LMFDB - Embedded newform 567.3.r.e.134.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,3,Mod(134,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.134"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	567.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,12,0,0,0,0,0,-104] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.4496309892$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 24 x^{13} + 53 x^{12} - 204 x^{11} + 558 x^{10} - 774 x^{9} + 828 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 24x^13 + 53x^12 - 204x^11 + 558x^10 - 774x^9 + 828x^8 - 1302x^7 + 2718x^6 - 3780x^5 + 3293x^4 - 1656x^3 + 450x^2 - 30*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{12} $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			134.2
Root			$2.18316 - 2.18316i$ of defining polynomial
Character	$\chi$	$=$	567.134
Dual form			567.3.r.e.512.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.97223 + 1.13867i) q^{2} +(0.593126 - 1.02732i) q^{4} +(-4.28273 - 2.47263i) q^{5} +(-1.32288 - 2.29129i) q^{7} -6.40785i q^{8} +11.2620 q^{10} +(-17.4844 + 10.0946i) q^{11} +(-12.9270 + 22.3903i) q^{13} +(5.21803 + 3.01263i) q^{14} +(9.66891 + 16.7470i) q^{16} -6.60531i q^{17} +5.53147 q^{19} +(-5.08040 + 2.93317i) q^{20} +(22.9888 - 39.8177i) q^{22} +(-12.5862 - 7.26667i) q^{23} +(-0.272153 - 0.471383i) q^{25} -58.8783i q^{26} -3.13853 q^{28} +(15.1448 - 8.74386i) q^{29} +(22.6963 - 39.3111i) q^{31} +(-15.9412 - 9.20364i) q^{32} +(7.52125 + 13.0272i) q^{34} +13.0840i q^{35} +40.8908 q^{37} +(-10.9093 + 6.29851i) q^{38} +(-15.8443 + 27.4431i) q^{40} +(-26.3350 - 15.2045i) q^{41} +(26.7653 + 46.3588i) q^{43} +23.9495i q^{44} +33.0973 q^{46} +(24.1224 - 13.9271i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(1.07350 + 0.619784i) q^{50} +(15.3347 + 26.5605i) q^{52} -6.45594i q^{53} +99.8411 q^{55} +(-14.6822 + 8.47678i) q^{56} +(-19.9127 + 34.4898i) q^{58} +(37.0702 + 21.4025i) q^{59} +(-17.7990 - 30.8288i) q^{61} +103.374i q^{62} -35.4317 q^{64} +(110.726 - 63.9277i) q^{65} +(41.8654 - 72.5131i) q^{67} +(-6.78580 - 3.91778i) q^{68} +(-14.8983 - 25.8046i) q^{70} +113.821i q^{71} -25.5762 q^{73} +(-80.6460 + 46.5610i) q^{74} +(3.28086 - 5.68262i) q^{76} +(46.2593 + 26.7078i) q^{77} +(-40.9472 - 70.9226i) q^{79} -95.6307i q^{80} +69.2516 q^{82} +(24.9287 - 14.3926i) q^{83} +(-16.3325 + 28.2888i) q^{85} +(-105.574 - 60.9535i) q^{86} +(64.6847 + 112.037i) q^{88} +5.92931i q^{89} +68.4034 q^{91} +(-14.9304 + 8.62010i) q^{92} +(-31.7166 + 54.9348i) q^{94} +(-23.6898 - 13.6773i) q^{95} +(47.2441 + 81.8291i) q^{97} -15.9413i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 104 q^{10} - 36 q^{13} - 132 q^{16} + 24 q^{19} + 136 q^{22} + 108 q^{25} + 112 q^{28} + 28 q^{31} + 12 q^{34} - 8 q^{37} - 336 q^{40} + 152 q^{43} + 216 q^{46} - 56 q^{49} + 272 q^{52}+ \cdots + 364 q^{97}+O(q^{100}) $ 16 * q + 12 * q^4 - 104 * q^10 - 36 * q^13 - 132 * q^16 + 24 * q^19 + 136 * q^22 + 108 * q^25 + 112 * q^28 + 28 * q^31 + 12 * q^34 - 8 * q^37 - 336 * q^40 + 152 * q^43 + 216 * q^46 - 56 * q^49 + 272 * q^52 + 392 * q^55 + 220 * q^58 - 180 * q^61 - 1400 * q^64 + 132 * q^67 - 196 * q^70 + 544 * q^73 - 544 * q^76 - 316 * q^79 + 56 * q^82 + 228 * q^85 - 112 * q^91 + 348 * q^94 + 364 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.97223	+	1.13867i	−0.986115	+	0.569334i	−0.904111	−	0.427298i	$-0.859465\pi$
$2$	−1.97223	+	1.13867i	−0.986115	+	0.569334i	−0.0820040	+	0.996632i	$0.526132\pi$
$3$		0			0
$3$		0			0
$4$	0.593126	−	1.02732i	0.148281	−	0.256831i
$5$	−4.28273	−	2.47263i	−0.856546	−	0.494527i	0.00630821	−	0.999980i	$-0.497992\pi$
$5$	−4.28273	−	2.47263i	−0.856546	−	0.494527i	−0.862854	+	0.505453i	$0.831325\pi$
$6$		0			0
$7$	−1.32288	−	2.29129i	−0.188982	−	0.327327i
$7$	−1.32288	−	2.29129i	−0.188982	−	0.327327i
$8$		−	6.40785i		−	0.800981i
$9$		0			0
$10$	11.2620			1.12620
$11$	−17.4844	+	10.0946i	−1.58949	+	0.917691i	−0.596097	+	0.802913i	$0.703282\pi$
$11$	−17.4844	+	10.0946i	−1.58949	+	0.917691i	−0.993391	+	0.114778i	$0.963384\pi$
$12$		0			0
$13$	−12.9270	+	22.3903i	−0.994387	+	1.72233i	−0.405565	+	0.914066i	$0.632925\pi$
$13$	−12.9270	+	22.3903i	−0.994387	+	1.72233i	−0.588822	+	0.808263i	$0.700408\pi$
$14$	5.21803	+	3.01263i	0.372716	+	0.215188i
$15$		0			0
$16$	9.66891	+	16.7470i	0.604307	+	1.04669i
$17$		−	6.60531i		−	0.388548i	−0.980947	−	0.194274i	$-0.937765\pi$
$17$		−	6.60531i		−	0.388548i	0.980947	−	0.194274i	$-0.0622351\pi$
$18$		0			0
$19$	5.53147			0.291130			0.145565	−	0.989349i	$-0.453500\pi$
$19$	5.53147			0.291130			0.145565	+	0.989349i	$0.453500\pi$
$20$	−5.08040	+	2.93317i	−0.254020	+	0.146658i
$21$		0			0
$22$	22.9888	−	39.8177i	1.04494	−	1.80990i
$23$	−12.5862	−	7.26667i	−0.547228	−	0.315942i	0.200775	−	0.979637i	$-0.435654\pi$
$23$	−12.5862	−	7.26667i	−0.547228	−	0.315942i	−0.748003	+	0.663695i	$0.768987\pi$
$24$		0			0
$25$	−0.272153	−	0.471383i	−0.0108861	−	0.0188553i
$26$		−	58.8783i		−	2.26455i
$27$		0			0
$28$	−3.13853			−0.112090
$29$	15.1448	−	8.74386i	0.522235	−	0.301512i	−0.215614	−	0.976479i	$-0.569175\pi$
$29$	15.1448	−	8.74386i	0.522235	−	0.301512i	0.737848	+	0.674966i	$0.235842\pi$
$30$		0			0
$31$	22.6963	−	39.3111i	0.732138	−	1.26810i	−0.223829	−	0.974628i	$-0.571856\pi$
$31$	22.6963	−	39.3111i	0.732138	−	1.26810i	0.955968	−	0.293472i	$-0.0948109\pi$
$32$	−15.9412	−	9.20364i	−0.498162	−	0.287614i
$33$		0			0
$34$	7.52125	+	13.0272i	0.221213	+	0.383153i
$35$			13.0840i			0.373827i
$36$		0			0
$37$	40.8908			1.10516			0.552578	−	0.833461i	$-0.313644\pi$
$37$	40.8908			1.10516			0.552578	+	0.833461i	$0.313644\pi$
$38$	−10.9093	+	6.29851i	−0.287088	+	0.165750i
$39$		0			0
$40$	−15.8443	+	27.4431i	−0.396107	+	0.686077i
$41$	−26.3350	−	15.2045i	−0.642317	−	0.370842i	0.143189	−	0.989695i	$-0.454264\pi$
$41$	−26.3350	−	15.2045i	−0.642317	−	0.370842i	−0.785507	+	0.618853i	$0.787598\pi$
$42$		0			0
$43$	26.7653	+	46.3588i	0.622448	+	1.07811i	0.989028	+	0.147725i	$0.0471951\pi$
$43$	26.7653	+	46.3588i	0.622448	+	1.07811i	−0.366580	+	0.930386i	$0.619472\pi$
$44$			23.9495i			0.544306i
$45$		0			0
$46$	33.0973			0.719506
$47$	24.1224	−	13.9271i	0.513242	−	0.296321i	−0.220923	−	0.975291i	$-0.570907\pi$
$47$	24.1224	−	13.9271i	0.513242	−	0.296321i	0.734165	+	0.678971i	$0.237574\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.0714286	+	0.123718i
$50$	1.07350	+	0.619784i	0.0214700	+	0.0123957i
$51$		0			0
$52$	15.3347	+	26.5605i	0.294898	+	0.510779i
$53$		−	6.45594i		−	0.121810i	−0.998144	−	0.0609051i	$-0.980601\pi$
$53$		−	6.45594i		−	0.121810i	0.998144	−	0.0609051i	$-0.0193987\pi$
$54$		0			0
$55$	99.8411			1.81529
$56$	−14.6822	+	8.47678i	−0.262182	+	0.151371i
$57$		0			0
$58$	−19.9127	+	34.4898i	−0.343322	+	0.594651i
$59$	37.0702	+	21.4025i	0.628308	+	0.362754i	0.780097	−	0.625659i	$-0.215170\pi$
$59$	37.0702	+	21.4025i	0.628308	+	0.362754i	−0.151788	+	0.988413i	$0.548503\pi$
$60$		0			0
$61$	−17.7990	−	30.8288i	−0.291787	−	0.505390i	0.682445	−	0.730937i	$-0.260917\pi$
$61$	−17.7990	−	30.8288i	−0.291787	−	0.505390i	−0.974232	+	0.225547i	$0.927583\pi$
$62$			103.374i			1.66732i
$63$		0			0
$64$	−35.4317			−0.553621
$65$	110.726	−	63.9277i	1.70348	−	0.983502i
$66$		0			0
$67$	41.8654	−	72.5131i	0.624857	−	1.08228i	−0.363711	−	0.931512i	$-0.618491\pi$
$67$	41.8654	−	72.5131i	0.624857	−	1.08228i	0.988568	−	0.150773i	$-0.0481761\pi$
$68$	−6.78580	−	3.91778i	−0.0997911	−	0.0576144i
$69$		0			0
$70$	−14.8983	−	25.8046i	−0.212832	−	0.368637i
$71$			113.821i			1.60311i	0.597923	+	0.801554i	$0.295993\pi$
$71$			113.821i			1.60311i	−0.597923	+	0.801554i	$0.704007\pi$
$72$		0			0
$73$	−25.5762			−0.350358			−0.175179	−	0.984537i	$-0.556050\pi$
$73$	−25.5762			−0.350358			−0.175179	+	0.984537i	$0.556050\pi$
$74$	−80.6460	+	46.5610i	−1.08981	+	0.629202i
$75$		0			0
$76$	3.28086	−	5.68262i	0.0431692	−	0.0747713i
$77$	46.2593	+	26.7078i	0.600770	+	0.346855i
$78$		0			0
$79$	−40.9472	−	70.9226i	−0.518319	−	0.897755i	−0.999773	−	0.0212836i	$-0.993225\pi$
$79$	−40.9472	−	70.9226i	−0.518319	−	0.897755i	0.481455	−	0.876471i	$-0.340109\pi$
$80$		−	95.6307i		−	1.19538i
$81$		0			0
$82$	69.2516			0.844532
$83$	24.9287	−	14.3926i	0.300346	−	0.173405i	−0.342252	−	0.939608i	$-0.611190\pi$
$83$	24.9287	−	14.3926i	0.300346	−	0.173405i	0.642598	+	0.766203i	$0.277856\pi$
$84$		0			0
$85$	−16.3325	+	28.2888i	−0.192147	+	0.332809i
$86$	−105.574	−	60.9535i	−1.22761	−	0.708761i
$87$		0			0
$88$	64.6847	+	112.037i	0.735053	+	1.27315i
$89$			5.92931i			0.0666214i	0.999445	+	0.0333107i	$0.0106051\pi$
$89$			5.92931i			0.0666214i	−0.999445	+	0.0333107i	$0.989395\pi$
$90$		0			0
$91$	68.4034			0.751686
$92$	−14.9304	+	8.62010i	−0.162287	+	0.0936967i
$93$		0			0
$94$	−31.7166	+	54.9348i	−0.337411	+	0.584412i
$95$	−23.6898	−	13.6773i	−0.249366	−	0.143972i
$96$		0			0
$97$	47.2441	+	81.8291i	0.487052	+	0.843599i	0.999889	−	0.0148868i	$-0.00473880\pi$
$97$	47.2441	+	81.8291i	0.487052	+	0.843599i	−0.512837	+	0.858486i	$0.671405\pi$
$98$		−	15.9413i		−	0.162667i
$99$		0			0
$100$	−0.645685			−0.00645685
$101$	106.566	−	61.5259i	1.05511	−	0.609168i	0.131034	−	0.991378i	$-0.458170\pi$
$101$	106.566	−	61.5259i	1.05511	−	0.609168i	0.924075	+	0.382210i	$0.124837\pi$
$102$		0			0
$103$	20.7877	−	36.0054i	0.201823	−	0.349567i	−0.747293	−	0.664495i	$-0.768647\pi$
$103$	20.7877	−	36.0054i	0.201823	−	0.349567i	0.949116	+	0.314927i	$0.101980\pi$
$104$	143.473	+	82.8344i	1.37955	+	0.796485i
$105$		0			0
$106$	7.35117	+	12.7326i	0.0693506	+	0.120119i
$107$		−	2.53060i		−	0.0236505i	−0.999930	−	0.0118252i	$-0.996236\pi$
$107$		−	2.53060i		−	0.0236505i	0.999930	−	0.0118252i	$-0.00376418\pi$
$108$		0			0
$109$	−27.9757			−0.256658			−0.128329	−	0.991732i	$-0.540961\pi$
$109$	−27.9757			−0.256658			−0.128329	+	0.991732i	$0.540961\pi$
$110$	−196.909	+	113.686i	−1.79009	+	1.03351i
$111$		0			0
$112$	25.5815	−	44.3085i	0.228406	−	0.395612i
$113$	158.923	+	91.7543i	1.40640	+	0.811985i	0.995039	−	0.0994877i	$-0.0317204\pi$
$113$	158.923	+	91.7543i	1.40640	+	0.811985i	0.411361	+	0.911473i	$0.365054\pi$
$114$		0			0
$115$	35.9356	+	62.2424i	0.312484	+	0.541238i
$116$		−	20.7448i		−	0.178835i
$117$		0			0
$118$	−97.4812			−0.826112
$119$	−15.1347	+	8.73801i	−0.127182	+	0.0734286i
$120$		0			0
$121$	143.302	−	248.206i	1.18431	−	2.05129i
$122$	70.2075	+	40.5343i	0.575471	+	0.332248i
$123$		0			0
$124$	−26.9235	−	46.6329i	−0.217125	−	0.376072i
$125$			126.323i			1.01059i
$126$		0			0
$127$	−117.574			−0.925780			−0.462890	−	0.886416i	$-0.653187\pi$
$127$	−117.574			−0.925780			−0.462890	+	0.886416i	$0.653187\pi$
$128$	133.644	−	77.1595i	1.04410	−	0.602809i
$129$		0			0
$130$	−145.585	+	252.160i	−1.11988	+	1.93969i
$131$	151.938	+	87.7212i	1.15983	+	0.669628i	0.951263	−	0.308380i	$-0.0997870\pi$
$131$	151.938	+	87.7212i	1.15983	+	0.669628i	0.208566	+	0.978008i	$0.433120\pi$
$132$		0			0
$133$	−7.31745	−	12.6742i	−0.0550184	−	0.0952947i
$134$			190.683i			1.42301i
$135$		0			0
$136$	−42.3258			−0.311219
$137$	3.22760	−	1.86346i	0.0235591	−	0.0136019i	−0.488174	−	0.872746i	$-0.662337\pi$
$137$	3.22760	−	1.86346i	0.0235591	−	0.0136019i	0.511733	+	0.859144i	$0.329004\pi$
$138$		0			0
$139$	−59.2250	+	102.581i	−0.426079	+	0.737991i	−0.996521	−	0.0833473i	$-0.973439\pi$
$139$	−59.2250	+	102.581i	−0.426079	+	0.737991i	0.570441	+	0.821338i	$0.306772\pi$
$140$	13.4415	+	7.76043i	0.0960104	+	0.0554317i
$141$		0			0
$142$	−129.604	−	224.480i	−0.912703	−	1.58085i
$143$		−	521.973i		−	3.65016i
$144$		0			0
$145$	−86.4815			−0.596424
$146$	50.4421	−	29.1227i	0.345494	−	0.199471i
$147$		0			0
$148$	24.2534	−	42.0081i	0.163874	−	0.283838i
$149$	−180.280	−	104.085i	−1.20993	−	0.698555i	−0.247188	−	0.968967i	$-0.579507\pi$
$149$	−180.280	−	104.085i	−1.20993	−	0.698555i	−0.962745	+	0.270412i	$0.912840\pi$
$150$		0			0
$151$	−38.8879	−	67.3558i	−0.257536	−	0.446065i	0.708046	−	0.706167i	$-0.249577\pi$
$151$	−38.8879	−	67.3558i	−0.257536	−	0.446065i	−0.965581	+	0.260102i	$0.916244\pi$
$152$		−	35.4448i		−	0.233190i
$153$		0			0
$154$	−121.645			−0.789904
$155$	−194.404	+	112.239i	−1.25422	+	0.724124i
$156$		0			0
$157$	−56.8433	+	98.4554i	−0.362059	+	0.627105i	−0.988300	−	0.152525i	$-0.951259\pi$
$157$	−56.8433	+	98.4554i	−0.362059	+	0.627105i	0.626241	+	0.779630i	$0.284593\pi$
$158$	161.515	+	93.2504i	1.02224	+	0.590193i
$159$		0			0
$160$	45.5145	+	78.8334i	0.284466	+	0.492709i
$161$			38.4516i			0.238830i
$162$		0			0
$163$	−143.154			−0.878243			−0.439122	−	0.898428i	$-0.644710\pi$
$163$	−143.154			−0.878243			−0.439122	+	0.898428i	$0.644710\pi$
$164$	−31.2400	+	18.0364i	−0.190488	+	0.109978i
$165$		0			0
$166$	−32.7768	+	56.7711i	−0.197451	+	0.341994i
$167$	−180.737	−	104.348i	−1.08226	−	0.624841i	−0.150752	−	0.988572i	$-0.548170\pi$
$167$	−180.737	−	104.348i	−1.08226	−	0.624841i	−0.931504	+	0.363731i	$0.881503\pi$
$168$		0			0
$169$	−249.716	−	432.521i	−1.47761	−	2.55930i
$170$		−	74.3892i		−	0.437584i
$171$		0			0
$172$	63.5007			0.369190
$173$	143.220	−	82.6880i	0.827860	−	0.477965i	−0.0252595	−	0.999681i	$-0.508041\pi$
$173$	143.220	−	82.6880i	0.827860	−	0.477965i	0.853119	+	0.521716i	$0.174708\pi$
$174$		0			0
$175$	−0.720050	+	1.24716i	−0.00411457	+	0.00712665i
$176$	−338.109	−	195.208i	−1.92108	−	1.10913i
$177$		0			0
$178$	−6.75151	−	11.6940i	−0.0379298	−	0.0656964i
$179$		−	6.53386i		−	0.0365020i	−0.999833	−	0.0182510i	$-0.994190\pi$
$179$		−	6.53386i		−	0.0365020i	0.999833	−	0.0182510i	$-0.00580980\pi$
$180$		0			0
$181$	47.6268			0.263132			0.131566	−	0.991307i	$-0.458000\pi$
$181$	47.6268			0.263132			0.131566	+	0.991307i	$0.458000\pi$
$182$	−134.907	+	77.8887i	−0.741249	+	0.427960i
$183$		0			0
$184$	−46.5637	+	80.6507i	−0.253064	+	0.438319i
$185$	−175.124	−	101.108i	−0.946617	−	0.546530i
$186$		0			0
$187$	66.6780	+	115.490i	0.356567	+	0.617592i
$188$		−	33.0420i		−	0.175755i
$189$		0			0
$190$	62.2956			0.327872
$191$	−51.7640	+	29.8860i	−0.271016	+	0.156471i	−0.629349	−	0.777123i	$-0.716678\pi$
$191$	−51.7640	+	29.8860i	−0.271016	+	0.156471i	0.358333	+	0.933594i	$0.383345\pi$
$192$		0			0
$193$	89.2701	−	154.620i	0.462540	−	0.801142i	−0.536547	−	0.843870i	$-0.680272\pi$
$193$	89.2701	−	154.620i	0.462540	−	0.801142i	0.999087	+	0.0427283i	$0.0136050\pi$
$194$	−186.352	−	107.591i	−0.960579	−	0.554590i
$195$		0			0
$196$	4.15188	+	7.19127i	0.0211831	+	0.0366901i
$197$			69.0446i			0.350480i	0.984526	+	0.175240i	$0.0560702\pi$
$197$			69.0446i			0.350480i	−0.984526	+	0.175240i	$0.943930\pi$
$198$		0			0
$199$	360.982			1.81398			0.906989	−	0.421155i	$-0.138375\pi$
$199$	360.982			1.81398			0.906989	+	0.421155i	$0.138375\pi$
$200$	−3.02055	+	1.74392i	−0.0151028	+	0.00871958i
$201$		0			0
$202$	−140.115	+	242.686i	−0.693639	+	1.20142i
$203$	−40.0694	−	23.1341i	−0.197386	−	0.113961i
$204$		0			0
$205$	75.1905	+	130.234i	0.366783	+	0.635287i
$206$			94.6813i			0.459618i
$207$		0			0
$208$	−499.961			−2.40366
$209$	−96.7143	+	55.8380i	−0.462748	+	0.267168i
$210$		0			0
$211$	22.5253	−	39.0150i	0.106755	−	0.184905i	−0.807699	−	0.589595i	$-0.799287\pi$
$211$	22.5253	−	39.0150i	0.106755	−	0.184905i	0.914454	+	0.404690i	$0.132621\pi$
$212$	−6.63234	−	3.82919i	−0.0312846	−	0.0180622i
$213$		0			0
$214$	2.88151	+	4.99092i	0.0134650	+	0.0233221i
$215$		−	264.723i		−	1.23127i
$216$		0			0
$217$	−120.097			−0.553445
$218$	55.1746	−	31.8551i	0.253094	−	0.146124i
$219$		0			0
$220$	59.2183	−	102.569i	0.269174	−	0.466223i
$221$	147.895	+	85.3871i	0.669207	+	0.386367i
$222$		0			0
$223$	92.9027	+	160.912i	0.416604	+	0.721580i	0.995595	−	0.0937541i	$-0.0298868\pi$
$223$	92.9027	+	160.912i	0.416604	+	0.721580i	−0.578991	+	0.815334i	$0.696553\pi$
$224$			48.7011i			0.217416i
$225$		0			0
$226$	−417.910			−1.84916
$227$	172.374	−	99.5199i	0.759355	−	0.438414i	−0.0697092	−	0.997567i	$-0.522207\pi$
$227$	172.374	−	99.5199i	0.759355	−	0.438414i	0.829064	+	0.559154i	$0.188874\pi$
$228$		0			0
$229$	160.618	−	278.199i	0.701389	−	1.21484i	−0.266590	−	0.963810i	$-0.585897\pi$
$229$	160.618	−	278.199i	0.701389	−	1.21484i	0.967979	−	0.251031i	$-0.0807696\pi$
$230$	−141.747	−	81.8375i	−0.616290	−	0.355815i
$231$		0			0
$232$	−56.0293	−	97.0456i	−0.241506	−	0.418300i
$233$			215.361i			0.924295i	0.886803	+	0.462147i	$0.152921\pi$
$233$			215.361i			0.924295i	−0.886803	+	0.462147i	$0.847079\pi$
$234$		0			0
$235$	−137.746			−0.586154
$236$	43.9746	−	25.3887i	0.186333	−	0.107579i
$237$		0			0
$238$	19.8994	−	34.4667i	0.0836108	−	0.144818i
$239$	143.166	+	82.6571i	0.599022	+	0.345846i	0.768657	−	0.639661i	$-0.220925\pi$
$239$	143.166	+	82.6571i	0.599022	+	0.345846i	−0.169635	+	0.985507i	$0.554259\pi$
$240$		0			0
$241$	−125.668	−	217.663i	−0.521443	−	0.903167i	−0.999689	−	0.0249403i	$-0.992060\pi$
$241$	−125.668	−	217.663i	−0.521443	−	0.903167i	0.478246	−	0.878226i	$-0.341273\pi$
$242$			652.693i			2.69708i
$243$		0			0
$244$	−42.2282			−0.173066
$245$	29.9791	−	17.3084i	0.122364	−	0.0706467i
$246$		0			0
$247$	−71.5055	+	123.851i	−0.289496	+	0.501422i
$248$	−251.900	−	145.434i	−1.01572	−	0.586429i
$249$		0			0
$250$	−143.840	−	249.139i	−0.575362	−	0.996556i
$251$			10.7301i			0.0427496i	0.999772	+	0.0213748i	$0.00680432\pi$
$251$			10.7301i			0.0427496i	−0.999772	+	0.0213748i	$0.993196\pi$
$252$		0			0
$253$	293.417			1.15975
$254$	231.883	−	133.878i	0.912925	−	0.527077i
$255$		0			0
$256$	−104.855	+	181.613i	−0.409588	+	0.709427i
$257$	29.7665	+	17.1857i	0.115823	+	0.0668703i	0.556792	−	0.830652i	$-0.312032\pi$
$257$	29.7665	+	17.1857i	0.115823	+	0.0668703i	−0.440969	+	0.897522i	$0.645365\pi$
$258$		0			0
$259$	−54.0934	−	93.6925i	−0.208855	−	0.361747i
$260$		−	151.669i		−	0.583341i
$261$		0			0
$262$	−399.541			−1.52497
$263$	−379.977	+	219.380i	−1.44478	+	0.834144i	−0.998163	−	0.0605810i	$-0.980705\pi$
$263$	−379.977	+	219.380i	−1.44478	+	0.834144i	−0.446617	+	0.894725i	$0.647371\pi$
$264$		0			0
$265$	−15.9632	+	27.6490i	−0.0602384	+	0.104336i
$266$	28.8634	+	16.6643i	0.108509	+	0.0626477i
$267$		0			0
$268$	−49.6629	−	86.0187i	−0.185309	−	0.320965i
$269$		−	244.971i		−	0.910673i	−0.890320	−	0.455336i	$-0.849519\pi$
$269$		−	244.971i		−	0.910673i	0.890320	−	0.455336i	$-0.150481\pi$
$270$		0			0
$271$	162.048			0.597962			0.298981	−	0.954259i	$-0.403353\pi$
$271$	162.048			0.597962			0.298981	+	0.954259i	$0.403353\pi$
$272$	110.619	−	63.8662i	0.406689	−	0.234802i
$273$		0			0
$274$	−4.24371	+	7.35033i	−0.0154880	+	0.0268260i
$275$	9.51686	+	5.49456i	0.0346068	+	0.0199802i
$276$		0			0
$277$	141.395	+	244.904i	0.510453	+	0.884130i	0.999927	+	0.0121124i	$0.00385560\pi$
$277$	141.395	+	244.904i	0.510453	+	0.884130i	−0.489474	+	0.872018i	$0.662811\pi$
$278$		−	269.750i		−	0.970325i
$279$		0			0
$280$	83.8400			0.299428
$281$	−59.0908	+	34.1161i	−0.210288	+	0.121410i	−0.601445	−	0.798914i	$-0.705408\pi$
$281$	−59.0908	+	34.1161i	−0.210288	+	0.121410i	0.391157	+	0.920324i	$0.372075\pi$
$282$		0			0
$283$	−97.3528	+	168.620i	−0.344003	+	0.595830i	−0.985172	−	0.171569i	$-0.945116\pi$
$283$	−97.3528	+	168.620i	−0.344003	+	0.595830i	0.641169	+	0.767399i	$0.278450\pi$
$284$	116.931	+	67.5100i	0.411728	+	0.237711i
$285$		0			0
$286$	594.354	+	1029.45i	2.07816	+	3.59948i
$287$			80.4548i			0.280330i
$288$		0			0
$289$	245.370			0.849031
$290$	170.561	−	98.4736i	0.588142	−	0.339564i
$291$		0			0
$292$	−15.1699	+	26.2750i	−0.0519517	+	0.0899829i
$293$	201.850	+	116.538i	0.688908	+	0.397741i	0.803203	−	0.595706i	$-0.203128\pi$
$293$	201.850	+	116.538i	0.688908	+	0.397741i	−0.114295	+	0.993447i	$0.536461\pi$
$294$		0			0
$295$	−105.841	−	183.322i	−0.358783	−	0.621431i
$296$		−	262.022i		−	0.885209i
$297$		0			0
$298$	474.071			1.59084
$299$	325.405	−	187.873i	1.08831	−	0.628338i
$300$		0			0
$301$	70.8142	−	122.654i	0.235263	−	0.407488i
$302$	153.392	+	88.5607i	0.507919	+	0.293247i
$303$		0			0
$304$	53.4833	+	92.6358i	0.175932	+	0.304723i
$305$			176.042i			0.577186i
$306$		0			0
$307$	167.051			0.544140			0.272070	−	0.962277i	$-0.412292\pi$
$307$	167.051			0.544140			0.272070	+	0.962277i	$0.412292\pi$
$308$	54.8752	−	31.6822i	0.178166	−	0.102864i
$309$		0			0
$310$	255.606	−	442.723i	0.824537	−	1.42814i
$311$	168.657	+	97.3739i	0.542304	+	0.313099i	0.746012	−	0.665932i	$-0.231966\pi$
$311$	168.657	+	97.3739i	0.542304	+	0.313099i	−0.203708	+	0.979032i	$0.565299\pi$
$312$		0			0
$313$	−164.148	−	284.313i	−0.524436	−	0.908349i	−0.999595	−	0.0284496i	$-0.990943\pi$
$313$	−164.148	−	284.313i	−0.524436	−	0.908349i	0.475160	−	0.879900i	$-0.342390\pi$
$314$		−	258.902i		−	0.824529i
$315$		0			0
$316$	−97.1474			−0.307428
$317$	−377.387	+	217.885i	−1.19050	+	0.687333i	−0.958419	−	0.285364i	$-0.907885\pi$
$317$	−377.387	+	217.885i	−1.19050	+	0.687333i	−0.232077	+	0.972697i	$0.574552\pi$
$318$		0			0
$319$	−176.532	+	305.762i	−0.553390	+	0.958500i
$320$	151.744	+	87.6097i	0.474201	+	0.273780i
$321$		0			0
$322$	−43.7836	−	75.8354i	−0.135974	−	0.235514i
$323$		−	36.5371i		−	0.113118i
$324$		0			0
$325$	14.0725			0.0433001
$326$	282.332	−	163.004i	0.866049	−	0.500013i
$327$		0			0
$328$	−97.4283	+	168.751i	−0.297037	+	0.514484i
$329$	−63.8219	−	36.8476i	−0.193987	−	0.111999i
$330$		0			0
$331$	−220.590	−	382.073i	−0.666436	−	1.15430i	−0.978894	−	0.204369i	$-0.934486\pi$
$331$	−220.590	−	382.073i	−0.666436	−	1.15430i	0.312458	−	0.949931i	$-0.398848\pi$
$332$		−	34.1465i		−	0.102851i
$333$		0			0
$334$	475.273			1.42297
$335$	−358.597	+	207.036i	−1.07044	+	0.618017i
$336$		0			0
$337$	113.496	−	196.580i	0.336782	−	0.583324i	−0.647043	−	0.762453i	$-0.723995\pi$
$337$	113.496	−	196.580i	0.336782	−	0.583324i	0.983826	+	0.179129i	$0.0573281\pi$
$338$	984.996	+	568.688i	2.91419	+	1.68251i
$339$		0			0
$340$	19.3745	+	33.5576i	0.0569838	+	0.0986988i
$341$			916.440i			2.68751i
$342$		0			0
$343$	18.5203			0.0539949
$344$	297.060	−	171.508i	0.863547	−	0.498569i
$345$		0			0
$346$	−188.308	+	326.159i	−0.544243	+	0.942657i
$347$	110.590	+	63.8489i	0.318702	+	0.184003i	0.650814	−	0.759237i	$-0.274428\pi$
$347$	110.590	+	63.8489i	0.318702	+	0.184003i	−0.332112	+	0.943240i	$0.607761\pi$
$348$		0			0
$349$	−34.2505	−	59.3236i	−0.0981390	−	0.169982i	0.812775	−	0.582577i	$-0.197956\pi$
$349$	−34.2505	−	59.3236i	−0.0981390	−	0.169982i	−0.910914	+	0.412595i	$0.864622\pi$
$350$		−	3.27959i		−	0.00937026i
$351$		0			0
$352$	371.628			1.05576
$353$	−377.699	+	218.065i	−1.06997	+	0.617747i	−0.928173	−	0.372149i	$-0.878621\pi$
$353$	−377.699	+	218.065i	−1.06997	+	0.617747i	−0.141796	+	0.989896i	$0.545288\pi$
$354$		0			0
$355$	281.437	−	487.463i	0.792780	−	1.37313i
$356$	6.09132	+	3.51682i	0.0171104	+	0.00987872i
$357$		0			0
$358$	7.43990	+	12.8863i	0.0207818	+	0.0359952i
$359$		−	557.516i		−	1.55297i	−0.630136	−	0.776485i	$-0.717001\pi$
$359$		−	557.516i		−	1.55297i	0.630136	−	0.776485i	$-0.282999\pi$
$360$		0			0
$361$	−330.403			−0.915243
$362$	−93.9310	+	54.2311i	−0.259478	+	0.149810i
$363$		0			0
$364$	40.5718	−	70.2725i	0.111461	−	0.193056i
$365$	109.536	+	63.2405i	0.300098	+	0.173262i
$366$		0			0
$367$	270.223	+	468.040i	0.736302	+	1.27531i	0.954150	+	0.299330i	$0.0967630\pi$
$367$	270.223	+	468.040i	0.736302	+	1.27531i	−0.217848	+	0.975983i	$0.569904\pi$
$368$		−	281.043i		−	0.763704i
$369$		0			0
$370$	460.513			1.24463
$371$	−14.7924	+	8.54041i	−0.0398717	+	0.0230200i
$372$		0			0
$373$	65.2390	−	112.997i	0.174903	−	0.302942i	−0.765224	−	0.643764i	$-0.777372\pi$
$373$	65.2390	−	112.997i	0.174903	−	0.302942i	0.940128	+	0.340822i	$0.110705\pi$
$374$	−263.009	−	151.848i	−0.703232	−	0.406011i
$375$		0			0
$376$	−89.2425	−	154.573i	−0.237347	−	0.411097i
$377$			452.128i			1.19928i
$378$		0			0
$379$	−345.177			−0.910757			−0.455379	−	0.890298i	$-0.650496\pi$
$379$	−345.177			−0.910757			−0.455379	+	0.890298i	$0.650496\pi$
$380$	−28.1021	+	16.2247i	−0.0739528	+	0.0426967i
$381$		0			0
$382$	68.0603	−	117.884i	0.178168	−	0.308597i
$383$	91.3895	+	52.7638i	0.238615	+	0.137764i	0.614540	−	0.788886i	$-0.289342\pi$
$383$	91.3895	+	52.7638i	0.238615	+	0.137764i	−0.375925	+	0.926650i	$0.622675\pi$
$384$		0			0
$385$	−132.077	−	228.765i	−0.343058	−	0.594194i
$386$			406.596i			1.05336i
$387$		0			0
$388$	112.087			0.288883
$389$	431.810	−	249.306i	1.11005	−	0.640889i	0.171209	−	0.985235i	$-0.445233\pi$
$389$	431.810	−	249.306i	1.11005	−	0.640889i	0.938843	+	0.344346i	$0.111899\pi$
$390$		0			0
$391$	−47.9986	+	83.1360i	−0.122759	+	0.212624i
$392$	38.8455	+	22.4275i	0.0990957	+	0.0572129i
$393$		0			0
$394$	−78.6188	−	136.172i	−0.199540	−	0.345614i
$395$			404.990i			1.02529i
$396$		0			0
$397$	119.497			0.301000			0.150500	−	0.988610i	$-0.451912\pi$
$397$	119.497			0.301000			0.150500	+	0.988610i	$0.451912\pi$
$398$	−711.938	+	411.038i	−1.78879	+	1.03276i
$399$		0			0
$400$	5.26285	−	9.11553i	0.0131571	−	0.0227888i
$401$	−521.622	−	301.159i	−1.30080	−	0.751019i	−0.320262	−	0.947329i	$-0.603771\pi$
$401$	−521.622	−	301.159i	−1.30080	−	0.751019i	−0.980542	+	0.196310i	$0.937104\pi$
$402$		0			0
$403$	586.791	+	1016.35i	1.45606	+	2.52197i
$404$		−	145.970i		−	0.361313i
$405$		0			0
$406$	105.368			0.259527
$407$	−714.949	+	412.776i	−1.75663	+	1.01419i
$408$		0			0
$409$	191.094	−	330.985i	0.467224	−	0.809255i	−0.532075	−	0.846697i	$-0.678588\pi$
$409$	191.094	−	330.985i	0.467224	−	0.809255i	0.999299	+	0.0374420i	$0.0119210\pi$
$410$	−296.586	−	171.234i	−0.723380	−	0.417644i
$411$		0			0
$412$	−24.6595	−	42.7115i	−0.0598532	−	0.103669i
$413$		−	113.251i		−	0.274216i
$414$		0			0
$415$	−142.351			−0.343014
$416$	412.144	−	237.952i	0.990731	−	0.571999i
$417$		0			0
$418$	127.162	−	220.251i	0.304215	−	0.526916i
$419$	−88.0354	−	50.8273i	−0.210108	−	0.121306i	0.391253	−	0.920283i	$-0.372042\pi$
$419$	−88.0354	−	50.8273i	−0.210108	−	0.121306i	−0.601362	+	0.798977i	$0.705375\pi$
$420$		0			0
$421$	212.986	+	368.903i	0.505905	+	0.876254i	0.999977	+	0.00683251i	$0.00217487\pi$
$421$	212.986	+	368.903i	0.505905	+	0.876254i	−0.494071	+	0.869421i	$0.664492\pi$
$422$			102.595i			0.243117i
$423$		0			0
$424$	−41.3687			−0.0975676
$425$	−3.11364	+	1.79766i	−0.00732620	+	0.00422978i
$426$		0			0
$427$	−47.0918	+	81.5653i	−0.110285	+	0.191019i
$428$	−2.59975	−	1.50096i	−0.00607418	−	0.00350693i
$429$		0			0
$430$	301.431	+	522.094i	0.701003	+	1.21417i
$431$		−	256.315i		−	0.594698i	−0.954769	−	0.297349i	$-0.903898\pi$
$431$		−	256.315i		−	0.594698i	0.954769	−	0.297349i	$-0.0961025\pi$
$432$		0			0
$433$	487.980			1.12697			0.563487	−	0.826125i	$-0.309460\pi$
$433$	487.980			1.12697			0.563487	+	0.826125i	$0.309460\pi$
$434$	236.860	−	136.751i	0.545760	−	0.315095i
$435$		0			0
$436$	−16.5931	+	28.7402i	−0.0380577	+	0.0659178i
$437$	−69.6205	−	40.1954i	−0.159315	−	0.0919803i
$438$		0			0
$439$	176.661	+	305.985i	0.402416	+	0.697006i	0.994017	−	0.109226i	$-0.0348371\pi$
$439$	176.661	+	305.985i	0.402416	+	0.697006i	−0.591601	+	0.806231i	$0.701504\pi$
$440$		−	639.766i		−	1.45401i
$441$		0			0
$442$	−388.910			−0.879887
$443$	−12.5628	+	7.25313i	−0.0283584	+	0.0163728i	−0.514112	−	0.857723i	$-0.671879\pi$
$443$	−12.5628	+	7.25313i	−0.0283584	+	0.0163728i	0.485754	+	0.874096i	$0.338545\pi$
$444$		0			0
$445$	14.6610	−	25.3936i	0.0329461	−	0.0570643i
$446$	−366.451	−	211.571i	−0.821639	−	0.474374i
$447$		0			0
$448$	46.8717	+	81.1843i	0.104624	+	0.181215i
$449$		−	848.396i		−	1.88952i	−0.327759	−	0.944761i	$-0.606293\pi$
$449$		−	848.396i		−	1.88952i	0.327759	−	0.944761i	$-0.393707\pi$
$450$		0			0
$451$	613.935			1.36127
$452$	188.523	−	108.844i	0.417086	−	0.240805i
$453$		0			0
$454$	−226.640	+	392.552i	−0.499207	+	0.864652i
$455$	−292.953	−	169.137i	−0.643854	−	0.371729i
$456$		0			0
$457$	−82.8418	−	143.486i	−0.181273	−	0.313974i	0.761041	−	0.648703i	$-0.224688\pi$
$457$	−82.8418	−	143.486i	−0.181273	−	0.313974i	−0.942314	+	0.334729i	$0.891355\pi$
$458$			731.562i			1.59730i
$459$		0			0
$460$	85.2574			0.185342
$461$	680.019	−	392.609i	1.47509	−	0.851646i	0.475489	−	0.879722i	$-0.342271\pi$
$461$	680.019	−	392.609i	1.47509	−	0.851646i	0.999606	+	0.0280756i	$0.00893792\pi$
$462$		0			0
$463$	287.505	−	497.973i	0.620960	−	1.07553i	−0.368347	−	0.929688i	$-0.620076\pi$
$463$	287.505	−	497.973i	0.620960	−	1.07553i	0.989307	−	0.145847i	$-0.0465906\pi$
$464$	292.867	+	169.087i	0.631180	+	0.364412i
$465$		0			0
$466$	−245.224	−	424.741i	−0.526232	−	0.911460i
$467$			773.867i			1.65710i	0.559913	+	0.828551i	$0.310834\pi$
$467$			773.867i			1.65710i	−0.559913	+	0.828551i	$0.689166\pi$
$468$		0			0
$469$	−221.531			−0.472348
$470$	271.667	−	156.847i	0.578015	−	0.333717i
$471$		0			0
$472$	137.144	−	237.540i	0.290559	−	0.503263i
$473$	−935.947	−	540.369i	−1.97875	−	1.14243i
$474$		0			0
$475$	−1.50541	−	2.60745i	−0.00316928	−	0.00548936i
$476$			20.7310i			0.0435524i
$477$		0			0
$478$	−376.476			−0.787606
$479$	424.238	−	244.934i	0.885675	−	0.511345i	0.0131497	−	0.999914i	$-0.495814\pi$
$479$	424.238	−	244.934i	0.885675	−	0.511345i	0.872525	+	0.488569i	$0.162481\pi$
$480$		0			0
$481$	−528.596	+	915.556i	−1.09895	+	1.90344i
$482$	495.692	+	286.188i	1.02841	+	0.593751i
$483$		0			0
$484$	−169.992	−	294.435i	−0.351224	−	0.608337i
$485$		−	467.269i		−	0.963442i
$486$		0			0
$487$	750.641			1.54136			0.770678	−	0.637224i	$-0.219918\pi$
$487$	750.641			1.54136			0.770678	+	0.637224i	$0.219918\pi$
$488$	−197.546	+	114.053i	−0.404808	+	0.233716i
$489$		0			0
$490$	−39.4171	+	68.2724i	−0.0804431	+	0.139332i
$491$	133.877	+	77.2939i	0.272662	+	0.157421i	0.630097	−	0.776517i	$-0.283015\pi$
$491$	133.877	+	77.2939i	0.272662	+	0.157421i	−0.357435	+	0.933938i	$0.616349\pi$
$492$		0			0
$493$	−57.7559	−	100.036i	−0.117152	−	0.202913i
$494$		−	325.684i		−	0.659279i
$495$		0			0
$496$	877.793			1.76974
$497$	260.796	−	150.571i	0.524740	−	0.302959i
$498$		0			0
$499$	72.2235	−	125.095i	0.144736	−	0.250691i	−0.784538	−	0.620081i	$-0.787100\pi$
$499$	72.2235	−	125.095i	0.144736	−	0.250691i	0.929275	+	0.369390i	$0.120433\pi$
$500$	129.775	+	74.9257i	0.259550	+	0.149851i
$501$		0			0
$502$	−12.2181	−	21.1623i	−0.0243388	−	0.0421560i
$503$			110.317i			0.219318i	0.993969	+	0.109659i	$0.0349760\pi$
$503$			110.317i			0.219318i	−0.993969	+	0.109659i	$0.965024\pi$
$504$		0			0
$505$	−608.525			−1.20500
$506$	−578.685	+	334.104i	−1.14365	+	0.660284i
$507$		0			0
$508$	−69.7362	+	120.787i	−0.137276	+	0.237769i
$509$	−406.577	−	234.737i	−0.798776	−	0.461173i	0.0442671	−	0.999020i	$-0.485905\pi$
$509$	−406.577	−	234.737i	−0.798776	−	0.461173i	−0.843043	+	0.537846i	$0.819238\pi$
$510$		0			0
$511$	33.8341	+	58.6024i	0.0662115	+	0.114682i
$512$			139.698i			0.272848i
$513$		0			0
$514$	−78.2750			−0.152286
$515$	−178.057	+	102.801i	−0.345741	+	0.199614i
$516$		0			0
$517$	−281.177	+	487.012i	−0.543862	+	0.941996i
$518$	213.369	+	123.189i	0.411910	+	0.237816i
$519$		0			0
$520$	−409.639	−	709.515i	−0.787767	−	1.36445i
$521$			470.639i			0.903338i	0.892186	+	0.451669i	$0.149171\pi$
$521$			470.639i			0.903338i	−0.892186	+	0.451669i	$0.850829\pi$
$522$		0			0
$523$	13.5759			0.0259577			0.0129788	−	0.999916i	$-0.495869\pi$
$523$	13.5759			0.0259577			0.0129788	+	0.999916i	$0.495869\pi$
$524$	180.236	−	104.059i	0.343962	−	0.198587i
$525$		0			0
$526$	499.601	−	865.335i	0.949813	−	1.64512i
$527$	−259.662	−	149.916i	−0.492718	−	0.284471i
$528$		0			0
$529$	−158.891	−	275.207i	−0.300361	−	0.520241i
$530$		−	72.7070i		−	0.137183i
$531$		0			0
$532$	−17.3607			−0.0326329
$533$	680.867	−	393.099i	1.27742	−	0.737521i
$534$		0			0
$535$	−6.25725	+	10.8379i	−0.0116958	+	0.0202577i
$536$	−464.652	−	268.267i	−0.866889	−	0.500499i
$537$		0			0
$538$	278.940	+	483.139i	0.518476	+	0.898028i
$539$		−	141.324i		−	0.262197i
$540$		0			0
$541$	15.7625			0.0291358			0.0145679	−	0.999894i	$-0.495363\pi$
$541$	15.7625			0.0291358			0.0145679	+	0.999894i	$0.495363\pi$
$542$	−319.595	+	184.518i	−0.589659	+	0.340440i
$543$		0			0
$544$	−60.7929	+	105.296i	−0.111752	+	0.193560i
$545$	119.813	+	69.1738i	0.219840	+	0.126924i
$546$		0			0
$547$	−29.6214	−	51.3058i	−0.0541525	−	0.0937948i	0.837678	−	0.546164i	$-0.183912\pi$
$547$	−29.6214	−	51.3058i	−0.0541525	−	0.0937948i	−0.891831	+	0.452369i	$0.850579\pi$
$548$		−	4.42106i		−	0.00806762i
$549$		0			0
$550$	−25.0259			−0.0455016
$551$	83.7731	−	48.3664i	0.152038	−	0.0877793i
$552$		0			0
$553$	−108.336	+	187.644i	−0.195906	+	0.339319i
$554$	−557.729	−	322.005i	−1.00673	−	0.581236i
$555$		0			0
$556$	70.2558	+	121.687i	0.126359	+	0.218861i
$557$		−	736.312i		−	1.32192i	−0.750419	−	0.660962i	$-0.770148\pi$
$557$		−	736.312i		−	1.32192i	0.750419	−	0.660962i	$-0.229852\pi$
$558$		0			0
$559$	−1383.98			−2.47582
$560$	−219.117	+	126.508i	−0.391281	+	0.225906i
$561$		0			0
$562$	77.6938	−	134.570i	0.138245	−	0.239448i
$563$	163.478	+	94.3841i	0.290370	+	0.167645i	0.638108	−	0.769946i	$-0.279717\pi$
$563$	163.478	+	94.3841i	0.290370	+	0.167645i	−0.347739	+	0.937591i	$0.613050\pi$
$564$		0			0
$565$	−453.750	−	785.918i	−0.803097	−	1.39100i
$566$		−	443.410i		−	0.783409i
$567$		0			0
$568$	729.345			1.28406
$569$	−696.949	+	402.384i	−1.22487	+	0.707177i	−0.965952	−	0.258723i	$-0.916698\pi$
$569$	−696.949	+	402.384i	−1.22487	+	0.707177i	−0.258915	+	0.965900i	$0.583365\pi$
$570$		0			0
$571$	−281.670	+	487.867i	−0.493293	+	0.854408i	−0.999970	−	0.00772743i	$-0.997540\pi$
$571$	−281.670	+	487.867i	−0.493293	+	0.854408i	0.506677	+	0.862136i	$0.330874\pi$
$572$	−536.235	−	309.596i	−0.937475	−	0.541251i
$573$		0			0
$574$	−91.6112	−	158.675i	−0.159601	−	0.276438i
$575$			7.91059i			0.0137576i
$576$		0			0
$577$	−389.601			−0.675218			−0.337609	−	0.941286i	$-0.609618\pi$
$577$	−389.601			−0.675218			−0.337609	+	0.941286i	$0.609618\pi$
$578$	−483.926	+	279.395i	−0.837242	+	0.483382i
$579$		0			0
$580$	−51.2944	+	88.8445i	−0.0884386	+	0.153180i
$581$	−65.9552	−	38.0793i	−0.113520	−	0.0655409i
$582$		0			0
$583$	65.1702	+	112.878i	0.111784	+	0.193616i
$584$			163.888i			0.280630i
$585$		0			0
$586$	−530.793			−0.905789
$587$	775.035	−	447.466i	1.32033	−	0.762294i	0.336550	−	0.941666i	$-0.390740\pi$
$587$	775.035	−	447.466i	1.32033	−	0.762294i	0.983781	+	0.179372i	$0.0574065\pi$
$588$		0			0
$589$	125.544	−	217.448i	0.213148	−	0.369182i
$590$	417.486	+	241.035i	0.707603	+	0.408535i
$591$		0			0
$592$	395.369	+	684.799i	0.667853	+	1.15676i
$593$		−	684.579i		−	1.15443i	−0.816591	−	0.577217i	$-0.804139\pi$
$593$		−	684.579i		−	1.15443i	0.816591	−	0.577217i	$-0.195861\pi$
$594$		0			0
$595$	86.4236			0.145250
$596$	−213.857	+	123.471i	−0.358821	+	0.207166i
$597$		0			0
$598$	−427.849	+	741.057i	−0.715467	+	1.23923i
$599$	138.112	+	79.7392i	0.230572	+	0.133121i	0.610836	−	0.791757i	$-0.290834\pi$
$599$	138.112	+	79.7392i	0.230572	+	0.133121i	−0.380264	+	0.924878i	$0.624167\pi$
$600$		0			0
$601$	217.493	+	376.708i	0.361884	+	0.626802i	0.988271	−	0.152710i	$-0.0488002\pi$
$601$	217.493	+	376.708i	0.361884	+	0.626802i	−0.626387	+	0.779513i	$0.715467\pi$
$602$			322.535i			0.535773i
$603$		0			0
$604$	−92.2616			−0.152751
$605$	−1227.45	+	708.667i	−2.02884	+	1.17135i
$606$		0			0
$607$	−112.234	+	194.396i	−0.184900	+	0.320256i	−0.943543	−	0.331250i	$-0.892530\pi$
$607$	−112.234	+	194.396i	−0.184900	+	0.320256i	0.758643	+	0.651507i	$0.225863\pi$
$608$	−88.1782	−	50.9097i	−0.145030	−	0.0837331i
$609$		0			0
$610$	−200.453	−	347.195i	−0.328612	−	0.569172i
$611$			720.143i			1.17863i
$612$		0			0
$613$	−550.312			−0.897735			−0.448868	−	0.893598i	$-0.648173\pi$
$613$	−550.312			−0.897735			−0.448868	+	0.893598i	$0.648173\pi$
$614$	−329.463	+	190.216i	−0.536585	+	0.309797i
$615$		0			0
$616$	171.140	−	296.422i	0.277824	−	0.481205i
$617$	60.4315	+	34.8902i	0.0979441	+	0.0565481i	0.548172	−	0.836366i	$-0.315324\pi$
$617$	60.4315	+	34.8902i	0.0979441	+	0.0565481i	−0.450228	+	0.892914i	$0.648657\pi$
$618$		0			0
$619$	−37.4084	−	64.7933i	−0.0604337	−	0.104674i	0.834226	−	0.551423i	$-0.185915\pi$
$619$	−37.4084	−	64.7933i	−0.0604337	−	0.104674i	−0.894659	+	0.446749i	$0.852582\pi$
$620$			266.288i			0.429497i
$621$		0			0
$622$	−443.506			−0.713032
$623$	13.5857	−	7.84373i	0.0218070	−	0.0125903i
$624$		0			0
$625$	305.548	−	529.225i	0.488877	−	0.846760i
$626$	647.476	+	373.821i	1.03431	+	0.597158i
$627$		0			0
$628$	67.4304	+	116.793i	0.107373	+	0.185976i
$629$		−	270.096i		−	0.429406i
$630$		0			0
$631$	576.881			0.914233			0.457116	−	0.889407i	$-0.348882\pi$
$631$	576.881			0.914233			0.457116	+	0.889407i	$0.348882\pi$
$632$	−454.461	+	262.383i	−0.719084	+	0.415163i
$633$		0			0
$634$	496.196	−	859.437i	0.782644	−	1.35558i
$635$	503.538	+	290.718i	0.792973	+	0.457823i
$636$		0			0
$637$	−90.4892	−	156.732i	−0.142055	−	0.246047i
$638$		−	804.043i		−	1.26025i
$639$		0			0
$640$	−763.149			−1.19242
$641$	700.255	−	404.293i	1.09244	−	0.630722i	0.158216	−	0.987404i	$-0.449426\pi$
$641$	700.255	−	404.293i	1.09244	−	0.630722i	0.934226	+	0.356683i	$0.116092\pi$
$642$		0			0
$643$	−455.934	+	789.701i	−0.709074	+	1.22815i	0.256128	+	0.966643i	$0.417553\pi$
$643$	−455.934	+	789.701i	−0.709074	+	1.22815i	−0.965201	+	0.261508i	$0.915780\pi$
$644$	39.5023	+	22.8066i	0.0613389	+	0.0354140i
$645$		0			0
$646$	41.6036	+	72.0596i	0.0644019	+	0.111547i
$647$			1259.24i			1.94628i	0.230210	+	0.973141i	$0.426059\pi$
$647$			1259.24i			1.94628i	−0.230210	+	0.973141i	$0.573941\pi$
$648$		0			0
$649$	−864.198			−1.33158
$650$	−27.7543	+	16.0239i	−0.0426989	+	0.0246522i
$651$		0			0
$652$	−84.9081	+	147.065i	−0.130227	+	0.225560i
$653$	138.161	+	79.7673i	0.211579	+	0.122155i	0.602045	−	0.798462i	$-0.294353\pi$
$653$	138.161	+	79.7673i	0.211579	+	0.122155i	−0.390466	+	0.920617i	$0.627686\pi$
$654$		0			0
$655$	−433.805	−	751.373i	−0.662298	−	1.14713i
$656$		−	588.045i		−	0.896410i
$657$		0			0
$658$	167.828			0.255058
$659$	−106.590	+	61.5397i	−0.161745	+	0.0933834i	−0.578688	−	0.815549i	$-0.696435\pi$
$659$	−106.590	+	61.5397i	−0.161745	+	0.0933834i	0.416943	+	0.908933i	$0.363102\pi$
$660$		0			0
$661$	358.676	−	621.245i	0.542626	−	0.939856i	−0.456126	−	0.889915i	$-0.650763\pi$
$661$	358.676	−	621.245i	0.542626	−	0.939856i	0.998752	−	0.0499410i	$-0.0159033\pi$
$662$	870.109	+	502.358i	1.31436	+	0.758848i
$663$		0			0
$664$	−92.2256	−	159.739i	−0.138894	−	0.240571i
$665$			72.3736i			0.108832i
$666$		0			0
$667$	−254.155			−0.381042
$668$	−214.399	+	123.784i	−0.320957	+	0.185305i
$669$		0			0
$670$	471.490	−	816.644i	0.703716	−	1.21887i
$671$	622.409	+	359.348i	0.927584	+	0.535541i
$672$		0			0
$673$	−332.159	−	575.317i	−0.493550	−	0.854854i	0.506422	−	0.862286i	$-0.330968\pi$
$673$	−332.159	−	575.317i	−0.493550	−	0.854854i	−0.999972	+	0.00743145i	$0.997634\pi$
$674$			516.935i			0.766966i
$675$		0			0
$676$	−592.453			−0.876410
$677$	405.971	−	234.387i	0.599661	−	0.346215i	−0.169247	−	0.985574i	$-0.554134\pi$
$677$	405.971	−	234.387i	0.599661	−	0.346215i	0.768908	+	0.639359i	$0.220800\pi$
$678$		0			0
$679$	124.996	−	216.500i	0.184088	−	0.318851i
$680$	181.270	+	104.656i	0.266574	+	0.153906i
$681$		0			0
$682$	−1043.52	−	1807.43i	−1.53009	−	2.65019i
$683$		−	633.346i		−	0.927300i	−0.886019	−	0.463650i	$-0.846540\pi$
$683$		−	633.346i		−	0.927300i	0.886019	−	0.463650i	$-0.153460\pi$
$684$		0			0
$685$	−18.4306			−0.0269060
$686$	−36.5262	+	21.0884i	−0.0532452	+	0.0307411i
$687$		0			0
$688$	−517.582	+	896.478i	−0.752299	+	1.30302i
$689$	144.550	+	83.4562i	0.209797	+	0.121126i
$690$		0			0
$691$	320.318	+	554.806i	0.463557	+	0.802904i	0.999135	−	0.0415818i	$-0.0132397\pi$
$691$	320.318	+	554.806i	0.463557	+	0.802904i	−0.535578	+	0.844485i	$0.679906\pi$
$692$		−	196.177i		−	0.283493i
$693$		0			0
$694$	−290.811			−0.419035
$695$	507.290	−	292.884i	0.729913	−	0.421415i
$696$		0			0
$697$	−100.431	+	173.951i	−0.144090	+	0.249571i
$698$	135.100	+	77.9999i	0.193553	+	0.111748i
$699$		0			0
$700$	0.854161	+	1.47945i	0.00122023	+	0.00211350i
$701$		−	963.347i		−	1.37425i	−0.726541	−	0.687123i	$-0.758873\pi$
$701$		−	963.347i		−	1.37425i	0.726541	−	0.687123i	$-0.241127\pi$
$702$		0			0
$703$	226.186			0.321744
$704$	619.501	−	357.669i	0.879973	−	0.508053i
$705$		0			0
$706$	496.606	−	860.147i	0.703408	−	1.21834i
$707$	−281.947	−	162.782i	−0.398794	−	0.230244i
$708$		0			0
$709$	117.952	+	204.299i	0.166364	+	0.288151i	0.937139	−	0.348957i	$-0.113464\pi$
$709$	117.952	+	204.299i	0.166364	+	0.288151i	−0.770775	+	0.637108i	$0.780131\pi$
$710$			1281.85i			1.80542i
$711$		0			0
$712$	37.9941			0.0533625
$713$	−571.322	+	329.853i	−0.801293	+	0.462627i
$714$		0			0
$715$	−1290.65	+	2235.47i	−1.80510	+	3.12653i
$716$	−6.71240	−	3.87540i	−0.00937485	−	0.00541258i
$717$		0			0
$718$	634.825	+	1099.55i	0.884158	+	1.53141i
$719$			87.8999i			0.122253i	0.998130	+	0.0611265i	$0.0194693\pi$
$719$			87.8999i			0.122253i	−0.998130	+	0.0611265i	$0.980531\pi$
$720$		0			0
$721$	−109.998			−0.152564
$722$	651.630	−	376.219i	0.902535	−	0.521079i
$723$		0			0
$724$	28.2487	−	48.9282i	0.0390175	−	0.0675804i
$725$	−8.24342	−	4.75934i	−0.0113702	−	0.00656461i
$726$		0			0
$727$	439.148	+	760.627i	0.604055	+	1.04625i	0.992200	+	0.124656i	$0.0397827\pi$
$727$	439.148	+	760.627i	0.604055	+	1.04625i	−0.388145	+	0.921598i	$0.626884\pi$
$728$		−	438.319i		−	0.602086i
$729$		0			0
$730$	−288.040			−0.394575
$731$	306.214	−	176.793i	0.418898	−	0.241851i
$732$		0			0
$733$	−81.0306	+	140.349i	−0.110547	+	0.191472i	−0.915991	−	0.401199i	$-0.868593\pi$
$733$	−81.0306	+	140.349i	−0.110547	+	0.191472i	0.805444	+	0.592672i	$0.201927\pi$
$734$	−1065.88	−	615.388i	−1.45216	−	0.838403i
$735$		0			0
$736$	133.760	+	231.679i	0.181739	+	0.314781i
$737$			1690.46i			2.29370i
$738$		0			0
$739$	42.1893			0.0570897			0.0285449	−	0.999593i	$-0.490913\pi$
$739$	42.1893			0.0570897			0.0285449	+	0.999593i	$0.490913\pi$
$740$	−207.741	+	119.939i	−0.280731	+	0.162080i
$741$		0			0
$742$	19.4494	−	33.6873i	0.0262121	−	0.0454007i
$743$	623.721	+	360.105i	0.839463	+	0.484664i	0.857082	−	0.515181i	$-0.172275\pi$
$743$	623.721	+	360.105i	0.839463	+	0.484664i	−0.0176189	+	0.999845i	$0.505609\pi$
$744$		0			0
$745$	514.727	+	891.533i	0.690909	+	1.19669i
$746$			297.142i			0.398313i
$747$		0			0
$748$	158.194			0.211489
$749$	−5.79833	+	3.34767i	−0.00774143	+	0.00446952i
$750$		0			0
$751$	−654.759	+	1134.08i	−0.871850	+	1.51009i	−0.0117695	+	0.999931i	$0.503746\pi$
$751$	−654.759	+	1134.08i	−0.871850	+	1.51009i	−0.860081	+	0.510158i	$0.829587\pi$
$752$	466.474	+	269.319i	0.620312	+	0.358137i
$753$		0			0
$754$	−514.824	−	891.701i	−0.682790	−	1.18263i
$755$			384.622i			0.509433i
$756$		0			0
$757$	−695.235			−0.918409			−0.459204	−	0.888331i	$-0.651865\pi$
$757$	−695.235			−0.918409			−0.459204	+	0.888331i	$0.651865\pi$
$758$	680.768	−	393.042i	0.898111	−	0.518525i
$759$		0			0
$760$	−87.6421	+	151.801i	−0.115319	+	0.199738i
$761$	918.217	+	530.133i	1.20659	+	0.696626i	0.962013	−	0.273003i	$-0.0880169\pi$
$761$	918.217	+	530.133i	1.20659	+	0.696626i	0.244579	+	0.969629i	$0.421350\pi$
$762$		0			0
$763$	37.0084	+	64.1005i	0.0485039	+	0.0840111i
$764$			70.9045i			0.0928070i
$765$		0			0
$766$	−240.322			−0.313736
$767$	−958.415	+	553.341i	−1.24956	+	0.721436i
$768$		0			0
$769$	627.823	−	1087.42i	0.816415	−	1.41407i	−0.0918928	−	0.995769i	$-0.529292\pi$
$769$	627.823	−	1087.42i	0.816415	−	1.41407i	0.908308	−	0.418303i	$-0.137375\pi$
$770$	520.974	+	300.784i	0.676589	+	0.390629i
$771$		0			0
$772$	−105.897	−	183.419i	−0.137172	−	0.237589i
$773$		−	1182.69i		−	1.53000i	−0.644033	−	0.764998i	$-0.722740\pi$
$773$		−	1182.69i		−	1.53000i	0.644033	−	0.764998i	$-0.277260\pi$
$774$		0			0
$775$	−24.7075			−0.0318806
$776$	524.348	−	302.733i	0.675707	−	0.390119i
$777$		0			0
$778$	−567.752	+	983.376i	−0.729759	+	1.26398i
$779$	−145.671	−	84.1035i	−0.186998	−	0.107963i
$780$		0			0
$781$	−1148.97	−	1990.08i	−1.47116	−	2.54812i
$782$		−	218.618i		−	0.279562i
$783$		0			0
$784$	−135.365			−0.172659
$785$	486.889	−	281.105i	0.620240	−	0.358096i
$786$		0			0
$787$	−315.165	+	545.881i	−0.400463	+	0.693623i	−0.993782	−	0.111345i	$-0.964484\pi$
$787$	−315.165	+	545.881i	−0.400463	+	0.693623i	0.593318	+	0.804968i	$0.297818\pi$
$788$	70.9312	+	40.9521i	0.0900142	+	0.0519697i
$789$		0			0
$790$	−461.149	−	798.733i	−0.583732	−	1.01105i
$791$		−	485.518i		−	0.613803i
$792$		0			0
$793$	920.354			1.16060
$794$	−235.676	+	136.067i	−0.296821	+	0.171370i
$795$		0			0
$796$	214.107	−	370.845i	0.268979	−	0.465886i
$797$	236.971	+	136.815i	0.297329	+	0.171663i	0.641242	−	0.767339i	$-0.278419\pi$
$797$	236.971	+	136.815i	0.297329	+	0.171663i	−0.343914	+	0.939001i	$0.611753\pi$
$798$		0			0
$799$	−91.9927	−	159.336i	−0.115135	−	0.199419i
$800$			10.0192i			0.0125240i
$801$		0			0
$802$	1371.68			1.71032
$803$	447.183	−	258.181i	0.556890	−	0.321521i
$804$		0			0
$805$	95.0768	−	164.678i	0.118108	−	0.204569i
$806$	−2314.57	−	1336.32i	−2.87168	−	1.65797i
$807$		0			0
$808$	−394.249	−	682.859i	−0.487931	−	0.845122i
$809$		−	182.061i		−	0.225044i	−0.993649	−	0.112522i	$-0.964107\pi$
$809$		−	182.061i		−	0.225044i	0.993649	−	0.112522i	$-0.0358929\pi$
$810$		0			0
$811$	98.8163			0.121845			0.0609225	−	0.998142i	$-0.480596\pi$
$811$	98.8163			0.121845			0.0609225	+	0.998142i	$0.480596\pi$
$812$	−47.5324	+	27.4428i	−0.0585374	+	0.0337966i
$813$		0			0
$814$	940.029	−	1628.18i	1.15483	−	2.00022i
$815$	613.088	+	353.967i	0.752256	+	0.434315i
$816$		0			0
$817$	148.051	+	256.433i	0.181213	+	0.313871i
$818$			870.372i			1.06402i
$819$		0			0
$820$	178.390			0.217548
$821$	490.263	−	283.054i	0.597154	−	0.344767i	−0.170767	−	0.985311i	$-0.554625\pi$
$821$	490.263	−	283.054i	0.597154	−	0.344767i	0.767921	+	0.640544i	$0.221291\pi$
$822$		0			0
$823$	−226.447	+	392.217i	−0.275148	+	0.476570i	−0.970172	−	0.242416i	$-0.922060\pi$
$823$	−226.447	+	392.217i	−0.275148	+	0.476570i	0.695025	+	0.718986i	$0.255393\pi$
$824$	−230.717	−	133.205i	−0.279997	−	0.161656i
$825$		0			0
$826$	128.956	+	223.358i	0.156121	+	0.270409i
$827$			1268.79i			1.53421i	0.641521	+	0.767105i	$0.278304\pi$
$827$			1268.79i			1.53421i	−0.641521	+	0.767105i	$0.721696\pi$
$828$		0			0
$829$	1017.98			1.22797			0.613983	−	0.789319i	$-0.289566\pi$
$829$	1017.98			1.22797			0.613983	+	0.789319i	$0.289566\pi$
$830$	280.748	−	162.090i	0.338251	−	0.195289i
$831$		0			0
$832$	458.027	−	793.326i	0.550513	−	0.953517i
$833$	40.0426	+	23.1186i	0.0480703	+	0.0277534i
$834$		0			0
$835$	516.031	+	893.792i	0.618001	+	1.07041i
$836$			132.476i			0.158464i
$837$		0			0
$838$	231.501			0.276255
$839$	1017.97	−	587.725i	1.21331	−	0.700507i	0.249834	−	0.968289i	$-0.419624\pi$
$839$	1017.97	−	587.725i	1.21331	−	0.700507i	0.963480	+	0.267782i	$0.0862907\pi$
$840$		0			0
$841$	−267.590	+	463.479i	−0.318181	+	0.551105i
$842$	−840.115	−	485.041i	−0.997762	−	0.576058i
$843$		0			0
$844$	−26.7207	−	46.2816i	−0.0316596	−	0.0548360i
$845$			2469.83i			2.92287i
$846$		0			0
$847$	−758.283			−0.895257
$848$	108.118	−	62.4219i	0.127498	−	0.0736107i
$849$		0			0
$850$	4.09387	−	7.09079i	0.00481632	−	0.00834210i
$851$	−514.661	−	297.140i	−0.604772	−	0.349165i
$852$		0			0
$853$	−529.136	−	916.490i	−0.620323	−	1.07443i	−0.989425	−	0.145043i	$-0.953668\pi$
$853$	−529.136	−	916.490i	−0.620323	−	1.07443i	0.369102	−	0.929389i	$-0.379665\pi$
$854$		−	214.487i		−	0.251156i
$855$		0			0
$856$	−16.2157			−0.0189436
$857$	−1206.13	+	696.357i	−1.40738	+	0.812552i	−0.995135	−	0.0985196i	$-0.968589\pi$
$857$	−1206.13	+	696.357i	−1.40738	+	0.812552i	−0.412247	+	0.911072i	$0.635256\pi$
$858$		0			0
$859$	374.131	−	648.014i	0.435543	−	0.754382i	−0.561797	−	0.827275i	$-0.689890\pi$
$859$	374.131	−	648.014i	0.435543	−	0.754382i	0.997340	+	0.0728929i	$0.0232231\pi$
$860$	−271.956	−	157.014i	−0.316228	−	0.182574i
$861$		0			0
$862$	291.857	+	505.511i	0.338581	+	0.586440i
$863$		−	908.810i		−	1.05308i	−0.850150	−	0.526541i	$-0.823489\pi$
$863$		−	908.810i		−	1.05308i	0.850150	−	0.526541i	$-0.176511\pi$
$864$		0			0
$865$	−817.829			−0.945467
$866$	−962.408	+	555.646i	−1.11133	+	0.641624i
$867$		0			0
$868$	−71.2329	+	123.379i	−0.0820656	+	0.142142i
$869$	1431.87	+	826.691i	1.64772	+	0.951313i
$870$		0			0
$871$	1082.39	+	1874.76i	1.24270	+	2.15242i
$872$			179.264i			0.205578i
$873$		0			0
$874$	183.077			0.209470
$875$	289.443	−	167.110i	0.330793	−	0.190983i
$876$		0			0
$877$	293.842	−	508.950i	0.335054	−	0.580330i	−0.648441	−	0.761265i	$-0.724579\pi$
$877$	293.842	−	508.950i	0.335054	−	0.580330i	0.983495	+	0.180934i	$0.0579121\pi$
$878$	−696.831	−	402.316i	−0.793657	−	0.458218i
$879$		0			0
$880$	965.354	+	1672.04i	1.09699	+	1.90005i
$881$		−	1218.08i		−	1.38261i	−0.722565	−	0.691303i	$-0.757037\pi$
$881$		−	1218.08i		−	1.38261i	0.722565	−	0.691303i	$-0.242963\pi$
$882$		0			0
$883$	−635.067			−0.719215			−0.359607	−	0.933104i	$-0.617089\pi$
$883$	−635.067			−0.719215			−0.359607	+	0.933104i	$0.617089\pi$
$884$	175.440	−	101.291i	0.198462	−	0.114582i
$885$		0			0
$886$	16.5178	−	28.6097i	0.0186431	−	0.0322908i
$887$	522.302	+	301.551i	0.588841	+	0.339967i	0.764639	−	0.644459i	$-0.222917\pi$
$887$	522.302	+	301.551i	0.588841	+	0.339967i	−0.175798	+	0.984426i	$0.556251\pi$
$888$		0			0
$889$	155.536	+	269.396i	0.174956	+	0.303033i
$890$			66.7760i			0.0750293i
$891$		0			0
$892$	220.412			0.247099
$893$	133.432	−	77.0372i	0.149420	−	0.0862679i
$894$		0			0
$895$	−16.1559	+	27.9828i	−0.0180512	+	0.0312657i
$896$	−353.589	−	204.145i	−0.394631	−	0.227840i
$897$		0			0
$898$	966.040	+	1673.23i	1.07577	+	1.86329i
$899$		−	793.812i		−	0.882995i
$900$		0			0
$901$	−42.6435			−0.0473291
$902$	−1210.82	+	699.067i	−1.34237	+	0.775019i
$903$		0			0
$904$	587.947	−	1018.35i	0.650384	−	1.12650i
$905$	−203.973	−	117.764i	−0.225384	−	0.130126i
$906$		0			0
$907$	−137.959	−	238.953i	−0.152105	−	0.263454i	0.779896	−	0.625909i	$-0.215272\pi$
$907$	−137.959	−	238.953i	−0.152105	−	0.263454i	−0.932001	+	0.362455i	$0.881939\pi$
$908$		−	236.111i		−	0.260035i
$909$		0			0
$910$	770.362			0.846551
$911$	446.099	−	257.555i	0.489680	−	0.282717i	−0.234762	−	0.972053i	$-0.575431\pi$
$911$	446.099	−	257.555i	0.489680	−	0.282717i	0.724442	+	0.689336i	$0.242098\pi$
$912$		0			0
$913$	−290.575	+	503.291i	−0.318264	+	0.551250i
$914$	326.766	+	188.658i	0.357512	+	0.206410i
$915$		0			0
$916$	−190.533	−	330.014i	−0.208006	−	0.360277i
$917$		−	464.177i		−	0.506191i
$918$		0			0
$919$	−245.344			−0.266968			−0.133484	−	0.991051i	$-0.542616\pi$
$919$	−245.344			−0.266968			−0.133484	+	0.991051i	$0.542616\pi$
$920$	398.839	−	230.270i	0.433521	−	0.250293i
$921$		0			0
$922$	−894.102	+	1548.63i	−0.969742	+	1.67964i
$923$	−2548.48	−	1471.36i	−2.76108	−	1.59411i
$924$		0			0
$925$	−11.1286	−	19.2752i	−0.0120309	−	0.0208381i
$926$			1309.49i			1.41413i
$927$		0			0
$928$	−321.901			−0.346876
$929$	−782.483	+	451.767i	−0.842285	+	0.486294i	−0.858040	−	0.513582i	$-0.828318\pi$
$929$	−782.483	+	451.767i	−0.842285	+	0.486294i	0.0157551	+	0.999876i	$0.494985\pi$
$930$		0			0
$931$	−19.3602	+	33.5328i	−0.0207950	+	0.0360180i
$932$	221.245	+	127.736i	0.237388	+	0.137056i
$933$		0			0
$934$	−881.177	−	1526.24i	−0.943444	−	1.63409i
$935$		−	659.481i		−	0.705328i
$936$		0			0
$937$	−1413.35			−1.50837			−0.754187	−	0.656660i	$-0.771969\pi$
$937$	−1413.35			−1.50837			−0.754187	+	0.656660i	$0.771969\pi$
$938$	436.910	−	252.250i	0.465789	−	0.268923i
$939$		0			0
$940$	−81.7009	+	141.510i	−0.0869158	+	0.150543i
$941$	−503.527	−	290.712i	−0.535098	−	0.308939i	0.207992	−	0.978131i	$-0.433307\pi$
$941$	−503.527	−	290.712i	−0.535098	−	0.308939i	−0.743090	+	0.669192i	$0.766641\pi$
$942$		0			0
$943$	220.973	+	382.736i	0.234329	+	0.405870i
$944$			827.755i			0.876859i
$945$		0			0
$946$	2461.20			2.60170
$947$	828.961	−	478.601i	0.875355	−	0.505386i	0.00623075	−	0.999981i	$-0.498017\pi$
$947$	828.961	−	478.601i	0.875355	−	0.505386i	0.869124	+	0.494594i	$0.164683\pi$
$948$		0			0
$949$	330.624	−	572.658i	0.348392	−	0.603433i
$950$	5.93803	+	3.42832i	0.00625055	+	0.00360876i
$951$		0			0
$952$	55.9918	+	96.9806i	0.0588149	+	0.101870i
$953$		−	1060.55i		−	1.11285i	−0.830898	−	0.556425i	$-0.812173\pi$
$953$		−	1060.55i		−	1.11285i	0.830898	−	0.556425i	$-0.187827\pi$
$954$		0			0
$955$	295.588			0.309517
$956$	169.831	−	98.0521i	0.177648	−	0.102565i
$957$		0			0
$958$	−557.797	+	966.133i	−0.582251	+	1.00849i
$959$	−8.53943	−	4.93024i	−0.00890451	−	0.00514102i
$960$		0			0
$961$	−549.743	−	952.183i	−0.572053	−	0.990825i
$962$		−	2407.58i		−	2.50268i
$963$		0			0
$964$	−298.147			−0.309282
$965$	−764.640	+	441.465i	−0.792373	+	0.457477i
$966$		0			0
$967$	825.645	−	1430.06i	0.853821	−	1.47886i	−0.0239143	−	0.999714i	$-0.507613\pi$
$967$	825.645	−	1430.06i	0.853821	−	1.47886i	0.877735	−	0.479147i	$-0.159054\pi$
$968$	−1590.47	−	918.257i	−1.64305	−	0.948613i
$969$		0			0
$970$	532.064	+	921.562i	0.548520	+	0.950064i
$971$		−	1166.15i		−	1.20098i	−0.799633	−	0.600490i	$-0.794972\pi$
$971$		−	1166.15i		−	1.20098i	0.799633	−	0.600490i	$-0.205028\pi$
$972$		0			0
$973$	313.389			0.322086
$974$	−1480.44	+	854.730i	−1.51995	+	0.877546i
$975$		0			0
$976$	344.194	−	596.162i	0.352658	−	0.610821i
$977$	9.92234	+	5.72867i	0.0101559	+	0.00586353i	0.505069	−	0.863079i	$-0.331467\pi$
$977$	9.92234	+	5.72867i	0.0101559	+	0.00586353i	−0.494913	+	0.868942i	$0.664800\pi$
$978$		0			0
$979$	−59.8540	−	103.670i	−0.0611379	−	0.105894i
$980$		−	41.0643i		−	0.0419024i
$981$		0			0
$982$	−352.048			−0.358501
$983$	−1100.12	+	635.153i	−1.11914	+	0.646138i	−0.941182	−	0.337900i	$-0.890283\pi$
$983$	−1100.12	+	635.153i	−1.11914	+	0.646138i	−0.177961	+	0.984038i	$0.556950\pi$
$984$		0			0
$985$	170.722	−	295.699i	0.173322	−	0.300202i
$986$	227.816	+	131.530i	0.231050	+	0.133397i
$987$		0			0
$988$	84.8236	+	146.919i	0.0858538	+	0.148703i
$989$		−	777.977i		−	0.786630i
$990$		0			0
$991$	107.860			0.108839			0.0544196	−	0.998518i	$-0.482669\pi$
$991$	107.860			0.108839			0.0544196	+	0.998518i	$0.482669\pi$
$992$	−723.611	+	417.777i	−0.729447	+	0.421146i
$993$		0			0
$994$	−342.899	+	593.919i	−0.344969	+	0.597504i
$995$	−1545.99	−	892.575i	−1.55375	−	0.897061i
$996$		0			0
$997$	104.387	+	180.803i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$997$	104.387	+	180.803i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$998$			328.954i			0.329613i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.3.r.e.134.2		16
3.2	odd	2	inner	567.3.r.e.134.7		16
9.2	odd	6	inner	567.3.r.e.512.2		16
9.4	even	3		189.3.b.c.134.2	✓	8
9.5	odd	6		189.3.b.c.134.7	yes	8
9.7	even	3	inner	567.3.r.e.512.7		16
36.23	even	6		3024.3.d.j.1457.3		8
36.31	odd	6		3024.3.d.j.1457.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.3.b.c.134.2	✓	8	9.4	even	3
189.3.b.c.134.7	yes	8	9.5	odd	6
567.3.r.e.134.2		16	1.1	even	1	trivial
567.3.r.e.134.7		16	3.2	odd	2	inner
567.3.r.e.512.2		16	9.2	odd	6	inner
567.3.r.e.512.7		16	9.7	even	3	inner
3024.3.d.j.1457.3		8	36.23	even	6
3024.3.d.j.1457.6		8	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	567.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.97223 + 1.13867i) q^{2} +(0.593126 - 1.02732i) q^{4} +(-4.28273 - 2.47263i) q^{5} +(-1.32288 - 2.29129i) q^{7} -6.40785i q^{8} +11.2620 q^{10} +(-17.4844 + 10.0946i) q^{11} +(-12.9270 + 22.3903i) q^{13} +(5.21803 + 3.01263i) q^{14} +(9.66891 + 16.7470i) q^{16} -6.60531i q^{17} +5.53147 q^{19} +(-5.08040 + 2.93317i) q^{20} +(22.9888 - 39.8177i) q^{22} +(-12.5862 - 7.26667i) q^{23} +(-0.272153 - 0.471383i) q^{25} -58.8783i q^{26} -3.13853 q^{28} +(15.1448 - 8.74386i) q^{29} +(22.6963 - 39.3111i) q^{31} +(-15.9412 - 9.20364i) q^{32} +(7.52125 + 13.0272i) q^{34} +13.0840i q^{35} +40.8908 q^{37} +(-10.9093 + 6.29851i) q^{38} +(-15.8443 + 27.4431i) q^{40} +(-26.3350 - 15.2045i) q^{41} +(26.7653 + 46.3588i) q^{43} +23.9495i q^{44} +33.0973 q^{46} +(24.1224 - 13.9271i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(1.07350 + 0.619784i) q^{50} +(15.3347 + 26.5605i) q^{52} -6.45594i q^{53} +99.8411 q^{55} +(-14.6822 + 8.47678i) q^{56} +(-19.9127 + 34.4898i) q^{58} +(37.0702 + 21.4025i) q^{59} +(-17.7990 - 30.8288i) q^{61} +103.374i q^{62} -35.4317 q^{64} +(110.726 - 63.9277i) q^{65} +(41.8654 - 72.5131i) q^{67} +(-6.78580 - 3.91778i) q^{68} +(-14.8983 - 25.8046i) q^{70} +113.821i q^{71} -25.5762 q^{73} +(-80.6460 + 46.5610i) q^{74} +(3.28086 - 5.68262i) q^{76} +(46.2593 + 26.7078i) q^{77} +(-40.9472 - 70.9226i) q^{79} -95.6307i q^{80} +69.2516 q^{82} +(24.9287 - 14.3926i) q^{83} +(-16.3325 + 28.2888i) q^{85} +(-105.574 - 60.9535i) q^{86} +(64.6847 + 112.037i) q^{88} +5.92931i q^{89} +68.4034 q^{91} +(-14.9304 + 8.62010i) q^{92} +(-31.7166 + 54.9348i) q^{94} +(-23.6898 - 13.6773i) q^{95} +(47.2441 + 81.8291i) q^{97} -15.9413i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 104 q^{10} - 36 q^{13} - 132 q^{16} + 24 q^{19} + 136 q^{22} + 108 q^{25} + 112 q^{28} + 28 q^{31} + 12 q^{34} - 8 q^{37} - 336 q^{40} + 152 q^{43} + 216 q^{46} - 56 q^{49} + 272 q^{52}+ \cdots + 364 q^{97}+O(q^{100}) \) 16 * q + 12 * q^4 - 104 * q^10 - 36 * q^13 - 132 * q^16 + 24 * q^19 + 136 * q^22 + 108 * q^25 + 112 * q^28 + 28 * q^31 + 12 * q^34 - 8 * q^37 - 336 * q^40 + 152 * q^43 + 216 * q^46 - 56 * q^49 + 272 * q^52 + 392 * q^55 + 220 * q^58 - 180 * q^61 - 1400 * q^64 + 132 * q^67 - 196 * q^70 + 544 * q^73 - 544 * q^76 - 316 * q^79 + 56 * q^82 + 228 * q^85 - 112 * q^91 + 348 * q^94 + 364 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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