$282$	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	$-0.659651\pi$
$293$		−	513.825i		−	1.75367i	0.480794	−	0.876834i	$-0.340349\pi$
$294$	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	$-0.686038\pi$
$311$		−	518.756i		−	1.66802i	0.551746	−	0.834012i	$-0.313962\pi$
$312$	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	$0.0196411\pi$
$317$			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
$320$		−	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	$-0.976208\pi$
$347$		−	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	$0.544645\pi$
$350$			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	$0.298952\pi$
$353$			569.797i			1.61416i	−0.590445	+	0.807078i	$0.701048\pi$
$354$	−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	$-0.875232\pi$
$359$		−	274.283i		−	0.764019i	0.924158	−	0.382010i	$-0.124768\pi$
$360$	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	$-0.761105\pi$
$383$		−	522.422i		−	1.36402i	0.731341	−	0.682012i	$-0.238895\pi$
$384$	−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	$0.287414\pi$
$389$			610.847i			1.57030i	−0.619306	+	0.785150i	$0.712586\pi$
$390$	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	$0.191811\pi$
$401$			454.557i			1.13356i	−0.823869	+	0.566780i	$0.808189\pi$
$402$	−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	$0.0372780\pi$
$419$			97.9159i			0.233690i	−0.993150	+	0.116845i	$0.962722\pi$
$420$	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	$0.110426\pi$
$431$			293.077i			0.679994i	−0.940427	+	0.339997i	$0.889574\pi$
$432$	−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	$-0.892679\pi$
$443$		−	293.096i		−	0.661615i	0.943698	−	0.330808i	$-0.107321\pi$
$444$	−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	$-0.773875\pi$
$449$		−	585.614i		−	1.30426i	0.758106	−	0.652132i	$-0.226125\pi$
$450$	−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	$0.205210\pi$
$461$			554.074i			1.20190i	−0.799288	+	0.600948i	$0.794790\pi$
$462$	−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	$-0.989528\pi$
$467$		−	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
$470$			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	$-0.721512\pi$
$479$		−	735.242i		−	1.53495i	0.641078	−	0.767476i	$-0.278488\pi$
$480$	−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	$-0.632357\pi$
$491$		−	898.323i		−	1.82958i	0.403933	−	0.914789i	$-0.367643\pi$
$492$	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	$-0.854825\pi$
$503$		−	443.077i		−	0.880868i	0.897785	−	0.440434i	$-0.145175\pi$
$504$	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	$0.0671168\pi$
$509$			213.062i			0.418590i	−0.977853	+	0.209295i	$0.932883\pi$
$510$	−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	$0.000977795\pi$
$521$			3.20085i			0.00614366i	−0.999995	+	0.00307183i	$0.999022\pi$
$522$	−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	$0.00114325\pi$
$557$			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
$560$		−	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	$-0.952624\pi$
$563$		−	166.970i		−	0.296572i	0.988945	−	0.148286i	$-0.0473756\pi$
$564$	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	$-0.956146\pi$
$569$		−	156.289i		−	0.274673i	0.990524	−	0.137337i	$-0.0438542\pi$
$570$	−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	$-0.948163\pi$
$587$		−	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
$590$		−	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	$-0.905846\pi$
$593$		−	345.719i		−	0.583001i	0.956571	−	0.291500i	$-0.0941544\pi$
$594$	−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	$0.199963\pi$
$599$			704.055i			1.17538i	−0.809085	+	0.587692i	$0.800037\pi$
$600$	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	$-0.664812\pi$
$617$		−	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	$0.520767\pi$
$620$		−	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	$0.0162656\pi$
$641$			65.4816i			0.102155i	−0.998695	+	0.0510777i	$0.983734\pi$
$642$	−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	$-0.883578\pi$
$647$		−	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
$650$			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	$-0.894477\pi$
$653$		−	425.064i		−	0.650941i	0.945552	−	0.325470i	$-0.105523\pi$
$654$	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	$0.0442831\pi$
$659$			182.769i			0.277343i	−0.990338	+	0.138671i	$0.955717\pi$
$660$	−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	$0.288463\pi$
$677$			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
$680$			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	$0.195989\pi$
$683$			788.926i			1.15509i	−0.816359	+	0.577545i	$0.804011\pi$
$684$	−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	$-0.584620\pi$
$701$		−	1352.75i		−	1.92974i	0.262721	−	0.964872i	$-0.415380\pi$
$702$	−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	$0.121845\pi$
$719$			537.103i			0.747014i	−0.927627	+	0.373507i	$0.878155\pi$
$720$	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	$0.000689524\pi$
$743$			3.21898i			0.00433241i	−0.999998	+	0.00216620i	$0.999310\pi$
$744$	−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	$-0.877677\pi$
$761$		−	570.597i		−	0.749800i	0.927065	−	0.374900i	$-0.122323\pi$
$762$	−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	$0.132070\pi$
$773$			623.203i			0.806214i	−0.915153	+	0.403107i	$0.867930\pi$
$774$	−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	$0.112247\pi$
$797$			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
$800$		−	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	$-0.887443\pi$
$809$		−	560.288i		−	0.692569i	0.938130	−	0.346284i	$-0.112557\pi$
$810$	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	$0.0126973\pi$
$821$			65.4816i			0.0797584i	−0.999205	+	0.0398792i	$0.987303\pi$
$822$	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	$0.203658\pi$
$827$			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	$0.435508\pi$
$830$			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	$-0.975436\pi$
$839$		−	129.363i		−	0.154187i	0.997024	−	0.0770934i	$-0.0245640\pi$
$840$	−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	$0.134432\pi$
$857$			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	$0.552323\pi$
$860$			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	$0.0780941\pi$
$863$			419.221i			0.485772i	−0.970055	+	0.242886i	$0.921906\pi$
$864$	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	$-0.860401\pi$
$881$		−	748.212i		−	0.849275i	0.905363	−	0.424638i	$-0.139599\pi$
$882$	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	$0.193903\pi$
$887$			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
$890$			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	$-0.814608\pi$
$911$		−	1002.19i		−	1.10010i	0.835131	−	0.550051i	$-0.185392\pi$
$912$	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	$0.200367\pi$
$929$			1093.84i			1.17744i	−0.808339	+	0.588718i	$0.799633\pi$
$930$	−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	$0.116044\pi$
$941$			671.008i			0.713079i	−0.934280	+	0.356540i	$0.883956\pi$
$942$	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	$-0.677167\pi$
$947$		−	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
$950$		−	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	$-0.881114\pi$
$953$		−	695.440i		−	0.729737i	0.931059	−	0.364869i	$-0.118886\pi$
$954$	−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	$0.204840\pi$
$971$			1165.24i			1.20004i	−0.799986	+	0.600019i	$0.795160\pi$
$972$	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	$0.121249\pi$
$977$			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
$980$		−	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	$0.174426\pi$
$983$			1024.21i			1.04192i	−0.853581	+	0.520960i	$0.825574\pi$
$984$	−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.11.4	yes	4
3.2	odd	2	inner	30.3.d.a.11.2	✓	4
4.3	odd	2		240.3.l.c.161.2		4
5.2	odd	4		150.3.b.b.149.1		8
5.3	odd	4		150.3.b.b.149.8		8
5.4	even	2		150.3.d.c.101.1		4
8.3	odd	2		960.3.l.f.641.3		4
8.5	even	2		960.3.l.e.641.2		4
9.2	odd	6		810.3.h.a.701.2		8
9.4	even	3		810.3.h.a.431.2		8
9.5	odd	6		810.3.h.a.431.3		8
9.7	even	3		810.3.h.a.701.3		8
12.11	even	2		240.3.l.c.161.1		4
15.2	even	4		150.3.b.b.149.7		8
15.8	even	4		150.3.b.b.149.2		8
15.14	odd	2		150.3.d.c.101.3		4
20.3	even	4		1200.3.c.k.449.3		8
20.7	even	4		1200.3.c.k.449.6		8
20.19	odd	2		1200.3.l.u.401.3		4
24.5	odd	2		960.3.l.e.641.1		4
24.11	even	2		960.3.l.f.641.4		4
60.23	odd	4		1200.3.c.k.449.5		8
60.47	odd	4		1200.3.c.k.449.4		8
60.59	even	2		1200.3.l.u.401.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.d.a.11.2	✓	4	3.2	odd	2	inner
30.3.d.a.11.4	yes	4	1.1	even	1	trivial
150.3.b.b.149.1		8	5.2	odd	4
150.3.b.b.149.2		8	15.8	even	4
150.3.b.b.149.7		8	15.2	even	4
150.3.b.b.149.8		8	5.3	odd	4
150.3.d.c.101.1		4	5.4	even	2
150.3.d.c.101.3		4	15.14	odd	2
240.3.l.c.161.1		4	12.11	even	2
240.3.l.c.161.2		4	4.3	odd	2
810.3.h.a.431.2		8	9.4	even	3
810.3.h.a.431.3		8	9.5	odd	6
810.3.h.a.701.2		8	9.2	odd	6
810.3.h.a.701.3		8	9.7	even	3
960.3.l.e.641.1		4	24.5	odd	2
960.3.l.e.641.2		4	8.5	even	2
960.3.l.f.641.3		4	8.3	odd	2
960.3.l.f.641.4		4	24.11	even	2
1200.3.c.k.449.3		8	20.3	even	4
1200.3.c.k.449.4		8	60.47	odd	4
1200.3.c.k.449.5		8	60.23	odd	4
1200.3.c.k.449.6		8	20.7	even	4
1200.3.l.u.401.3		4	20.19	odd	2
1200.3.l.u.401.4		4	60.59	even	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} -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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 8 q^{4} - 4 q^{6} + 8 q^{7} - 8 q^{9} - 8 q^{12} - 40 q^{13} + 20 q^{15} + 16 q^{16} + 32 q^{18} + 32 q^{19} - 52 q^{21} + 48 q^{22} + 8 q^{24} - 20 q^{25} + 28 q^{27} - 16 q^{28} - 20 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) \) 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

Introduction

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