LMFDB - Embedded newform 234.3.i.b.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,3,Mod(73,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("234.73");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	234.i (of order $4$, degree $2$, 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:	$6.37603818603$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	234.109
Dual form			234.3.i.b.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-4.73205 + 4.73205i) q^{5} +(-2.73205 - 2.73205i) q^{7} +(2.00000 + 2.00000i) q^{8} -9.46410i q^{10} +(-1.73205 - 1.73205i) q^{11} +(9.92820 - 8.39230i) q^{13} +5.46410 q^{14} -4.00000 q^{16} -29.3205i q^{17} +(-11.2679 + 11.2679i) q^{19} +(9.46410 + 9.46410i) q^{20} +3.46410 q^{22} -29.3205i q^{23} -19.7846i q^{25} +(-1.53590 + 18.3205i) q^{26} +(-5.46410 + 5.46410i) q^{28} -31.8564 q^{29} +(26.9808 - 26.9808i) q^{31} +(4.00000 - 4.00000i) q^{32} +(29.3205 + 29.3205i) q^{34} +25.8564 q^{35} +(-30.8564 - 30.8564i) q^{37} -22.5359i q^{38} -18.9282 q^{40} +(14.4449 - 14.4449i) q^{41} +25.1769i q^{43} +(-3.46410 + 3.46410i) q^{44} +(29.3205 + 29.3205i) q^{46} +(41.1962 + 41.1962i) q^{47} -34.0718i q^{49} +(19.7846 + 19.7846i) q^{50} +(-16.7846 - 19.8564i) q^{52} -2.28719 q^{53} +16.3923 q^{55} -10.9282i q^{56} +(31.8564 - 31.8564i) q^{58} +(-54.6218 - 54.6218i) q^{59} -7.42563 q^{61} +53.9615i q^{62} +8.00000i q^{64} +(-7.26795 + 86.6936i) q^{65} +(-60.6936 + 60.6936i) q^{67} -58.6410 q^{68} +(-25.8564 + 25.8564i) q^{70} +(-38.9090 + 38.9090i) q^{71} +(40.3205 + 40.3205i) q^{73} +61.7128 q^{74} +(22.5359 + 22.5359i) q^{76} +9.46410i q^{77} -148.210 q^{79} +(18.9282 - 18.9282i) q^{80} +28.8897i q^{82} +(-73.7987 + 73.7987i) q^{83} +(138.746 + 138.746i) q^{85} +(-25.1769 - 25.1769i) q^{86} -6.92820i q^{88} +(-25.5167 - 25.5167i) q^{89} +(-50.0526 - 4.19615i) q^{91} -58.6410 q^{92} -82.3923 q^{94} -106.641i q^{95} +(-86.0333 + 86.0333i) q^{97} +(34.0718 + 34.0718i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 12 q^{5} - 4 q^{7} + 8 q^{8} + 12 q^{13} + 8 q^{14} - 16 q^{16} - 52 q^{19} + 24 q^{20} - 20 q^{26} - 8 q^{28} - 72 q^{29} + 4 q^{31} + 16 q^{32} + 48 q^{34} + 48 q^{35} - 68 q^{37} - 48 q^{40}+ \cdots + 164 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 12 * q^5 - 4 * q^7 + 8 * q^8 + 12 * q^13 + 8 * q^14 - 16 * q^16 - 52 * q^19 + 24 * q^20 - 20 * q^26 - 8 * q^28 - 72 * q^29 + 4 * q^31 + 16 * q^32 + 48 * q^34 + 48 * q^35 - 68 * q^37 - 48 * q^40 - 60 * q^41 + 48 * q^46 + 144 * q^47 - 4 * q^50 + 16 * q^52 - 120 * q^53 + 24 * q^55 + 72 * q^58 + 24 * q^59 + 192 * q^61 - 36 * q^65 - 28 * q^67 - 96 * q^68 - 48 * q^70 - 24 * q^71 + 92 * q^73 + 136 * q^74 + 104 * q^76 - 288 * q^79 + 48 * q^80 + 72 * q^83 + 264 * q^85 + 24 * q^86 - 12 * q^89 - 124 * q^91 - 96 * q^92 - 288 * q^94 - 164 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	2.00000i		−	0.500000i
$5$	−4.73205	+	4.73205i	−0.946410	+	0.946410i	−0.998635	−	0.0522252i	$-0.983369\pi$
$5$	−4.73205	+	4.73205i	−0.946410	+	0.946410i	0.0522252	+	0.998635i	$0.483369\pi$
$6$		0			0
$7$	−2.73205	−	2.73205i	−0.390293	−	0.390293i	0.484499	−	0.874792i	$-0.339002\pi$
$7$	−2.73205	−	2.73205i	−0.390293	−	0.390293i	−0.874792	+	0.484499i	$0.839002\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$		0			0
$10$		−	9.46410i		−	0.946410i
$11$	−1.73205	−	1.73205i	−0.157459	−	0.157459i	0.623981	−	0.781440i	$-0.285514\pi$
$11$	−1.73205	−	1.73205i	−0.157459	−	0.157459i	−0.781440	+	0.623981i	$0.785514\pi$
$12$		0			0
$13$	9.92820	−	8.39230i	0.763708	−	0.645562i
$13$	9.92820	−	8.39230i	0.763708	−	0.645562i
$14$	5.46410			0.390293
$15$		0			0
$16$	−4.00000			−0.250000
$17$		−	29.3205i		−	1.72474i	−0.506282	−	0.862368i	$-0.668981\pi$
$17$		−	29.3205i		−	1.72474i	0.506282	−	0.862368i	$-0.331019\pi$
$18$		0			0
$19$	−11.2679	+	11.2679i	−0.593050	+	0.593050i	−0.938454	−	0.345404i	$-0.887742\pi$
$19$	−11.2679	+	11.2679i	−0.593050	+	0.593050i	0.345404	+	0.938454i	$0.387742\pi$
$20$	9.46410	+	9.46410i	0.473205	+	0.473205i
$21$		0			0
$22$	3.46410			0.157459
$23$		−	29.3205i		−	1.27480i	−0.770531	−	0.637402i	$-0.780009\pi$
$23$		−	29.3205i		−	1.27480i	0.770531	−	0.637402i	$-0.219991\pi$
$24$		0			0
$25$		−	19.7846i		−	0.791384i
$26$	−1.53590	+	18.3205i	−0.0590730	+	0.704635i
$27$		0			0
$28$	−5.46410	+	5.46410i	−0.195146	+	0.195146i
$29$	−31.8564			−1.09850			−0.549248	−	0.835659i	$-0.685086\pi$
$29$	−31.8564			−1.09850			−0.549248	+	0.835659i	$0.685086\pi$
$30$		0			0
$31$	26.9808	−	26.9808i	0.870347	−	0.870347i	−0.122163	−	0.992510i	$-0.538983\pi$
$31$	26.9808	−	26.9808i	0.870347	−	0.870347i	0.992510	+	0.122163i	$0.0389830\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$		0			0
$34$	29.3205	+	29.3205i	0.862368	+	0.862368i
$35$	25.8564			0.738754
$36$		0			0
$37$	−30.8564	−	30.8564i	−0.833957	−	0.833957i	0.154099	−	0.988055i	$-0.450753\pi$
$37$	−30.8564	−	30.8564i	−0.833957	−	0.833957i	−0.988055	+	0.154099i	$0.950753\pi$
$38$		−	22.5359i		−	0.593050i
$39$		0			0
$40$	−18.9282			−0.473205
$41$	14.4449	−	14.4449i	0.352314	−	0.352314i	−0.508656	−	0.860970i	$-0.669858\pi$
$41$	14.4449	−	14.4449i	0.352314	−	0.352314i	0.860970	+	0.508656i	$0.169858\pi$
$42$		0			0
$43$			25.1769i			0.585510i	0.956188	+	0.292755i	$0.0945720\pi$
$43$			25.1769i			0.585510i	−0.956188	+	0.292755i	$0.905428\pi$
$44$	−3.46410	+	3.46410i	−0.0787296	+	0.0787296i
$45$		0			0
$46$	29.3205	+	29.3205i	0.637402	+	0.637402i
$47$	41.1962	+	41.1962i	0.876514	+	0.876514i	0.993172	−	0.116658i	$-0.0372182\pi$
$47$	41.1962	+	41.1962i	0.876514	+	0.876514i	−0.116658	+	0.993172i	$0.537218\pi$
$48$		0			0
$49$		−	34.0718i		−	0.695343i
$50$	19.7846	+	19.7846i	0.395692	+	0.395692i
$51$		0			0
$52$	−16.7846	−	19.8564i	−0.322781	−	0.381854i
$53$	−2.28719			−0.0431545			−0.0215772	−	0.999767i	$-0.506869\pi$
$53$	−2.28719			−0.0431545			−0.0215772	+	0.999767i	$0.506869\pi$
$54$		0			0
$55$	16.3923			0.298042
$56$		−	10.9282i		−	0.195146i
$57$		0			0
$58$	31.8564	−	31.8564i	0.549248	−	0.549248i
$59$	−54.6218	−	54.6218i	−0.925793	−	0.925793i	0.0716379	−	0.997431i	$-0.477177\pi$
$59$	−54.6218	−	54.6218i	−0.925793	−	0.925793i	−0.997431	+	0.0716379i	$0.977177\pi$
$60$		0			0
$61$	−7.42563			−0.121732			−0.0608658	−	0.998146i	$-0.519386\pi$
$61$	−7.42563			−0.121732			−0.0608658	+	0.998146i	$0.519386\pi$
$62$			53.9615i			0.870347i
$63$		0			0
$64$			8.00000i			0.125000i
$65$	−7.26795	+	86.6936i	−0.111815	+	1.33375i
$66$		0			0
$67$	−60.6936	+	60.6936i	−0.905874	+	0.905874i	−0.995936	−	0.0900619i	$-0.971294\pi$
$67$	−60.6936	+	60.6936i	−0.905874	+	0.905874i	0.0900619	+	0.995936i	$0.471294\pi$
$68$	−58.6410			−0.862368
$69$		0			0
$70$	−25.8564	+	25.8564i	−0.369377	+	0.369377i
$71$	−38.9090	+	38.9090i	−0.548014	+	0.548014i	−0.925866	−	0.377852i	$-0.876663\pi$
$71$	−38.9090	+	38.9090i	−0.548014	+	0.548014i	0.377852	+	0.925866i	$0.376663\pi$
$72$		0			0
$73$	40.3205	+	40.3205i	0.552336	+	0.552336i	0.927114	−	0.374779i	$-0.122281\pi$
$73$	40.3205	+	40.3205i	0.552336	+	0.552336i	−0.374779	+	0.927114i	$0.622281\pi$
$74$	61.7128			0.833957
$75$		0			0
$76$	22.5359	+	22.5359i	0.296525	+	0.296525i
$77$			9.46410i			0.122910i
$78$		0			0
$79$	−148.210			−1.87608			−0.938039	−	0.346528i	$-0.887360\pi$
$79$	−148.210			−1.87608			−0.938039	+	0.346528i	$0.887360\pi$
$80$	18.9282	−	18.9282i	0.236603	−	0.236603i
$81$		0			0
$82$			28.8897i			0.352314i
$83$	−73.7987	+	73.7987i	−0.889141	+	0.889141i	−0.994441	−	0.105300i	$-0.966420\pi$
$83$	−73.7987	+	73.7987i	−0.889141	+	0.889141i	0.105300	+	0.994441i	$0.466420\pi$
$84$		0			0
$85$	138.746	+	138.746i	1.63231	+	1.63231i
$86$	−25.1769	−	25.1769i	−0.292755	−	0.292755i
$87$		0			0
$88$		−	6.92820i		−	0.0787296i
$89$	−25.5167	−	25.5167i	−0.286704	−	0.286704i	0.549071	−	0.835775i	$-0.314981\pi$
$89$	−25.5167	−	25.5167i	−0.286704	−	0.286704i	−0.835775	+	0.549071i	$0.814981\pi$
$90$		0			0
$91$	−50.0526	−	4.19615i	−0.550028	−	0.0461116i
$92$	−58.6410			−0.637402
$93$		0			0
$94$	−82.3923			−0.876514
$95$		−	106.641i		−	1.12254i
$96$		0			0
$97$	−86.0333	+	86.0333i	−0.886941	+	0.886941i	−0.994228	−	0.107287i	$-0.965784\pi$
$97$	−86.0333	+	86.0333i	−0.886941	+	0.886941i	0.107287	+	0.994228i	$0.465784\pi$
$98$	34.0718	+	34.0718i	0.347671	+	0.347671i
$99$		0			0
$100$	−39.5692			−0.395692
$101$		−	104.536i		−	1.03501i	−0.855681	−	0.517504i	$-0.826861\pi$
$101$		−	104.536i		−	1.03501i	0.855681	−	0.517504i	$-0.173139\pi$
$102$		0			0
$103$			36.6795i			0.356112i	0.984020	+	0.178056i	$0.0569808\pi$
$103$			36.6795i			0.356112i	−0.984020	+	0.178056i	$0.943019\pi$
$104$	36.6410	+	3.07180i	0.352317	+	0.0295365i
$105$		0			0
$106$	2.28719	−	2.28719i	0.0215772	−	0.0215772i
$107$	123.464			1.15387			0.576935	−	0.816790i	$-0.304249\pi$
$107$	123.464			1.15387			0.576935	+	0.816790i	$0.304249\pi$
$108$		0			0
$109$	119.315	−	119.315i	1.09464	−	1.09464i	0.0996097	−	0.995027i	$-0.468241\pi$
$109$	119.315	−	119.315i	1.09464	−	1.09464i	0.995027	−	0.0996097i	$-0.0317594\pi$
$110$	−16.3923	+	16.3923i	−0.149021	+	0.149021i
$111$		0			0
$112$	10.9282	+	10.9282i	0.0975732	+	0.0975732i
$113$	184.277			1.63077			0.815384	−	0.578920i	$-0.196526\pi$
$113$	184.277			1.63077			0.815384	+	0.578920i	$0.196526\pi$
$114$		0			0
$115$	138.746	+	138.746i	1.20649	+	1.20649i
$116$			63.7128i			0.549248i
$117$		0			0
$118$	109.244			0.925793
$119$	−80.1051	+	80.1051i	−0.673152	+	0.673152i
$120$		0			0
$121$		−	115.000i		−	0.950413i
$122$	7.42563	−	7.42563i	0.0608658	−	0.0608658i
$123$		0			0
$124$	−53.9615	−	53.9615i	−0.435174	−	0.435174i
$125$	−24.6795	−	24.6795i	−0.197436	−	0.197436i
$126$		0			0
$127$		−	173.962i		−	1.36978i	−0.728648	−	0.684888i	$-0.759851\pi$
$127$		−	173.962i		−	1.36978i	0.728648	−	0.684888i	$-0.240149\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−79.4256	−	93.9615i	−0.610966	−	0.722781i
$131$	−121.110			−0.924506			−0.462253	−	0.886748i	$-0.652959\pi$
$131$	−121.110			−0.924506			−0.462253	+	0.886748i	$0.652959\pi$
$132$		0			0
$133$	61.5692			0.462926
$134$		−	121.387i		−	0.905874i
$135$		0			0
$136$	58.6410	−	58.6410i	0.431184	−	0.431184i
$137$	130.053	+	130.053i	0.949289	+	0.949289i	0.998775	−	0.0494861i	$-0.0157583\pi$
$137$	130.053	+	130.053i	0.949289	+	0.949289i	−0.0494861	+	0.998775i	$0.515758\pi$
$138$		0			0
$139$	−27.1384			−0.195241			−0.0976203	−	0.995224i	$-0.531123\pi$
$139$	−27.1384			−0.195241			−0.0976203	+	0.995224i	$0.531123\pi$
$140$		−	51.7128i		−	0.369377i
$141$		0			0
$142$		−	77.8179i		−	0.548014i
$143$	−31.7321	−	2.66025i	−0.221902	−	0.0186032i
$144$		0			0
$145$	150.746	−	150.746i	1.03963	−	1.03963i
$146$	−80.6410			−0.552336
$147$		0			0
$148$	−61.7128	+	61.7128i	−0.416978	+	0.416978i
$149$	168.224	−	168.224i	1.12902	−	1.12902i	0.138686	−	0.990336i	$-0.455712\pi$
$149$	168.224	−	168.224i	1.12902	−	1.12902i	0.990336	−	0.138686i	$-0.0442878\pi$
$150$		0			0
$151$	−38.4064	−	38.4064i	−0.254347	−	0.254347i	0.568403	−	0.822750i	$-0.307561\pi$
$151$	−38.4064	−	38.4064i	−0.254347	−	0.254347i	−0.822750	+	0.568403i	$0.807561\pi$
$152$	−45.0718			−0.296525
$153$		0			0
$154$	−9.46410	−	9.46410i	−0.0614552	−	0.0614552i
$155$			255.349i			1.64741i
$156$		0			0
$157$	−227.215			−1.44723			−0.723616	−	0.690203i	$-0.757521\pi$
$157$	−227.215			−1.44723			−0.723616	+	0.690203i	$0.757521\pi$
$158$	148.210	−	148.210i	0.938039	−	0.938039i
$159$		0			0
$160$			37.8564i			0.236603i
$161$	−80.1051	+	80.1051i	−0.497547	+	0.497547i
$162$		0			0
$163$	12.4449	+	12.4449i	0.0763489	+	0.0763489i	0.744250	−	0.667901i	$-0.232807\pi$
$163$	12.4449	+	12.4449i	0.0763489	+	0.0763489i	−0.667901	+	0.744250i	$0.732807\pi$
$164$	−28.8897	−	28.8897i	−0.176157	−	0.176157i
$165$		0			0
$166$		−	147.597i		−	0.889141i
$167$	−119.512	−	119.512i	−0.715638	−	0.715638i	0.252071	−	0.967709i	$-0.418888\pi$
$167$	−119.512	−	119.512i	−0.715638	−	0.715638i	−0.967709	+	0.252071i	$0.918888\pi$
$168$		0			0
$169$	28.1384	−	166.641i	0.166500	−	0.986042i
$170$	−277.492			−1.63231
$171$		0			0
$172$	50.3538			0.292755
$173$		−	69.3975i		−	0.401141i	−0.979679	−	0.200571i	$-0.935720\pi$
$173$		−	69.3975i		−	0.401141i	0.979679	−	0.200571i	$-0.0642796\pi$
$174$		0			0
$175$	−54.0526	+	54.0526i	−0.308872	+	0.308872i
$176$	6.92820	+	6.92820i	0.0393648	+	0.0393648i
$177$		0			0
$178$	51.0333			0.286704
$179$			165.282i			0.923363i	0.887046	+	0.461682i	$0.152754\pi$
$179$			165.282i			0.923363i	−0.887046	+	0.461682i	$0.847246\pi$
$180$		0			0
$181$			283.856i			1.56827i	0.620592	+	0.784134i	$0.286892\pi$
$181$			283.856i			1.56827i	−0.620592	+	0.784134i	$0.713108\pi$
$182$	54.2487	−	45.8564i	0.298070	−	0.251958i
$183$		0			0
$184$	58.6410	−	58.6410i	0.318701	−	0.318701i
$185$	292.028			1.57853
$186$		0			0
$187$	−50.7846	+	50.7846i	−0.271575	+	0.271575i
$188$	82.3923	−	82.3923i	0.438257	−	0.438257i
$189$		0			0
$190$	106.641	+	106.641i	0.561269	+	0.561269i
$191$	−9.28203			−0.0485970			−0.0242985	−	0.999705i	$-0.507735\pi$
$191$	−9.28203			−0.0485970			−0.0242985	+	0.999705i	$0.507735\pi$
$192$		0			0
$193$	−21.7180	−	21.7180i	−0.112528	−	0.112528i	0.648601	−	0.761129i	$-0.275355\pi$
$193$	−21.7180	−	21.7180i	−0.112528	−	0.112528i	−0.761129	+	0.648601i	$0.775355\pi$
$194$		−	172.067i		−	0.886941i
$195$		0			0
$196$	−68.1436			−0.347671
$197$	112.732	−	112.732i	0.572244	−	0.572244i	−0.360511	−	0.932755i	$-0.617398\pi$
$197$	112.732	−	112.732i	0.572244	−	0.572244i	0.932755	+	0.360511i	$0.117398\pi$
$198$		0			0
$199$		−	245.100i		−	1.23166i	−0.787880	−	0.615829i	$-0.788821\pi$
$199$		−	245.100i		−	1.23166i	0.787880	−	0.615829i	$-0.211179\pi$
$200$	39.5692	−	39.5692i	0.197846	−	0.197846i
$201$		0			0
$202$	104.536	+	104.536i	0.517504	+	0.517504i
$203$	87.0333	+	87.0333i	0.428736	+	0.428736i
$204$		0			0
$205$			136.708i			0.666867i
$206$	−36.6795	−	36.6795i	−0.178056	−	0.178056i
$207$		0			0
$208$	−39.7128	+	33.5692i	−0.190927	+	0.161390i
$209$	39.0333			0.186762
$210$		0			0
$211$	345.282			1.63641			0.818204	−	0.574928i	$-0.194970\pi$
$211$	345.282			1.63641			0.818204	+	0.574928i	$0.194970\pi$
$212$			4.57437i			0.0215772i
$213$		0			0
$214$	−123.464	+	123.464i	−0.576935	+	0.576935i
$215$	−119.138	−	119.138i	−0.554132	−	0.554132i
$216$		0			0
$217$	−147.426			−0.679381
$218$			238.631i			1.09464i
$219$		0			0
$220$		−	32.7846i		−	0.149021i
$221$	−246.067	−	291.100i	−1.11342	−	1.31719i
$222$		0			0
$223$	170.588	−	170.588i	0.764971	−	0.764971i	−0.212246	−	0.977216i	$-0.568078\pi$
$223$	170.588	−	170.588i	0.764971	−	0.764971i	0.977216	+	0.212246i	$0.0680777\pi$
$224$	−21.8564			−0.0975732
$225$		0			0
$226$	−184.277	+	184.277i	−0.815384	+	0.815384i
$227$	−169.368	+	169.368i	−0.746114	+	0.746114i	−0.973747	−	0.227633i	$-0.926901\pi$
$227$	−169.368	+	169.368i	−0.746114	+	0.746114i	0.227633	+	0.973747i	$0.426901\pi$
$228$		0			0
$229$	141.823	+	141.823i	0.619315	+	0.619315i	0.945356	−	0.326041i	$-0.105715\pi$
$229$	141.823	+	141.823i	0.619315	+	0.619315i	−0.326041	+	0.945356i	$0.605715\pi$
$230$	−277.492			−1.20649
$231$		0			0
$232$	−63.7128	−	63.7128i	−0.274624	−	0.274624i
$233$			128.038i			0.549521i	0.961513	+	0.274761i	$0.0885986\pi$
$233$			128.038i			0.549521i	−0.961513	+	0.274761i	$0.911401\pi$
$234$		0			0
$235$	−389.885			−1.65908
$236$	−109.244	+	109.244i	−0.462896	+	0.462896i
$237$		0			0
$238$		−	160.210i		−	0.673152i
$239$	−88.0192	+	88.0192i	−0.368281	+	0.368281i	−0.866850	−	0.498569i	$-0.833859\pi$
$239$	−88.0192	+	88.0192i	−0.368281	+	0.368281i	0.498569	+	0.866850i	$0.333859\pi$
$240$		0			0
$241$	−147.459	−	147.459i	−0.611863	−	0.611863i	0.331568	−	0.943431i	$-0.392422\pi$
$241$	−147.459	−	147.459i	−0.611863	−	0.611863i	−0.943431	+	0.331568i	$0.892422\pi$
$242$	115.000	+	115.000i	0.475207	+	0.475207i
$243$		0			0
$244$			14.8513i			0.0608658i
$245$	161.229	+	161.229i	0.658079	+	0.658079i
$246$		0			0
$247$	−17.3064	+	206.435i	−0.0700665	+	0.835767i
$248$	107.923			0.435174
$249$		0			0
$250$	49.3590			0.197436
$251$			181.377i			0.722617i	0.932446	+	0.361308i	$0.117670\pi$
$251$			181.377i			0.722617i	−0.932446	+	0.361308i	$0.882330\pi$
$252$		0			0
$253$	−50.7846	+	50.7846i	−0.200730	+	0.200730i
$254$	173.962	+	173.962i	0.684888	+	0.684888i
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	297.664i		−	1.15823i	−0.815247	−	0.579113i	$-0.803399\pi$
$257$		−	297.664i		−	1.15823i	0.815247	−	0.579113i	$-0.196601\pi$
$258$		0			0
$259$			168.603i			0.650975i
$260$	173.387	+	14.5359i	0.666874	+	0.0559073i
$261$		0			0
$262$	121.110	−	121.110i	0.462253	−	0.462253i
$263$	−22.8897			−0.0870332			−0.0435166	−	0.999053i	$-0.513856\pi$
$263$	−22.8897			−0.0870332			−0.0435166	+	0.999053i	$0.513856\pi$
$264$		0			0
$265$	10.8231	−	10.8231i	0.0408418	−	0.0408418i
$266$	−61.5692	+	61.5692i	−0.231463	+	0.231463i
$267$		0			0
$268$	121.387	+	121.387i	0.452937	+	0.452937i
$269$	−220.774			−0.820722			−0.410361	−	0.911923i	$-0.634597\pi$
$269$	−220.774			−0.820722			−0.410361	+	0.911923i	$0.634597\pi$
$270$		0			0
$271$	148.953	+	148.953i	0.549641	+	0.549641i	0.926337	−	0.376696i	$-0.122940\pi$
$271$	148.953	+	148.953i	0.549641	+	0.549641i	−0.376696	+	0.926337i	$0.622940\pi$
$272$			117.282i			0.431184i
$273$		0			0
$274$	−260.105			−0.949289
$275$	−34.2679	+	34.2679i	−0.124611	+	0.124611i
$276$		0			0
$277$		−	27.2154i		−	0.0982505i	−0.998793	−	0.0491253i	$-0.984357\pi$
$277$		−	27.2154i		−	0.0982505i	0.998793	−	0.0491253i	$-0.0156434\pi$
$278$	27.1384	−	27.1384i	0.0976203	−	0.0976203i
$279$		0			0
$280$	51.7128	+	51.7128i	0.184689	+	0.184689i
$281$	51.6218	+	51.6218i	0.183707	+	0.183707i	0.792969	−	0.609262i	$-0.208534\pi$
$281$	51.6218	+	51.6218i	0.183707	+	0.183707i	−0.609262	+	0.792969i	$0.708534\pi$
$282$		0			0
$283$			93.8076i			0.331476i	0.986170	+	0.165738i	$0.0530006\pi$
$283$			93.8076i			0.331476i	−0.986170	+	0.165738i	$0.946999\pi$
$284$	77.8179	+	77.8179i	0.274007	+	0.274007i
$285$		0			0
$286$	34.3923	−	29.0718i	0.120253	−	0.101650i
$287$	−78.9282			−0.275011
$288$		0			0
$289$	−570.692			−1.97471
$290$			301.492i			1.03963i
$291$		0			0
$292$	80.6410	−	80.6410i	0.276168	−	0.276168i
$293$	120.042	+	120.042i	0.409701	+	0.409701i	0.881634	−	0.471934i	$-0.156444\pi$
$293$	120.042	+	120.042i	0.409701	+	0.409701i	−0.471934	+	0.881634i	$0.656444\pi$
$294$		0			0
$295$	516.946			1.75236
$296$		−	123.426i		−	0.416978i
$297$		0			0
$298$			336.449i			1.12902i
$299$	−246.067	−	291.100i	−0.822965	−	0.973578i
$300$		0			0
$301$	68.7846	−	68.7846i	0.228520	−	0.228520i
$302$	76.8128			0.254347
$303$		0			0
$304$	45.0718	−	45.0718i	0.148262	−	0.148262i
$305$	35.1384	−	35.1384i	0.115208	−	0.115208i
$306$		0			0
$307$	7.48849	+	7.48849i	0.0243925	+	0.0243925i	0.719198	−	0.694805i	$-0.244509\pi$
$307$	7.48849	+	7.48849i	0.0243925	+	0.0243925i	−0.694805	+	0.719198i	$0.744509\pi$
$308$	18.9282			0.0614552
$309$		0			0
$310$	−255.349	−	255.349i	−0.823705	−	0.823705i
$311$		−	289.377i		−	0.930472i	−0.885187	−	0.465236i	$-0.845969\pi$
$311$		−	289.377i		−	0.930472i	0.885187	−	0.465236i	$-0.154031\pi$
$312$		0			0
$313$	346.841			1.10812			0.554059	−	0.832477i	$-0.313078\pi$
$313$	346.841			1.10812			0.554059	+	0.832477i	$0.313078\pi$
$314$	227.215	−	227.215i	0.723616	−	0.723616i
$315$		0			0
$316$			296.420i			0.938039i
$317$	97.0192	−	97.0192i	0.306054	−	0.306054i	−0.537322	−	0.843377i	$-0.680564\pi$
$317$	97.0192	−	97.0192i	0.306054	−	0.306054i	0.843377	+	0.537322i	$0.180564\pi$
$318$		0			0
$319$	55.1769	+	55.1769i	0.172968	+	0.172968i
$320$	−37.8564	−	37.8564i	−0.118301	−	0.118301i
$321$		0			0
$322$		−	160.210i		−	0.497547i
$323$	330.382	+	330.382i	1.02285	+	1.02285i
$324$		0			0
$325$	−166.038	−	196.426i	−0.510888	−	0.604387i
$326$	−24.8897			−0.0763489
$327$		0			0
$328$	57.7795			0.176157
$329$		−	225.100i		−	0.684194i
$330$		0			0
$331$	−126.130	+	126.130i	−0.381056	+	0.381056i	−0.871483	−	0.490427i	$-0.836841\pi$
$331$	−126.130	+	126.130i	−0.381056	+	0.381056i	0.490427	+	0.871483i	$0.336841\pi$
$332$	147.597	+	147.597i	0.444570	+	0.444570i
$333$		0			0
$334$	239.023			0.715638
$335$		−	574.410i		−	1.71466i
$336$		0			0
$337$			423.061i			1.25538i	0.778465	+	0.627688i	$0.215998\pi$
$337$			423.061i			1.25538i	−0.778465	+	0.627688i	$0.784002\pi$
$338$	138.503	+	194.779i	0.409771	+	0.576271i
$339$		0			0
$340$	277.492	−	277.492i	0.816154	−	0.816154i
$341$	−93.4641			−0.274088
$342$		0			0
$343$	−226.956	+	226.956i	−0.661680	+	0.661680i
$344$	−50.3538	+	50.3538i	−0.146377	+	0.146377i
$345$		0			0
$346$	69.3975	+	69.3975i	0.200571	+	0.200571i
$347$	191.867			0.552930			0.276465	−	0.961024i	$-0.410837\pi$
$347$	191.867			0.552930			0.276465	+	0.961024i	$0.410837\pi$
$348$		0			0
$349$	36.7898	+	36.7898i	0.105415	+	0.105415i	0.757847	−	0.652432i	$-0.226251\pi$
$349$	36.7898	+	36.7898i	0.105415	+	0.105415i	−0.652432	+	0.757847i	$0.726251\pi$
$350$		−	108.105i		−	0.308872i
$351$		0			0
$352$	−13.8564			−0.0393648
$353$	−117.870	+	117.870i	−0.333911	+	0.333911i	−0.854070	−	0.520159i	$-0.825873\pi$
$353$	−117.870	+	117.870i	−0.333911	+	0.333911i	0.520159	+	0.854070i	$0.325873\pi$
$354$		0			0
$355$		−	368.238i		−	1.03729i
$356$	−51.0333	+	51.0333i	−0.143352	+	0.143352i
$357$		0			0
$358$	−165.282	−	165.282i	−0.461682	−	0.461682i
$359$	−13.1192	−	13.1192i	−0.0365437	−	0.0365437i	0.688599	−	0.725143i	$-0.258226\pi$
$359$	−13.1192	−	13.1192i	−0.0365437	−	0.0365437i	−0.725143	+	0.688599i	$0.758226\pi$
$360$		0			0
$361$			107.067i			0.296583i
$362$	−283.856	−	283.856i	−0.784134	−	0.784134i
$363$		0			0
$364$	−8.39230	+	100.105i	−0.0230558	+	0.275014i
$365$	−381.597			−1.04547
$366$		0			0
$367$	−600.708			−1.63681			−0.818403	−	0.574645i	$-0.805140\pi$
$367$	−600.708			−1.63681			−0.818403	+	0.574645i	$0.805140\pi$
$368$			117.282i			0.318701i
$369$		0			0
$370$	−292.028	+	292.028i	−0.789265	+	0.789265i
$371$	6.24871	+	6.24871i	0.0168429	+	0.0168429i
$372$		0			0
$373$	671.836			1.80117			0.900584	−	0.434682i	$-0.143139\pi$
$373$	671.836			1.80117			0.900584	+	0.434682i	$0.143139\pi$
$374$		−	101.569i		−	0.271575i
$375$		0			0
$376$			164.785i			0.438257i
$377$	−316.277	+	267.349i	−0.838931	+	0.709148i
$378$		0			0
$379$	158.799	−	158.799i	0.418994	−	0.418994i	−0.465863	−	0.884857i	$-0.654256\pi$
$379$	158.799	−	158.799i	0.418994	−	0.418994i	0.884857	+	0.465863i	$0.154256\pi$
$380$	−213.282			−0.561269
$381$		0			0
$382$	9.28203	−	9.28203i	0.0242985	−	0.0242985i
$383$	−233.445	+	233.445i	−0.609517	+	0.609517i	−0.942820	−	0.333303i	$-0.891837\pi$
$383$	−233.445	+	233.445i	−0.609517	+	0.609517i	0.333303	+	0.942820i	$0.391837\pi$
$384$		0			0
$385$	−44.7846	−	44.7846i	−0.116324	−	0.116324i
$386$	43.4359			0.112528
$387$		0			0
$388$	172.067	+	172.067i	0.443471	+	0.443471i
$389$			27.6950i			0.0711953i	0.999366	+	0.0355976i	$0.0113335\pi$
$389$			27.6950i			0.0711953i	−0.999366	+	0.0355976i	$0.988667\pi$
$390$		0			0
$391$	−859.692			−2.19870
$392$	68.1436	−	68.1436i	0.173836	−	0.173836i
$393$		0			0
$394$			225.464i			0.572244i
$395$	701.338	−	701.338i	1.77554	−	1.77554i
$396$		0			0
$397$	−398.692	−	398.692i	−1.00426	−	1.00426i	−0.999991	−	0.00427158i	$-0.998640\pi$
$397$	−398.692	−	398.692i	−1.00426	−	1.00426i	−0.00427158	−	0.999991i	$-0.501360\pi$
$398$	245.100	+	245.100i	0.615829	+	0.615829i
$399$		0			0
$400$			79.1384i			0.197846i
$401$	139.450	+	139.450i	0.347756	+	0.347756i	0.859273	−	0.511517i	$-0.170916\pi$
$401$	139.450	+	139.450i	0.347756	+	0.347756i	−0.511517	+	0.859273i	$0.670916\pi$
$402$		0			0
$403$	41.4397	−	494.301i	0.102828	−	1.22655i
$404$	−209.072			−0.517504
$405$		0			0
$406$	−174.067			−0.428736
$407$			106.890i			0.262628i
$408$		0			0
$409$	401.813	−	401.813i	0.982427	−	0.982427i	−0.0174209	−	0.999848i	$-0.505546\pi$
$409$	401.813	−	401.813i	0.982427	−	0.982427i	0.999848	+	0.0174209i	$0.00554553\pi$
$410$	−136.708	−	136.708i	−0.333433	−	0.333433i
$411$		0			0
$412$	73.3590			0.178056
$413$			298.459i			0.722661i
$414$		0			0
$415$		−	698.438i		−	1.68298i
$416$	6.14359	−	73.2820i	0.0147683	−	0.176159i
$417$		0			0
$418$	−39.0333	+	39.0333i	−0.0933812	+	0.0933812i
$419$	−139.177			−0.332164			−0.166082	−	0.986112i	$-0.553112\pi$
$419$	−139.177			−0.332164			−0.166082	+	0.986112i	$0.553112\pi$
$420$		0			0
$421$	360.244	−	360.244i	0.855685	−	0.855685i	−0.135141	−	0.990826i	$-0.543149\pi$
$421$	360.244	−	360.244i	0.855685	−	0.855685i	0.990826	+	0.135141i	$0.0431487\pi$
$422$	−345.282	+	345.282i	−0.818204	+	0.818204i
$423$		0			0
$424$	−4.57437	−	4.57437i	−0.0107886	−	0.0107886i
$425$	−580.095			−1.36493
$426$		0			0
$427$	20.2872	+	20.2872i	0.0475110	+	0.0475110i
$428$		−	246.928i		−	0.576935i
$429$		0			0
$430$	238.277			0.554132
$431$	−213.522	+	213.522i	−0.495410	+	0.495410i	−0.910006	−	0.414596i	$-0.863923\pi$
$431$	−213.522	+	213.522i	−0.495410	+	0.495410i	0.414596	+	0.910006i	$0.363923\pi$
$432$		0			0
$433$		−	446.708i		−	1.03166i	−0.856692	−	0.515829i	$-0.827484\pi$
$433$		−	446.708i		−	1.03166i	0.856692	−	0.515829i	$-0.172516\pi$
$434$	147.426	−	147.426i	0.339690	−	0.339690i
$435$		0			0
$436$	−238.631	−	238.631i	−0.547318	−	0.547318i
$437$	330.382	+	330.382i	0.756023	+	0.756023i
$438$		0			0
$439$		−	164.238i		−	0.374119i	−0.982349	−	0.187060i	$-0.940104\pi$
$439$		−	164.238i		−	0.374119i	0.982349	−	0.187060i	$-0.0598958\pi$
$440$	32.7846	+	32.7846i	0.0745105	+	0.0745105i
$441$		0			0
$442$	537.167	+	45.0333i	1.21531	+	0.101885i
$443$	458.736			1.03552			0.517761	−	0.855526i	$-0.326766\pi$
$443$	458.736			1.03552			0.517761	+	0.855526i	$0.326766\pi$
$444$		0			0
$445$	241.492			0.542679
$446$			341.177i			0.764971i
$447$		0			0
$448$	21.8564	−	21.8564i	0.0487866	−	0.0487866i
$449$	−221.776	−	221.776i	−0.493932	−	0.493932i	0.415610	−	0.909543i	$-0.363568\pi$
$449$	−221.776	−	221.776i	−0.493932	−	0.493932i	−0.909543	+	0.415610i	$0.863568\pi$
$450$		0			0
$451$	−50.0385			−0.110950
$452$		−	368.554i		−	0.815384i
$453$		0			0
$454$		−	338.736i		−	0.746114i
$455$	256.708	−	216.995i	0.564193	−	0.476912i
$456$		0			0
$457$	52.9615	−	52.9615i	0.115890	−	0.115890i	−0.646784	−	0.762673i	$-0.723886\pi$
$457$	52.9615	−	52.9615i	0.115890	−	0.115890i	0.762673	+	0.646784i	$0.223886\pi$
$458$	−283.646			−0.619315
$459$		0			0
$460$	277.492	−	277.492i	0.603244	−	0.603244i
$461$	−67.4500	+	67.4500i	−0.146312	+	0.146312i	−0.776468	−	0.630156i	$-0.782991\pi$
$461$	−67.4500	+	67.4500i	−0.146312	+	0.146312i	0.630156	+	0.776468i	$0.282991\pi$
$462$		0			0
$463$	549.247	+	549.247i	1.18628	+	1.18628i	0.978088	+	0.208191i	$0.0667576\pi$
$463$	549.247	+	549.247i	1.18628	+	1.18628i	0.208191	+	0.978088i	$0.433242\pi$
$464$	127.426			0.274624
$465$		0			0
$466$	−128.038	−	128.038i	−0.274761	−	0.274761i
$467$		−	30.1821i		−	0.0646297i	−0.999478	−	0.0323148i	$-0.989712\pi$
$467$		−	30.1821i		−	0.0646297i	0.999478	−	0.0323148i	$-0.0102879\pi$
$468$		0			0
$469$	331.636			0.707113
$470$	389.885	−	389.885i	0.829542	−	0.829542i
$471$		0			0
$472$		−	218.487i		−	0.462896i
$473$	43.6077	−	43.6077i	0.0921939	−	0.0921939i
$474$		0			0
$475$	222.932	+	222.932i	0.469330	+	0.469330i
$476$	160.210	+	160.210i	0.336576	+	0.336576i
$477$		0			0
$478$		−	176.038i		−	0.368281i
$479$	258.870	+	258.870i	0.540439	+	0.540439i	0.923658	−	0.383218i	$-0.125184\pi$
$479$	258.870	+	258.870i	0.540439	+	0.540439i	−0.383218	+	0.923658i	$0.625184\pi$
$480$		0			0
$481$	−565.305	−	47.3923i	−1.17527	−	0.0985287i
$482$	294.918			0.611863
$483$		0			0
$484$	−230.000			−0.475207
$485$		−	814.228i		−	1.67882i
$486$		0			0
$487$	−274.560	+	274.560i	−0.563779	+	0.563779i	−0.930379	−	0.366600i	$-0.880522\pi$
$487$	−274.560	+	274.560i	−0.563779	+	0.563779i	0.366600	+	0.930379i	$0.380522\pi$
$488$	−14.8513	−	14.8513i	−0.0304329	−	0.0304329i
$489$		0			0
$490$	−322.459			−0.658079
$491$			220.726i			0.449543i	0.974412	+	0.224771i	$0.0721635\pi$
$491$			220.726i			0.449543i	−0.974412	+	0.224771i	$0.927836\pi$
$492$		0			0
$493$			934.046i			1.89462i
$494$	−189.128	−	223.741i	−0.382850	−	0.452917i
$495$		0			0
$496$	−107.923	+	107.923i	−0.217587	+	0.217587i
$497$	212.603			0.427772
$498$		0			0
$499$	−625.065	+	625.065i	−1.25264	+	1.25264i	−0.298102	+	0.954534i	$0.596353\pi$
$499$	−625.065	+	625.065i	−1.25264	+	1.25264i	−0.954534	+	0.298102i	$0.903647\pi$
$500$	−49.3590	+	49.3590i	−0.0987180	+	0.0987180i
$501$		0			0
$502$	−181.377	−	181.377i	−0.361308	−	0.361308i
$503$	696.018			1.38373			0.691867	−	0.722025i	$-0.256789\pi$
$503$	696.018			1.38373			0.691867	+	0.722025i	$0.256789\pi$
$504$		0			0
$505$	494.669	+	494.669i	0.979543	+	0.979543i
$506$		−	101.569i		−	0.200730i
$507$		0			0
$508$	−347.923			−0.684888
$509$	−401.678	+	401.678i	−0.789151	+	0.789151i	−0.981355	−	0.192204i	$-0.938437\pi$
$509$	−401.678	+	401.678i	−0.789151	+	0.789151i	0.192204	+	0.981355i	$0.438437\pi$
$510$		0			0
$511$		−	220.315i		−	0.431146i
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	297.664	+	297.664i	0.579113	+	0.579113i
$515$	−173.569	−	173.569i	−0.337028	−	0.337028i
$516$		0			0
$517$		−	142.708i		−	0.276030i
$518$	−168.603	−	168.603i	−0.325488	−	0.325488i
$519$		0			0
$520$	−187.923	+	158.851i	−0.361390	+	0.305483i
$521$	602.651			1.15672			0.578360	−	0.815782i	$-0.303693\pi$
$521$	602.651			1.15672			0.578360	+	0.815782i	$0.303693\pi$
$522$		0			0
$523$	854.677			1.63418			0.817091	−	0.576509i	$-0.195586\pi$
$523$	854.677			1.63418			0.817091	+	0.576509i	$0.195586\pi$
$524$			242.221i			0.462253i
$525$		0			0
$526$	22.8897	−	22.8897i	0.0435166	−	0.0435166i
$527$	−791.090	−	791.090i	−1.50112	−	1.50112i
$528$		0			0
$529$	−330.692			−0.625127
$530$			21.6462i			0.0408418i
$531$		0			0
$532$		−	123.138i		−	0.231463i
$533$	22.1858	−	264.637i	0.0416245	−	0.496505i
$534$		0			0
$535$	−584.238	+	584.238i	−1.09203	+	1.09203i
$536$	−242.774			−0.452937
$537$		0			0
$538$	220.774	−	220.774i	0.410361	−	0.410361i
$539$	−59.0141	+	59.0141i	−0.109488	+	0.109488i
$540$		0			0
$541$	−344.244	−	344.244i	−0.636310	−	0.636310i	0.313333	−	0.949643i	$-0.398554\pi$
$541$	−344.244	−	344.244i	−0.636310	−	0.636310i	−0.949643	+	0.313333i	$0.898554\pi$
$542$	−297.905			−0.549641
$543$		0			0
$544$	−117.282	−	117.282i	−0.215592	−	0.215592i
$545$			1129.21i			2.07195i
$546$		0			0
$547$	842.200			1.53967			0.769835	−	0.638242i	$-0.220338\pi$
$547$	842.200			1.53967			0.769835	+	0.638242i	$0.220338\pi$
$548$	260.105	−	260.105i	0.474644	−	0.474644i
$549$		0			0
$550$		−	68.5359i		−	0.124611i
$551$	358.956	−	358.956i	0.651463	−	0.651463i
$552$		0			0
$553$	404.918	+	404.918i	0.732220	+	0.732220i
$554$	27.2154	+	27.2154i	0.0491253	+	0.0491253i
$555$		0			0
$556$			54.2769i			0.0976203i
$557$	−99.2576	−	99.2576i	−0.178200	−	0.178200i	0.612370	−	0.790571i	$-0.290216\pi$
$557$	−99.2576	−	99.2576i	−0.178200	−	0.178200i	−0.790571	+	0.612370i	$0.790216\pi$
$558$		0			0
$559$	211.292	+	249.962i	0.377983	+	0.447158i
$560$	−103.426			−0.184689
$561$		0			0
$562$	−103.244			−0.183707
$563$			647.174i			1.14951i	0.818326	+	0.574755i	$0.194903\pi$
$563$			647.174i			1.14951i	−0.818326	+	0.574755i	$0.805097\pi$
$564$		0			0
$565$	−872.008	+	872.008i	−1.54338	+	1.54338i
$566$	−93.8076	−	93.8076i	−0.165738	−	0.165738i
$567$		0			0
$568$	−155.636			−0.274007
$569$			701.223i			1.23238i	0.787598	+	0.616189i	$0.211324\pi$
$569$			701.223i			1.23238i	−0.787598	+	0.616189i	$0.788676\pi$
$570$		0			0
$571$		−	218.746i		−	0.383093i	−0.981484	−	0.191547i	$-0.938650\pi$
$571$		−	218.746i		−	0.383093i	0.981484	−	0.191547i	$-0.0613503\pi$
$572$	−5.32051	+	63.4641i	−0.00930159	+	0.110951i
$573$		0			0
$574$	78.9282	−	78.9282i	0.137506	−	0.137506i
$575$	−580.095			−1.00886
$576$		0			0
$577$	−12.3590	+	12.3590i	−0.0214194	+	0.0214194i	−0.717735	−	0.696316i	$-0.754821\pi$
$577$	−12.3590	+	12.3590i	−0.0214194	+	0.0214194i	0.696316	+	0.717735i	$0.254821\pi$
$578$	570.692	−	570.692i	0.987357	−	0.987357i
$579$		0			0
$580$	−301.492	−	301.492i	−0.519814	−	0.519814i
$581$	403.244			0.694051
$582$		0			0
$583$	3.96152	+	3.96152i	0.00679507	+	0.00679507i
$584$			161.282i			0.276168i
$585$		0			0
$586$	−240.084			−0.409701
$587$	106.219	−	106.219i	0.180953	−	0.180953i	−0.610818	−	0.791771i	$-0.709159\pi$
$587$	106.219	−	106.219i	0.180953	−	0.180953i	0.791771	+	0.610818i	$0.209159\pi$
$588$		0			0
$589$			608.036i			1.03232i
$590$	−516.946	+	516.946i	−0.876180	+	0.876180i
$591$		0			0
$592$	123.426	+	123.426i	0.208489	+	0.208489i
$593$	−770.645	−	770.645i	−1.29957	−	1.29957i	−0.928675	−	0.370895i	$-0.879051\pi$
$593$	−770.645	−	770.645i	−1.29957	−	1.29957i	−0.370895	−	0.928675i	$-0.620949\pi$
$594$		0			0
$595$		−	758.123i		−	1.27416i
$596$	−336.449	−	336.449i	−0.564511	−	0.564511i
$597$		0			0
$598$	537.167	+	45.0333i	0.898272	+	0.0753066i
$599$	130.392			0.217683			0.108842	−	0.994059i	$-0.465286\pi$
$599$	130.392			0.217683			0.108842	+	0.994059i	$0.465286\pi$
$600$		0			0
$601$	−551.108			−0.916984			−0.458492	−	0.888698i	$-0.651610\pi$
$601$	−551.108			−0.916984			−0.458492	+	0.888698i	$0.651610\pi$
$602$			137.569i			0.228520i
$603$		0			0
$604$	−76.8128	+	76.8128i	−0.127173	+	0.127173i
$605$	544.186	+	544.186i	0.899481	+	0.899481i
$606$		0			0
$607$	63.6001			0.104778			0.0523889	−	0.998627i	$-0.483316\pi$
$607$	63.6001			0.104778			0.0523889	+	0.998627i	$0.483316\pi$
$608$			90.1436i			0.148262i
$609$		0			0
$610$			70.2769i			0.115208i
$611$	754.734	+	63.2731i	1.23524	+	0.103557i
$612$		0			0
$613$	−26.3487	+	26.3487i	−0.0429832	+	0.0429832i	−0.728272	−	0.685289i	$-0.759676\pi$
$613$	−26.3487	+	26.3487i	−0.0429832	+	0.0429832i	0.685289	+	0.728272i	$0.259676\pi$
$614$	−14.9770			−0.0243925
$615$		0			0
$616$	−18.9282	+	18.9282i	−0.0307276	+	0.0307276i
$617$	−375.391	+	375.391i	−0.608413	+	0.608413i	−0.942531	−	0.334118i	$-0.891562\pi$
$617$	−375.391	+	375.391i	−0.608413	+	0.608413i	0.334118	+	0.942531i	$0.391562\pi$
$618$		0			0
$619$	264.070	+	264.070i	0.426608	+	0.426608i	0.887471	−	0.460863i	$-0.152460\pi$
$619$	264.070	+	264.070i	0.426608	+	0.426608i	−0.460863	+	0.887471i	$0.652460\pi$
$620$	510.697			0.823705
$621$		0			0
$622$	289.377	+	289.377i	0.465236	+	0.465236i
$623$			139.426i			0.223797i
$624$		0			0
$625$	728.184			1.16510
$626$	−346.841	+	346.841i	−0.554059	+	0.554059i
$627$		0			0
$628$			454.431i			0.723616i
$629$	−904.726	+	904.726i	−1.43836	+	1.43836i
$630$		0			0
$631$	−441.594	−	441.594i	−0.699831	−	0.699831i	0.264543	−	0.964374i	$-0.414779\pi$
$631$	−441.594	−	441.594i	−0.699831	−	0.699831i	−0.964374	+	0.264543i	$0.914779\pi$
$632$	−296.420	−	296.420i	−0.469020	−	0.469020i
$633$		0			0
$634$			194.038i			0.306054i
$635$	823.195	+	823.195i	1.29637	+	1.29637i
$636$		0			0
$637$	−285.941	−	338.272i	−0.448887	−	0.531039i
$638$	−110.354			−0.172968
$639$		0			0
$640$	75.7128			0.118301
$641$		−	829.910i		−	1.29471i	−0.762188	−	0.647356i	$-0.775875\pi$
$641$		−	829.910i		−	1.29471i	0.762188	−	0.647356i	$-0.224125\pi$
$642$		0			0
$643$	424.196	−	424.196i	0.659714	−	0.659714i	−0.295598	−	0.955312i	$-0.595519\pi$
$643$	424.196	−	424.196i	0.659714	−	0.659714i	0.955312	+	0.295598i	$0.0955190\pi$
$644$	160.210	+	160.210i	0.248774	+	0.248774i
$645$		0			0
$646$	−660.764			−1.02285
$647$			477.913i			0.738660i	0.929298	+	0.369330i	$0.120413\pi$
$647$			477.913i			0.738660i	−0.929298	+	0.369330i	$0.879587\pi$
$648$		0			0
$649$			189.215i			0.291549i
$650$	362.464	+	30.3872i	0.557637	+	0.0467495i
$651$		0			0
$652$	24.8897	−	24.8897i	0.0381744	−	0.0381744i
$653$	243.380			0.372710			0.186355	−	0.982482i	$-0.440333\pi$
$653$	243.380			0.372710			0.186355	+	0.982482i	$0.440333\pi$
$654$		0			0
$655$	573.100	−	573.100i	0.874962	−	0.874962i
$656$	−57.7795	+	57.7795i	−0.0880784	+	0.0880784i
$657$		0			0
$658$	225.100	+	225.100i	0.342097	+	0.342097i
$659$	190.677			0.289343			0.144671	−	0.989480i	$-0.453788\pi$
$659$	190.677			0.289343			0.144671	+	0.989480i	$0.453788\pi$
$660$		0			0
$661$	−446.149	−	446.149i	−0.674960	−	0.674960i	0.283895	−	0.958855i	$-0.408373\pi$
$661$	−446.149	−	446.149i	−0.674960	−	0.674960i	−0.958855	+	0.283895i	$0.908373\pi$
$662$		−	252.259i		−	0.381056i
$663$		0			0
$664$	−295.195			−0.444570
$665$	−291.349	+	291.349i	−0.438118	+	0.438118i
$666$		0			0
$667$			934.046i			1.40037i
$668$	−239.023	+	239.023i	−0.357819	+	0.357819i
$669$		0			0
$670$	574.410	+	574.410i	0.857329	+	0.857329i
$671$	12.8616	+	12.8616i	0.0191678	+	0.0191678i
$672$		0			0
$673$			176.221i			0.261843i	0.991393	+	0.130922i	$0.0417936\pi$
$673$			176.221i			0.261843i	−0.991393	+	0.130922i	$0.958206\pi$
$674$	−423.061	−	423.061i	−0.627688	−	0.627688i
$675$		0			0
$676$	−333.282	−	56.2769i	−0.493021	−	0.0832498i
$677$	−672.600			−0.993500			−0.496750	−	0.867894i	$-0.665473\pi$
$677$	−672.600			−0.993500			−0.496750	+	0.867894i	$0.665473\pi$
$678$		0			0
$679$	470.095			0.692334
$680$			554.985i			0.816154i
$681$		0			0
$682$	93.4641	−	93.4641i	0.137044	−	0.137044i
$683$	−306.191	−	306.191i	−0.448303	−	0.448303i	0.446487	−	0.894790i	$-0.352675\pi$
$683$	−306.191	−	306.191i	−0.448303	−	0.448303i	−0.894790	+	0.446487i	$0.852675\pi$
$684$		0			0
$685$	−1230.83			−1.79683
$686$		−	453.913i		−	0.661680i
$687$		0			0
$688$		−	100.708i		−	0.146377i
$689$	−22.7077	+	19.1948i	−0.0329574	+	0.0278589i
$690$		0			0
$691$	−474.865	+	474.865i	−0.687215	+	0.687215i	−0.961615	−	0.274401i	$-0.911521\pi$
$691$	−474.865	+	474.865i	−0.687215	+	0.687215i	0.274401	+	0.961615i	$0.411521\pi$
$692$	−138.795			−0.200571
$693$		0			0
$694$	−191.867	+	191.867i	−0.276465	+	0.276465i
$695$	128.420	−	128.420i	0.184778	−	0.184778i
$696$		0			0
$697$	−423.531	−	423.531i	−0.607648	−	0.607648i
$698$	−73.5795			−0.105415
$699$		0			0
$700$	108.105	+	108.105i	0.154436	+	0.154436i
$701$			204.480i			0.291697i	0.989307	+	0.145848i	$0.0465912\pi$
$701$			204.480i			0.291697i	−0.989307	+	0.145848i	$0.953409\pi$
$702$		0			0
$703$	695.377			0.989156
$704$	13.8564	−	13.8564i	0.0196824	−	0.0196824i
$705$		0			0
$706$		−	235.741i		−	0.333911i
$707$	−285.597	+	285.597i	−0.403957	+	0.403957i
$708$		0			0
$709$	−629.018	−	629.018i	−0.887190	−	0.887190i	0.107062	−	0.994252i	$-0.465856\pi$
$709$	−629.018	−	629.018i	−0.887190	−	0.887190i	−0.994252	+	0.107062i	$0.965856\pi$
$710$	368.238	+	368.238i	0.518646	+	0.518646i
$711$		0			0
$712$		−	102.067i		−	0.143352i
$713$	−791.090	−	791.090i	−1.10952	−	1.10952i
$714$		0			0
$715$	162.746	−	137.569i	0.227617	−	0.192405i
$716$	330.564			0.461682
$717$		0			0
$718$	26.2384			0.0365437
$719$		−	863.290i		−	1.20068i	−0.799745	−	0.600340i	$-0.795032\pi$
$719$		−	863.290i		−	1.20068i	0.799745	−	0.600340i	$-0.204968\pi$
$720$		0			0
$721$	100.210	−	100.210i	0.138988	−	0.138988i
$722$	−107.067	−	107.067i	−0.148292	−	0.148292i
$723$		0			0
$724$	567.713			0.784134
$725$			630.267i			0.869333i
$726$		0			0
$727$		−	605.577i		−	0.832980i	−0.909140	−	0.416490i	$-0.863260\pi$
$727$		−	605.577i		−	0.832980i	0.909140	−	0.416490i	$-0.136740\pi$
$728$	−91.7128	−	108.497i	−0.125979	−	0.149035i
$729$		0			0
$730$	381.597	−	381.597i	0.522736	−	0.522736i
$731$	738.200			1.00985
$732$		0			0
$733$	205.946	−	205.946i	0.280963	−	0.280963i	−0.552530	−	0.833493i	$-0.686337\pi$
$733$	205.946	−	205.946i	0.280963	−	0.280963i	0.833493	+	0.552530i	$0.186337\pi$
$734$	600.708	−	600.708i	0.818403	−	0.818403i
$735$		0			0
$736$	−117.282	−	117.282i	−0.159351	−	0.159351i
$737$	210.249			0.285276
$738$		0			0
$739$	−58.7884	−	58.7884i	−0.0795513	−	0.0795513i	0.666212	−	0.745763i	$-0.267915\pi$
$739$	−58.7884	−	58.7884i	−0.0795513	−	0.0795513i	−0.745763	+	0.666212i	$0.767915\pi$
$740$		−	584.056i		−	0.789265i
$741$		0			0
$742$	−12.4974			−0.0168429
$743$	885.509	−	885.509i	1.19180	−	1.19180i	0.215241	−	0.976561i	$-0.430946\pi$
$743$	885.509	−	885.509i	1.19180	−	1.19180i	0.976561	−	0.215241i	$-0.0690536\pi$
$744$		0			0
$745$			1592.09i			2.13704i
$746$	−671.836	+	671.836i	−0.900584	+	0.900584i
$747$		0			0
$748$	101.569	+	101.569i	0.135788	+	0.135788i
$749$	−337.310	−	337.310i	−0.450347	−	0.450347i
$750$		0			0
$751$			19.5720i			0.0260612i	0.999915	+	0.0130306i	$0.00414789\pi$
$751$			19.5720i			0.0260612i	−0.999915	+	0.0130306i	$0.995852\pi$
$752$	−164.785	−	164.785i	−0.219128	−	0.219128i
$753$		0			0
$754$	48.9282	−	583.626i	0.0648915	−	0.774039i
$755$	363.482			0.481433
$756$		0			0
$757$	677.836			0.895424			0.447712	−	0.894178i	$-0.352239\pi$
$757$	677.836			0.895424			0.447712	+	0.894178i	$0.352239\pi$
$758$			317.597i			0.418994i
$759$		0			0
$760$	213.282	−	213.282i	0.280634	−	0.280634i
$761$	62.4449	+	62.4449i	0.0820563	+	0.0820563i	0.746944	−	0.664887i	$-0.231520\pi$
$761$	62.4449	+	62.4449i	0.0820563	+	0.0820563i	−0.664887	+	0.746944i	$0.731520\pi$
$762$		0			0
$763$	−651.951			−0.854458
$764$			18.5641i			0.0242985i
$765$		0			0
$766$		−	466.890i		−	0.609517i
$767$	−1000.70	−	83.8935i	−1.30469	−	0.109379i
$768$		0			0
$769$	−71.5950	+	71.5950i	−0.0931014	+	0.0931014i	−0.752124	−	0.659022i	$-0.770970\pi$
$769$	−71.5950	+	71.5950i	−0.0931014	+	0.0931014i	0.659022	+	0.752124i	$0.270970\pi$
$770$	89.5692			0.116324
$771$		0			0
$772$	−43.4359	+	43.4359i	−0.0562642	+	0.0562642i
$773$	778.817	−	778.817i	1.00752	−	1.00752i	0.00755317	−	0.999971i	$-0.497596\pi$
$773$	778.817	−	778.817i	1.00752	−	1.00752i	0.999971	−	0.00755317i	$-0.00240427\pi$
$774$		0			0
$775$	−533.804	−	533.804i	−0.688779	−	0.688779i
$776$	−344.133			−0.443471
$777$		0			0
$778$	−27.6950	−	27.6950i	−0.0355976	−	0.0355976i
$779$			325.528i			0.417879i
$780$		0			0
$781$	134.785			0.172580
$782$	859.692	−	859.692i	1.09935	−	1.09935i
$783$		0			0
$784$			136.287i			0.173836i
$785$	1075.19	−	1075.19i	1.36967	−	1.36967i
$786$		0			0
$787$	548.883	+	548.883i	0.697437	+	0.697437i	0.963857	−	0.266420i	$-0.0858407\pi$
$787$	548.883	+	548.883i	0.697437	+	0.697437i	−0.266420	+	0.963857i	$0.585841\pi$
$788$	−225.464	−	225.464i	−0.286122	−	0.286122i
$789$		0			0
$790$			1402.68i			1.77554i
$791$	−503.454	−	503.454i	−0.636478	−	0.636478i
$792$		0			0
$793$	−73.7231	+	62.3181i	−0.0929674	+	0.0785853i
$794$	797.384			1.00426
$795$		0			0
$796$	−490.200			−0.615829
$797$		−	41.5871i		−	0.0521795i	−0.999660	−	0.0260898i	$-0.991694\pi$
$797$		−	41.5871i		−	0.0521795i	0.999660	−	0.0260898i	$-0.00830557\pi$
$798$		0			0
$799$	1207.89	−	1207.89i	1.51175	−	1.51175i
$800$	−79.1384	−	79.1384i	−0.0989230	−	0.0989230i
$801$		0			0
$802$	−278.900			−0.347756
$803$		−	139.674i		−	0.173941i
$804$		0			0
$805$		−	758.123i		−	0.941768i
$806$	452.862	+	535.741i	0.561863	+	0.664691i
$807$		0			0
$808$	209.072	−	209.072i	0.258752	−	0.258752i
$809$	1338.40			1.65439			0.827194	−	0.561916i	$-0.189936\pi$
$809$	1338.40			1.65439			0.827194	+	0.561916i	$0.189936\pi$
$810$		0			0
$811$	257.258	−	257.258i	0.317210	−	0.317210i	−0.530484	−	0.847695i	$-0.677990\pi$
$811$	257.258	−	257.258i	0.317210	−	0.317210i	0.847695	+	0.530484i	$0.177990\pi$
$812$	174.067	−	174.067i	0.214368	−	0.214368i
$813$		0			0
$814$	−106.890	−	106.890i	−0.131314	−	0.131314i
$815$	−117.779			−0.144515
$816$		0			0
$817$	−283.692	−	283.692i	−0.347236	−	0.347236i
$818$			803.626i			0.982427i
$819$		0			0
$820$	273.415			0.333433
$821$	306.873	−	306.873i	0.373779	−	0.373779i	−0.495072	−	0.868852i	$-0.664858\pi$
$821$	306.873	−	306.873i	0.373779	−	0.373779i	0.868852	+	0.495072i	$0.164858\pi$
$822$		0			0
$823$		−	1037.92i		−	1.26114i	−0.776131	−	0.630571i	$-0.782821\pi$
$823$		−	1037.92i		−	1.26114i	0.776131	−	0.630571i	$-0.217179\pi$
$824$	−73.3590	+	73.3590i	−0.0890279	+	0.0890279i
$825$		0			0
$826$	−298.459	−	298.459i	−0.361330	−	0.361330i
$827$	−658.153	−	658.153i	−0.795831	−	0.795831i	0.186604	−	0.982435i	$-0.440252\pi$
$827$	−658.153	−	658.153i	−0.795831	−	0.795831i	−0.982435	+	0.186604i	$0.940252\pi$
$828$		0			0
$829$		−	372.354i		−	0.449160i	−0.974456	−	0.224580i	$-0.927899\pi$
$829$		−	372.354i		−	0.449160i	0.974456	−	0.224580i	$-0.0721010\pi$
$830$	698.438	+	698.438i	0.841492	+	0.841492i
$831$		0			0
$832$	67.1384	+	79.4256i	0.0806952	+	0.0954635i
$833$	−999.002			−1.19928
$834$		0			0
$835$	1131.07			1.35457
$836$		−	78.0666i		−	0.0933812i
$837$		0			0
$838$	139.177	−	139.177i	0.166082	−	0.166082i
$839$	−1018.87	−	1018.87i	−1.21438	−	1.21438i	−0.969570	−	0.244813i	$-0.921273\pi$
$839$	−1018.87	−	1018.87i	−1.21438	−	1.21438i	−0.244813	−	0.969570i	$-0.578727\pi$
$840$		0			0
$841$	173.831			0.206695
$842$			720.487i			0.855685i
$843$		0			0
$844$		−	690.564i		−	0.818204i
$845$	655.401	+	921.706i	0.775623	+	1.09078i
$846$		0			0
$847$	−314.186	+	314.186i	−0.370940	+	0.370940i
$848$	9.14875			0.0107886
$849$		0			0
$850$	580.095	−	580.095i	0.682464	−	0.682464i
$851$	−904.726	+	904.726i	−1.06313	+	1.06313i
$852$		0			0
$853$	−366.790	−	366.790i	−0.430000	−	0.430000i	0.458628	−	0.888628i	$-0.348341\pi$
$853$	−366.790	−	366.790i	−0.430000	−	0.430000i	−0.888628	+	0.458628i	$0.848341\pi$
$854$	−40.5744			−0.0475110
$855$		0			0
$856$	246.928	+	246.928i	0.288468	+	0.288468i
$857$		−	469.244i		−	0.547542i	−0.961795	−	0.273771i	$-0.911729\pi$
$857$		−	469.244i		−	0.547542i	0.961795	−	0.273771i	$-0.0882711\pi$
$858$		0			0
$859$	−1238.66			−1.44197			−0.720987	−	0.692948i	$-0.756311\pi$
$859$	−1238.66			−1.44197			−0.720987	+	0.692948i	$0.756311\pi$
$860$	−238.277	+	238.277i	−0.277066	+	0.277066i
$861$		0			0
$862$		−	427.044i		−	0.495410i
$863$	5.71143	−	5.71143i	0.00661811	−	0.00661811i	−0.703790	−	0.710408i	$-0.748510\pi$
$863$	5.71143	−	5.71143i	0.00661811	−	0.00661811i	0.710408	+	0.703790i	$0.248510\pi$
$864$		0			0
$865$	328.392	+	328.392i	0.379644	+	0.379644i
$866$	446.708	+	446.708i	0.515829	+	0.515829i
$867$		0			0
$868$			294.851i			0.339690i
$869$	256.708	+	256.708i	0.295406	+	0.295406i
$870$		0			0
$871$	−93.2192	+	1111.94i	−0.107025	+	1.27662i
$872$	477.261			0.547318
$873$		0			0
$874$	−660.764			−0.756023
$875$			134.851i			0.154116i
$876$		0			0
$877$	591.287	−	591.287i	0.674216	−	0.674216i	−0.284469	−	0.958685i	$-0.591817\pi$
$877$	591.287	−	591.287i	0.674216	−	0.674216i	0.958685	+	0.284469i	$0.0918174\pi$
$878$	164.238	+	164.238i	0.187060	+	0.187060i
$879$		0			0
$880$	−65.5692			−0.0745105
$881$		−	663.997i		−	0.753686i	−0.926277	−	0.376843i	$-0.877010\pi$
$881$		−	663.997i		−	0.753686i	0.926277	−	0.376843i	$-0.122990\pi$
$882$		0			0
$883$		−	570.192i		−	0.645744i	−0.946443	−	0.322872i	$-0.895352\pi$
$883$		−	570.192i		−	0.645744i	0.946443	−	0.322872i	$-0.104648\pi$
$884$	−582.200	+	492.133i	−0.658597	+	0.556712i
$885$		0			0
$886$	−458.736	+	458.736i	−0.517761	+	0.517761i
$887$	−481.031			−0.542312			−0.271156	−	0.962535i	$-0.587406\pi$
$887$	−481.031			−0.542312			−0.271156	+	0.962535i	$0.587406\pi$
$888$		0			0
$889$	−475.272	+	475.272i	−0.534614	+	0.534614i
$890$	−241.492	+	241.492i	−0.271340	+	0.271340i
$891$		0			0
$892$	−341.177	−	341.177i	−0.382485	−	0.382485i
$893$	−928.392			−1.03963
$894$		0			0
$895$	−782.123	−	782.123i	−0.873880	−	0.873880i
$896$			43.7128i			0.0487866i
$897$		0			0
$898$	443.551			0.493932
$899$	−859.510	+	859.510i	−0.956074	+	0.956074i
$900$		0			0
$901$			67.0615i			0.0744301i
$902$	50.0385	−	50.0385i	0.0554750	−	0.0554750i
$903$		0			0
$904$	368.554	+	368.554i	0.407692	+	0.407692i
$905$	−1343.22	−	1343.22i	−1.48422	−	1.48422i
$906$		0			0
$907$			193.331i			0.213154i	0.994304	+	0.106577i	$0.0339891\pi$
$907$			193.331i			0.213154i	−0.994304	+	0.106577i	$0.966011\pi$
$908$	338.736	+	338.736i	0.373057	+	0.373057i
$909$		0			0
$910$	−39.7128	+	473.703i	−0.0436405	+	0.520552i
$911$	868.743			0.953615			0.476808	−	0.879008i	$-0.341794\pi$
$911$	868.743			0.953615			0.476808	+	0.879008i	$0.341794\pi$
$912$		0			0
$913$	255.646			0.280007
$914$			105.923i			0.115890i
$915$		0			0
$916$	283.646	−	283.646i	0.309657	−	0.309657i
$917$	330.879	+	330.879i	0.360828	+	0.360828i
$918$		0			0
$919$	389.108			0.423403			0.211702	−	0.977334i	$-0.432100\pi$
$919$	389.108			0.423403			0.211702	+	0.977334i	$0.432100\pi$
$920$			554.985i			0.603244i
$921$		0			0
$922$		−	134.900i		−	0.146312i
$923$	−59.7602	+	712.832i	−0.0647456	+	0.772299i
$924$		0			0
$925$	−610.482	+	610.482i	−0.659980	+	0.659980i
$926$	−1098.49			−1.18628
$927$		0			0
$928$	−127.426	+	127.426i	−0.137312	+	0.137312i
$929$	429.870	−	429.870i	0.462724	−	0.462724i	−0.436823	−	0.899547i	$-0.643897\pi$
$929$	429.870	−	429.870i	0.462724	−	0.462724i	0.899547	+	0.436823i	$0.143897\pi$
$930$		0			0
$931$	383.919	+	383.919i	0.412373	+	0.412373i
$932$	256.077			0.274761
$933$		0			0
$934$	30.1821	+	30.1821i	0.0323148	+	0.0323148i
$935$		−	480.631i		−	0.514044i
$936$		0			0
$937$	916.441			0.978059			0.489029	−	0.872267i	$-0.337351\pi$
$937$	916.441			0.978059			0.489029	+	0.872267i	$0.337351\pi$
$938$	−331.636	+	331.636i	−0.353556	+	0.353556i
$939$		0			0
$940$			779.769i			0.829542i
$941$	−835.601	+	835.601i	−0.887993	+	0.887993i	−0.994330	−	0.106337i	$-0.966088\pi$
$941$	−835.601	+	835.601i	−0.887993	+	0.887993i	0.106337	+	0.994330i	$0.466088\pi$
$942$		0			0
$943$	−423.531	−	423.531i	−0.449131	−	0.449131i
$944$	218.487	+	218.487i	0.231448	+	0.231448i
$945$		0			0
$946$			87.2154i			0.0921939i
$947$	378.506	+	378.506i	0.399690	+	0.399690i	0.878124	−	0.478434i	$-0.158795\pi$
$947$	378.506	+	378.506i	0.399690	+	0.399690i	−0.478434	+	0.878124i	$0.658795\pi$
$948$		0			0
$949$	738.692	+	61.9282i	0.778390	+	0.0652563i
$950$	−445.864			−0.469330
$951$		0			0
$952$	−320.420			−0.336576
$953$			839.556i			0.880961i	0.897762	+	0.440481i	$0.145192\pi$
$953$			839.556i			0.880961i	−0.897762	+	0.440481i	$0.854808\pi$
$954$		0			0
$955$	43.9230	−	43.9230i	0.0459927	−	0.0459927i
$956$	176.038	+	176.038i	0.184141	+	0.184141i
$957$		0			0
$958$	−517.741			−0.540439
$959$		−	710.620i		−	0.741001i
$960$		0			0
$961$		−	494.923i		−	0.515008i
$962$	612.697	−	517.913i	0.636900	−	0.538371i
$963$		0			0
$964$	−294.918	+	294.918i	−0.305931	+	0.305931i
$965$	205.541			0.212996
$966$		0			0
$967$	−375.745	+	375.745i	−0.388567	+	0.388567i	−0.874176	−	0.485609i	$-0.838598\pi$
$967$	−375.745	+	375.745i	−0.388567	+	0.388567i	0.485609	+	0.874176i	$0.338598\pi$
$968$	230.000	−	230.000i	0.237603	−	0.237603i
$969$		0			0
$970$	814.228	+	814.228i	0.839410	+	0.839410i
$971$	−134.523			−0.138541			−0.0692703	−	0.997598i	$-0.522067\pi$
$971$	−134.523			−0.138541			−0.0692703	+	0.997598i	$0.522067\pi$
$972$		0			0
$973$	74.1436	+	74.1436i	0.0762010	+	0.0762010i
$974$		−	549.121i		−	0.563779i
$975$		0			0
$976$	29.7025			0.0304329
$977$	−708.060	+	708.060i	−0.724729	+	0.724729i	−0.969565	−	0.244836i	$-0.921266\pi$
$977$	−708.060	+	708.060i	−0.724729	+	0.724729i	0.244836	+	0.969565i	$0.421266\pi$
$978$		0			0
$979$			88.3923i			0.0902884i
$980$	322.459	−	322.459i	0.329040	−	0.329040i
$981$		0			0
$982$	−220.726	−	220.726i	−0.224771	−	0.224771i
$983$	904.881	+	904.881i	0.920530	+	0.920530i	0.997067	−	0.0765369i	$-0.0243863\pi$
$983$	904.881	+	904.881i	0.920530	+	0.920530i	−0.0765369	+	0.997067i	$0.524386\pi$
$984$		0			0
$985$			1066.91i			1.08315i
$986$	−934.046	−	934.046i	−0.947308	−	0.947308i
$987$		0			0
$988$	412.869	+	34.6128i	0.417884	+	0.0350332i
$989$	738.200			0.746410
$990$		0			0
$991$	29.0155			0.0292790			0.0146395	−	0.999893i	$-0.495340\pi$
$991$	29.0155			0.0292790			0.0146395	+	0.999893i	$0.495340\pi$
$992$		−	215.846i		−	0.217587i
$993$		0			0
$994$	−212.603	+	212.603i	−0.213886	+	0.213886i
$995$	1159.83	+	1159.83i	1.16565	+	1.16565i
$996$		0			0
$997$	336.123			0.337134			0.168567	−	0.985690i	$-0.446086\pi$
$997$	336.123			0.337134			0.168567	+	0.985690i	$0.446086\pi$
$998$		−	1250.13i		−	1.25264i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.3.i.b.109.1		4
3.2	odd	2		78.3.f.a.31.1	✓	4
12.11	even	2		624.3.ba.a.577.2		4
13.8	odd	4	inner	234.3.i.b.73.1		4
39.5	even	4		1014.3.f.a.775.1		4
39.8	even	4		78.3.f.a.73.1	yes	4
39.38	odd	2		1014.3.f.a.577.1		4
156.47	odd	4		624.3.ba.a.385.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.f.a.31.1	✓	4	3.2	odd	2
78.3.f.a.73.1	yes	4	39.8	even	4
234.3.i.b.73.1		4	13.8	odd	4	inner
234.3.i.b.109.1		4	1.1	even	1	trivial
624.3.ba.a.385.2		4	156.47	odd	4
624.3.ba.a.577.2		4	12.11	even	2
1014.3.f.a.577.1		4	39.38	odd	2
1014.3.f.a.775.1		4	39.5	even	4

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	234.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.00000i q^{4} +(-4.73205 + 4.73205i) q^{5} +(-2.73205 - 2.73205i) q^{7} +(2.00000 + 2.00000i) q^{8} -9.46410i q^{10} +(-1.73205 - 1.73205i) q^{11} +(9.92820 - 8.39230i) q^{13} +5.46410 q^{14} -4.00000 q^{16} -29.3205i q^{17} +(-11.2679 + 11.2679i) q^{19} +(9.46410 + 9.46410i) q^{20} +3.46410 q^{22} -29.3205i q^{23} -19.7846i q^{25} +(-1.53590 + 18.3205i) q^{26} +(-5.46410 + 5.46410i) q^{28} -31.8564 q^{29} +(26.9808 - 26.9808i) q^{31} +(4.00000 - 4.00000i) q^{32} +(29.3205 + 29.3205i) q^{34} +25.8564 q^{35} +(-30.8564 - 30.8564i) q^{37} -22.5359i q^{38} -18.9282 q^{40} +(14.4449 - 14.4449i) q^{41} +25.1769i q^{43} +(-3.46410 + 3.46410i) q^{44} +(29.3205 + 29.3205i) q^{46} +(41.1962 + 41.1962i) q^{47} -34.0718i q^{49} +(19.7846 + 19.7846i) q^{50} +(-16.7846 - 19.8564i) q^{52} -2.28719 q^{53} +16.3923 q^{55} -10.9282i q^{56} +(31.8564 - 31.8564i) q^{58} +(-54.6218 - 54.6218i) q^{59} -7.42563 q^{61} +53.9615i q^{62} +8.00000i q^{64} +(-7.26795 + 86.6936i) q^{65} +(-60.6936 + 60.6936i) q^{67} -58.6410 q^{68} +(-25.8564 + 25.8564i) q^{70} +(-38.9090 + 38.9090i) q^{71} +(40.3205 + 40.3205i) q^{73} +61.7128 q^{74} +(22.5359 + 22.5359i) q^{76} +9.46410i q^{77} -148.210 q^{79} +(18.9282 - 18.9282i) q^{80} +28.8897i q^{82} +(-73.7987 + 73.7987i) q^{83} +(138.746 + 138.746i) q^{85} +(-25.1769 - 25.1769i) q^{86} -6.92820i q^{88} +(-25.5167 - 25.5167i) q^{89} +(-50.0526 - 4.19615i) q^{91} -58.6410 q^{92} -82.3923 q^{94} -106.641i q^{95} +(-86.0333 + 86.0333i) q^{97} +(34.0718 + 34.0718i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 12 q^{5} - 4 q^{7} + 8 q^{8} + 12 q^{13} + 8 q^{14} - 16 q^{16} - 52 q^{19} + 24 q^{20} - 20 q^{26} - 8 q^{28} - 72 q^{29} + 4 q^{31} + 16 q^{32} + 48 q^{34} + 48 q^{35} - 68 q^{37} - 48 q^{40}+ \cdots + 164 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 12 * q^5 - 4 * q^7 + 8 * q^8 + 12 * q^13 + 8 * q^14 - 16 * q^16 - 52 * q^19 + 24 * q^20 - 20 * q^26 - 8 * q^28 - 72 * q^29 + 4 * q^31 + 16 * q^32 + 48 * q^34 + 48 * q^35 - 68 * q^37 - 48 * q^40 - 60 * q^41 + 48 * q^46 + 144 * q^47 - 4 * q^50 + 16 * q^52 - 120 * q^53 + 24 * q^55 + 72 * q^58 + 24 * q^59 + 192 * q^61 - 36 * q^65 - 28 * q^67 - 96 * q^68 - 48 * q^70 - 24 * q^71 + 92 * q^73 + 136 * q^74 + 104 * q^76 - 288 * q^79 + 48 * q^80 + 72 * q^83 + 264 * q^85 + 24 * q^86 - 12 * q^89 - 124 * q^91 - 96 * q^92 - 288 * q^94 - 164 * q^97 + 164 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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