LMFDB - Embedded newform 882.3.n.b.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,3,Mod(19,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("882.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	882.n (of order $6$, degree $2$, not 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:	$24.0327593166$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			325.1
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	882.325
Dual form			882.3.n.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(2.74264 - 1.58346i) q^{5} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(2.74264 - 1.58346i) q^{5} +2.82843 q^{8} +(-3.87868 - 2.23936i) q^{10} +(-6.62132 + 11.4685i) q^{11} -5.49333i q^{13} +(-2.00000 - 3.46410i) q^{16} +(-11.7426 - 6.77962i) q^{17} +(0.621320 - 0.358719i) q^{19} +6.33386i q^{20} +18.7279 q^{22} +(-1.13604 - 1.96768i) q^{23} +(-7.48528 + 12.9649i) q^{25} +(-6.72792 + 3.88437i) q^{26} -20.4853 q^{29} +(-21.3198 - 12.3090i) q^{31} +(-2.82843 + 4.89898i) q^{32} +19.1757i q^{34} +(-32.4706 - 56.2407i) q^{37} +(-0.878680 - 0.507306i) q^{38} +(7.75736 - 4.47871i) q^{40} +21.0308i q^{41} +6.48528 q^{43} +(-13.2426 - 22.9369i) q^{44} +(-1.60660 + 2.78272i) q^{46} +(41.3787 - 23.8900i) q^{47} +21.1716 q^{50} +(9.51472 + 5.49333i) q^{52} +(11.0147 - 19.0781i) q^{53} +41.9385i q^{55} +(14.4853 + 25.0892i) q^{58} +(-72.5330 - 41.8770i) q^{59} +(-57.3823 + 33.1297i) q^{61} +34.8151i q^{62} +8.00000 q^{64} +(-8.69848 - 15.0662i) q^{65} +(-46.3198 + 80.2283i) q^{67} +(23.4853 - 13.5592i) q^{68} +48.4264 q^{71} +(-113.441 - 65.4953i) q^{73} +(-45.9203 + 79.5363i) q^{74} +1.43488i q^{76} +(38.1066 + 66.0026i) q^{79} +(-10.9706 - 6.33386i) q^{80} +(25.7574 - 14.8710i) q^{82} -107.981i q^{83} -42.9411 q^{85} +(-4.58579 - 7.94282i) q^{86} +(-18.7279 + 32.4377i) q^{88} +(-145.412 + 83.9535i) q^{89} +4.54416 q^{92} +(-58.5183 - 33.7856i) q^{94} +(1.13604 - 1.96768i) q^{95} +25.5816i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 6 q^{5}+O(q^{10}) $ 4 * q - 4 * q^4 - 6 * q^5	$ 4 q - 4 q^{4} - 6 q^{5} - 24 q^{10} - 18 q^{11} - 8 q^{16} - 30 q^{17} - 6 q^{19} + 24 q^{22} - 30 q^{23} + 4 q^{25} + 24 q^{26} - 48 q^{29} + 42 q^{31} - 62 q^{37} - 12 q^{38} + 48 q^{40} - 8 q^{43} - 36 q^{44} + 36 q^{46} + 174 q^{47} + 96 q^{50} + 72 q^{52} + 78 q^{53} + 24 q^{58} - 78 q^{59} + 42 q^{61} + 32 q^{64} + 84 q^{65} - 58 q^{67} + 60 q^{68} + 24 q^{71} - 318 q^{73} - 96 q^{74} + 110 q^{79} + 24 q^{80} + 120 q^{82} - 36 q^{85} - 24 q^{86} - 24 q^{88} - 378 q^{89} + 120 q^{92} + 12 q^{94} + 30 q^{95}+O(q^{100}) $ 4 * q - 4 * q^4 - 6 * q^5 - 24 * q^10 - 18 * q^11 - 8 * q^16 - 30 * q^17 - 6 * q^19 + 24 * q^22 - 30 * q^23 + 4 * q^25 + 24 * q^26 - 48 * q^29 + 42 * q^31 - 62 * q^37 - 12 * q^38 + 48 * q^40 - 8 * q^43 - 36 * q^44 + 36 * q^46 + 174 * q^47 + 96 * q^50 + 72 * q^52 + 78 * q^53 + 24 * q^58 - 78 * q^59 + 42 * q^61 + 32 * q^64 + 84 * q^65 - 58 * q^67 + 60 * q^68 + 24 * q^71 - 318 * q^73 - 96 * q^74 + 110 * q^79 + 24 * q^80 + 120 * q^82 - 36 * q^85 - 24 * q^86 - 24 * q^88 - 378 * q^89 + 120 * q^92 + 12 * q^94 + 30 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	2.74264	−	1.58346i	0.548528	−	0.316693i	−0.200000	−	0.979796i	$-0.564094\pi$
$5$	2.74264	−	1.58346i	0.548528	−	0.316693i	0.748528	+	0.663103i	$0.230761\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	2.82843			0.353553
$9$		0			0
$10$	−3.87868	−	2.23936i	−0.387868	−	0.223936i
$11$	−6.62132	+	11.4685i	−0.601938	+	1.04259i	0.390589	+	0.920565i	$0.372271\pi$
$11$	−6.62132	+	11.4685i	−0.601938	+	1.04259i	−0.992527	+	0.122022i	$0.961062\pi$
$12$		0			0
$13$		−	5.49333i		−	0.422563i	−0.977425	−	0.211282i	$-0.932236\pi$
$13$		−	5.49333i		−	0.422563i	0.977425	−	0.211282i	$-0.0677638\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−11.7426	−	6.77962i	−0.690744	−	0.398801i	0.113147	−	0.993578i	$-0.463907\pi$
$17$	−11.7426	−	6.77962i	−0.690744	−	0.398801i	−0.803891	+	0.594777i	$0.797240\pi$
$18$		0			0
$19$	0.621320	−	0.358719i	0.0327011	−	0.0188800i	−0.483560	−	0.875311i	$-0.660657\pi$
$19$	0.621320	−	0.358719i	0.0327011	−	0.0188800i	0.516261	+	0.856431i	$0.327323\pi$
$20$			6.33386i			0.316693i
$21$		0			0
$22$	18.7279			0.851269
$23$	−1.13604	−	1.96768i	−0.0493930	−	0.0855512i	0.840272	−	0.542165i	$-0.182395\pi$
$23$	−1.13604	−	1.96768i	−0.0493930	−	0.0855512i	−0.889665	+	0.456614i	$0.849062\pi$
$24$		0			0
$25$	−7.48528	+	12.9649i	−0.299411	+	0.518596i
$26$	−6.72792	+	3.88437i	−0.258766	+	0.149399i
$27$		0			0
$28$		0			0
$29$	−20.4853			−0.706389			−0.353195	−	0.935550i	$-0.614905\pi$
$29$	−20.4853			−0.706389			−0.353195	+	0.935550i	$0.614905\pi$
$30$		0			0
$31$	−21.3198	−	12.3090i	−0.687736	−	0.397064i	0.115028	−	0.993362i	$-0.463304\pi$
$31$	−21.3198	−	12.3090i	−0.687736	−	0.397064i	−0.802763	+	0.596298i	$0.796638\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$			19.1757i			0.563990i
$35$		0			0
$36$		0			0
$37$	−32.4706	−	56.2407i	−0.877583	−	1.52002i	−0.853986	−	0.520296i	$-0.825821\pi$
$37$	−32.4706	−	56.2407i	−0.877583	−	1.52002i	−0.0235970	−	0.999722i	$-0.507512\pi$
$38$	−0.878680	−	0.507306i	−0.0231231	−	0.0133502i
$39$		0			0
$40$	7.75736	−	4.47871i	0.193934	−	0.111968i
$41$			21.0308i			0.512946i	0.966551	+	0.256473i	$0.0825605\pi$
$41$			21.0308i			0.512946i	−0.966551	+	0.256473i	$0.917439\pi$
$42$		0			0
$43$	6.48528			0.150820			0.0754102	−	0.997153i	$-0.475973\pi$
$43$	6.48528			0.150820			0.0754102	+	0.997153i	$0.475973\pi$
$44$	−13.2426	−	22.9369i	−0.300969	−	0.521294i
$45$		0			0
$46$	−1.60660	+	2.78272i	−0.0349261	+	0.0604938i
$47$	41.3787	−	23.8900i	0.880397	−	0.508298i	0.00960801	−	0.999954i	$-0.496942\pi$
$47$	41.3787	−	23.8900i	0.880397	−	0.508298i	0.870789	+	0.491656i	$0.163608\pi$
$48$		0			0
$49$		0			0
$50$	21.1716			0.423431
$51$		0			0
$52$	9.51472	+	5.49333i	0.182975	+	0.105641i
$53$	11.0147	−	19.0781i	0.207825	−	0.359963i	−0.743204	−	0.669065i	$-0.766695\pi$
$53$	11.0147	−	19.0781i	0.207825	−	0.359963i	0.951029	+	0.309101i	$0.100028\pi$
$54$		0			0
$55$			41.9385i			0.762518i
$56$		0			0
$57$		0			0
$58$	14.4853	+	25.0892i	0.249746	+	0.432573i
$59$	−72.5330	−	41.8770i	−1.22937	−	0.709779i	−0.262474	−	0.964939i	$-0.584538\pi$
$59$	−72.5330	−	41.8770i	−1.22937	−	0.709779i	−0.966899	+	0.255160i	$0.917872\pi$
$60$		0			0
$61$	−57.3823	+	33.1297i	−0.940693	+	0.543109i	−0.890177	−	0.455614i	$-0.849420\pi$
$61$	−57.3823	+	33.1297i	−0.940693	+	0.543109i	−0.0505153	+	0.998723i	$0.516086\pi$
$62$			34.8151i			0.561534i
$63$		0			0
$64$	8.00000			0.125000
$65$	−8.69848	−	15.0662i	−0.133823	−	0.231788i
$66$		0			0
$67$	−46.3198	+	80.2283i	−0.691340	+	1.19744i	0.280058	+	0.959983i	$0.409646\pi$
$67$	−46.3198	+	80.2283i	−0.691340	+	1.19744i	−0.971399	+	0.237454i	$0.923687\pi$
$68$	23.4853	−	13.5592i	0.345372	−	0.199400i
$69$		0			0
$70$		0			0
$71$	48.4264			0.682062			0.341031	−	0.940052i	$-0.389224\pi$
$71$	48.4264			0.682062			0.341031	+	0.940052i	$0.389224\pi$
$72$		0			0
$73$	−113.441	−	65.4953i	−1.55399	−	0.897195i	−0.997811	−	0.0661316i	$-0.978934\pi$
$73$	−113.441	−	65.4953i	−1.55399	−	0.897195i	−0.556177	−	0.831064i	$-0.687732\pi$
$74$	−45.9203	+	79.5363i	−0.620545	+	1.07482i
$75$		0			0
$76$			1.43488i			0.0188800i
$77$		0			0
$78$		0			0
$79$	38.1066	+	66.0026i	0.482362	+	0.835476i	0.999795	−	0.0202482i	$-0.00644564\pi$
$79$	38.1066	+	66.0026i	0.482362	+	0.835476i	−0.517433	+	0.855724i	$0.673112\pi$
$80$	−10.9706	−	6.33386i	−0.137132	−	0.0791732i
$81$		0			0
$82$	25.7574	−	14.8710i	0.314114	−	0.181354i
$83$		−	107.981i		−	1.30098i	−0.759514	−	0.650491i	$-0.774563\pi$
$83$		−	107.981i		−	1.30098i	0.759514	−	0.650491i	$-0.225437\pi$
$84$		0			0
$85$	−42.9411			−0.505190
$86$	−4.58579	−	7.94282i	−0.0533231	−	0.0923583i
$87$		0			0
$88$	−18.7279	+	32.4377i	−0.212817	+	0.368610i
$89$	−145.412	+	83.9535i	−1.63384	+	0.943297i	−0.650945	+	0.759125i	$0.725627\pi$
$89$	−145.412	+	83.9535i	−1.63384	+	0.943297i	−0.982894	+	0.184173i	$0.941039\pi$
$90$		0			0
$91$		0			0
$92$	4.54416			0.0493930
$93$		0			0
$94$	−58.5183	−	33.7856i	−0.622535	−	0.359421i
$95$	1.13604	−	1.96768i	0.0119583	−	0.0207124i
$96$		0			0
$97$			25.5816i			0.263728i	0.991268	+	0.131864i	$0.0420962\pi$
$97$			25.5816i			0.263728i	−0.991268	+	0.131864i	$0.957904\pi$
$98$		0			0
$99$		0			0
$100$	−14.9706	−	25.9298i	−0.149706	−	0.259298i
$101$	24.6838	+	14.2512i	0.244394	+	0.141101i	0.617194	−	0.786811i	$-0.288269\pi$
$101$	24.6838	+	14.2512i	0.244394	+	0.141101i	−0.372801	+	0.927911i	$0.621603\pi$
$102$		0			0
$103$	−48.9228	+	28.2456i	−0.474979	+	0.274229i	−0.718322	−	0.695711i	$-0.755089\pi$
$103$	−48.9228	+	28.2456i	−0.474979	+	0.274229i	0.243343	+	0.969940i	$0.421756\pi$
$104$		−	15.5375i		−	0.149399i
$105$		0			0
$106$	−31.1543			−0.293909
$107$	23.8051	+	41.2316i	0.222477	+	0.385342i	0.955560	−	0.294798i	$-0.0952523\pi$
$107$	23.8051	+	41.2316i	0.222477	+	0.385342i	−0.733082	+	0.680140i	$0.761919\pi$
$108$		0			0
$109$	−37.6543	+	65.2192i	−0.345453	+	0.598341i	−0.985436	−	0.170047i	$-0.945608\pi$
$109$	−37.6543	+	65.2192i	−0.345453	+	0.598341i	0.639983	+	0.768389i	$0.278941\pi$
$110$	51.3640	−	29.6550i	0.466945	−	0.269591i
$111$		0			0
$112$		0			0
$113$	−85.4558			−0.756246			−0.378123	−	0.925755i	$-0.623430\pi$
$113$	−85.4558			−0.756246			−0.378123	+	0.925755i	$0.623430\pi$
$114$		0			0
$115$	−6.23149	−	3.59775i	−0.0541869	−	0.0312848i
$116$	20.4853	−	35.4815i	0.176597	−	0.305875i
$117$		0			0
$118$			118.446i			1.00378i
$119$		0			0
$120$		0			0
$121$	−27.1838	−	47.0837i	−0.224659	−	0.389121i
$122$	81.1508	+	46.8524i	0.665170	+	0.384036i
$123$		0			0
$124$	42.6396	−	24.6180i	0.343868	−	0.198532i
$125$			126.584i			1.01267i
$126$		0			0
$127$	−60.6619			−0.477653			−0.238826	−	0.971062i	$-0.576763\pi$
$127$	−60.6619			−0.477653			−0.238826	+	0.971062i	$0.576763\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−12.3015	+	21.3068i	−0.0946270	+	0.163899i
$131$	−115.136	+	66.4738i	−0.878901	+	0.507434i	−0.870296	−	0.492529i	$-0.836072\pi$
$131$	−115.136	+	66.4738i	−0.878901	+	0.507434i	−0.00860515	+	0.999963i	$0.502739\pi$
$132$		0			0
$133$		0			0
$134$	131.012			0.977703
$135$		0			0
$136$	−33.2132	−	19.1757i	−0.244215	−	0.140997i
$137$	−58.7132	+	101.694i	−0.428564	+	0.742294i	−0.996746	−	0.0806089i	$-0.974314\pi$
$137$	−58.7132	+	101.694i	−0.428564	+	0.742294i	0.568182	+	0.822903i	$0.307647\pi$
$138$		0			0
$139$			68.5857i			0.493422i	0.969089	+	0.246711i	$0.0793499\pi$
$139$			68.5857i			0.493422i	−0.969089	+	0.246711i	$0.920650\pi$
$140$		0			0
$141$		0			0
$142$	−34.2426	−	59.3100i	−0.241145	−	0.417676i
$143$	63.0000	+	36.3731i	0.440559	+	0.254357i
$144$		0			0
$145$	−56.1838	+	32.4377i	−0.387474	+	0.223708i
$146$			185.249i			1.26883i
$147$		0			0
$148$	129.882			0.877583
$149$	−13.1985	−	22.8604i	−0.0885804	−	0.153426i	0.818331	−	0.574747i	$-0.194900\pi$
$149$	−13.1985	−	22.8604i	−0.0885804	−	0.153426i	−0.906911	+	0.421322i	$0.861566\pi$
$150$		0			0
$151$	67.1066	−	116.232i	0.444415	−	0.769749i	−0.553597	−	0.832785i	$-0.686745\pi$
$151$	67.1066	−	116.232i	0.444415	−	0.769749i	0.998011	+	0.0630363i	$0.0200784\pi$
$152$	1.75736	−	1.01461i	0.0115616	−	0.00667508i
$153$		0			0
$154$		0			0
$155$	−77.9634			−0.502990
$156$		0			0
$157$	196.323	+	113.347i	1.25047	+	0.721958i	0.971202	−	0.238256i	$-0.0765759\pi$
$157$	196.323	+	113.347i	1.25047	+	0.721958i	0.279265	+	0.960214i	$0.409909\pi$
$158$	53.8909	−	93.3417i	0.341081	−	0.590770i
$159$		0			0
$160$			17.9149i			0.111968i
$161$		0			0
$162$		0			0
$163$	45.9889	+	79.6550i	0.282140	+	0.488681i	0.971912	−	0.235346i	$-0.0756223\pi$
$163$	45.9889	+	79.6550i	0.282140	+	0.488681i	−0.689771	+	0.724027i	$0.742289\pi$
$164$	−36.4264	−	21.0308i	−0.222112	−	0.128237i
$165$		0			0
$166$	−132.250	+	76.3544i	−0.796685	+	0.459967i
$167$		−	203.482i		−	1.21845i	−0.792996	−	0.609227i	$-0.791480\pi$
$167$		−	203.482i		−	1.21845i	0.792996	−	0.609227i	$-0.208520\pi$
$168$		0			0
$169$	138.823			0.821440
$170$	30.3640	+	52.5919i	0.178612	+	0.309364i
$171$		0			0
$172$	−6.48528	+	11.2328i	−0.0377051	+	0.0653072i
$173$	61.3234	−	35.4051i	0.354470	−	0.204654i	−0.312182	−	0.950022i	$-0.601060\pi$
$173$	61.3234	−	35.4051i	0.354470	−	0.204654i	0.666652	+	0.745369i	$0.267727\pi$
$174$		0			0
$175$		0			0
$176$	52.9706			0.300969
$177$		0			0
$178$	205.643	+	118.728i	1.15530	+	0.667012i
$179$	54.4081	−	94.2376i	0.303956	−	0.526467i	−0.673072	−	0.739577i	$-0.735026\pi$
$179$	54.4081	−	94.2376i	0.303956	−	0.526467i	0.977028	+	0.213109i	$0.0683591\pi$
$180$		0			0
$181$		−	99.6607i		−	0.550611i	−0.961357	−	0.275306i	$-0.911221\pi$
$181$		−	99.6607i		−	0.550611i	0.961357	−	0.275306i	$-0.0887791\pi$
$182$		0			0
$183$		0			0
$184$	−3.21320	−	5.56543i	−0.0174631	−	0.0302469i
$185$	−178.110	−	102.832i	−0.962758	−	0.555848i
$186$		0			0
$187$	155.504	−	89.7800i	0.831570	−	0.480107i
$188$			95.5600i			0.508298i
$189$		0			0
$190$	−3.21320			−0.0169116
$191$	34.9523	+	60.5391i	0.182996	+	0.316959i	0.942899	−	0.333077i	$-0.108087\pi$
$191$	34.9523	+	60.5391i	0.182996	+	0.316959i	−0.759903	+	0.650036i	$0.774754\pi$
$192$		0			0
$193$	16.1690	−	28.0056i	0.0837774	−	0.145107i	−0.821092	−	0.570796i	$-0.806635\pi$
$193$	16.1690	−	28.0056i	0.0837774	−	0.145107i	0.904870	+	0.425689i	$0.139968\pi$
$194$	31.3310	−	18.0889i	0.161500	−	0.0932419i
$195$		0			0
$196$		0			0
$197$	−277.103			−1.40661			−0.703306	−	0.710887i	$-0.748294\pi$
$197$	−277.103			−1.40661			−0.703306	+	0.710887i	$0.748294\pi$
$198$		0			0
$199$	−145.011	−	83.7222i	−0.728699	−	0.420715i	0.0892469	−	0.996010i	$-0.471554\pi$
$199$	−145.011	−	83.7222i	−0.728699	−	0.420715i	−0.817946	+	0.575295i	$0.804887\pi$
$200$	−21.1716	+	36.6702i	−0.105858	+	0.183351i
$201$		0			0
$202$		−	40.3084i		−	0.199547i
$203$		0			0
$204$		0			0
$205$	33.3015	+	57.6799i	0.162446	+	0.281365i
$206$	69.1873	+	39.9453i	0.335861	+	0.193909i
$207$		0			0
$208$	−19.0294	+	10.9867i	−0.0914877	+	0.0528204i
$209$			9.50079i			0.0454583i
$210$		0			0
$211$	−128.073			−0.606982			−0.303491	−	0.952834i	$-0.598152\pi$
$211$	−128.073			−0.606982			−0.303491	+	0.952834i	$0.598152\pi$
$212$	22.0294	+	38.1561i	0.103912	+	0.179982i
$213$		0			0
$214$	33.6655	−	58.3103i	0.157315	−	0.272478i
$215$	17.7868	−	10.2692i	0.0827293	−	0.0477638i
$216$		0			0
$217$		0			0
$218$	106.503			0.488544
$219$		0			0
$220$	−72.6396	−	41.9385i	−0.330180	−	0.190630i
$221$	−37.2426	+	64.5061i	−0.168519	+	0.291883i
$222$		0			0
$223$		−	417.169i		−	1.87071i	−0.353705	−	0.935357i	$-0.615078\pi$
$223$		−	417.169i		−	1.87071i	0.353705	−	0.935357i	$-0.384922\pi$
$224$		0			0
$225$		0			0
$226$	60.4264	+	104.662i	0.267373	+	0.463104i
$227$	201.143	+	116.130i	0.886093	+	0.511586i	0.872663	−	0.488324i	$-0.162391\pi$
$227$	201.143	+	116.130i	0.886093	+	0.511586i	0.0134307	+	0.999910i	$0.495725\pi$
$228$		0			0
$229$	72.4188	−	41.8110i	0.316239	−	0.182581i	−0.333476	−	0.942759i	$-0.608222\pi$
$229$	72.4188	−	41.8110i	0.316239	−	0.182581i	0.649715	+	0.760178i	$0.274888\pi$
$230$			10.1760i			0.0442434i
$231$		0			0
$232$	−57.9411			−0.249746
$233$	109.537	+	189.723i	0.470114	+	0.814261i	0.999416	−	0.0341721i	$-0.0108794\pi$
$233$	109.537	+	189.723i	0.470114	+	0.814261i	−0.529302	+	0.848434i	$0.677546\pi$
$234$		0			0
$235$	75.6579	−	131.043i	0.321949	−	0.557631i
$236$	145.066	−	83.7539i	0.614687	−	0.354889i
$237$		0			0
$238$		0			0
$239$	−193.103			−0.807961			−0.403980	−	0.914768i	$-0.632374\pi$
$239$	−193.103			−0.807961			−0.403980	+	0.914768i	$0.632374\pi$
$240$		0			0
$241$	−42.8970	−	24.7666i	−0.177996	−	0.102766i	0.408355	−	0.912823i	$-0.366103\pi$
$241$	−42.8970	−	24.7666i	−0.177996	−	0.102766i	−0.586351	+	0.810057i	$0.699436\pi$
$242$	−38.4437	+	66.5864i	−0.158858	+	0.275150i
$243$		0			0
$244$		−	132.519i		−	0.543109i
$245$		0			0
$246$		0			0
$247$	−1.97056	−	3.41311i	−0.00797799	−	0.0138183i
$248$	−60.3015	−	34.8151i	−0.243151	−	0.140383i
$249$		0			0
$250$	155.033	−	89.5083i	0.620132	−	0.358033i
$251$		−	162.524i		−	0.647507i	−0.946141	−	0.323754i	$-0.895055\pi$
$251$		−	162.524i		−	0.647507i	0.946141	−	0.323754i	$-0.104945\pi$
$252$		0			0
$253$	30.0883			0.118926
$254$	42.8944	+	74.2954i	0.168876	+	0.292501i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−85.8747	+	49.5798i	−0.334143	+	0.192917i	−0.657679	−	0.753298i	$-0.728462\pi$
$257$	−85.8747	+	49.5798i	−0.334143	+	0.192917i	0.323536	+	0.946216i	$0.395128\pi$
$258$		0			0
$259$		0			0
$260$	34.7939			0.133823
$261$		0			0
$262$	162.827	+	94.0082i	0.621477	+	0.358810i
$263$	217.173	−	376.154i	0.825751	−	1.43024i	−0.0755923	−	0.997139i	$-0.524085\pi$
$263$	217.173	−	376.154i	0.825751	−	1.43024i	0.901344	−	0.433105i	$-0.142582\pi$
$264$		0			0
$265$		−	69.7657i		−	0.263267i
$266$		0			0
$267$		0			0
$268$	−92.6396	−	160.457i	−0.345670	−	0.598718i
$269$	−79.1619	−	45.7041i	−0.294282	−	0.169904i	0.345589	−	0.938386i	$-0.387679\pi$
$269$	−79.1619	−	45.7041i	−0.294282	−	0.169904i	−0.639871	+	0.768482i	$0.721012\pi$
$270$		0			0
$271$	−14.8051	+	8.54772i	−0.0546313	+	0.0315414i	−0.527067	−	0.849824i	$-0.676708\pi$
$271$	−14.8051	+	8.54772i	−0.0546313	+	0.0315414i	0.472436	+	0.881365i	$0.343375\pi$
$272$			54.2369i			0.199400i
$273$		0			0
$274$	166.066			0.606080
$275$	−99.1249	−	171.689i	−0.360454	−	0.624325i
$276$		0			0
$277$	200.206	−	346.766i	0.722764	−	1.25186i	−0.237124	−	0.971479i	$-0.576205\pi$
$277$	200.206	−	346.766i	0.722764	−	1.25186i	0.959888	−	0.280385i	$-0.0904620\pi$
$278$	84.0000	−	48.4974i	0.302158	−	0.174451i
$279$		0			0
$280$		0			0
$281$	538.690			1.91705			0.958524	−	0.285012i	$-0.0919976\pi$
$281$	538.690			1.91705			0.958524	+	0.285012i	$0.0919976\pi$
$282$		0			0
$283$	267.783	+	154.604i	0.946229	+	0.546306i	0.891907	−	0.452218i	$-0.149367\pi$
$283$	267.783	+	154.604i	0.946229	+	0.546306i	0.0543215	+	0.998523i	$0.482700\pi$
$284$	−48.4264	+	83.8770i	−0.170516	+	0.295342i
$285$		0			0
$286$		−	102.879i		−	0.359715i
$287$		0			0
$288$		0			0
$289$	−52.5736	−	91.0601i	−0.181916	−	0.315087i
$290$	79.4558	+	45.8739i	0.273986	+	0.158186i
$291$		0			0
$292$	226.882	−	130.991i	0.776994	−	0.448598i
$293$		−	327.391i		−	1.11738i	−0.829378	−	0.558688i	$-0.811305\pi$
$293$		−	327.391i		−	1.11738i	0.829378	−	0.558688i	$-0.188695\pi$
$294$		0			0
$295$	−265.243			−0.899128
$296$	−91.8406	−	159.073i	−0.310272	−	0.537408i
$297$		0			0
$298$	−18.6655	+	32.3296i	−0.0626358	+	0.108488i
$299$	−10.8091	+	6.24063i	−0.0361508	+	0.0208717i
$300$		0			0
$301$		0			0
$302$	−189.806			−0.628497
$303$		0			0
$304$	−2.48528	−	1.43488i	−0.00817527	−	0.00471999i
$305$	−104.919	+	181.725i	−0.343998	+	0.595821i
$306$		0			0
$307$			256.140i			0.834331i	0.908831	+	0.417165i	$0.136976\pi$
$307$			256.140i			0.834331i	−0.908831	+	0.417165i	$0.863024\pi$
$308$		0			0
$309$		0			0
$310$	55.1285	+	95.4853i	0.177834	+	0.308017i
$311$	187.349	+	108.166i	0.602409	+	0.347801i	0.769989	−	0.638057i	$-0.220262\pi$
$311$	187.349	+	108.166i	0.602409	+	0.347801i	−0.167580	+	0.985859i	$0.553595\pi$
$312$		0			0
$313$	−135.809	+	78.4092i	−0.433893	+	0.250509i	−0.701004	−	0.713157i	$-0.747264\pi$
$313$	−135.809	+	78.4092i	−0.433893	+	0.250509i	0.267110	+	0.963666i	$0.413931\pi$
$314$		−	320.595i		−	1.02100i
$315$		0			0
$316$	−152.426			−0.482362
$317$	−224.015	−	388.005i	−0.706671	−	1.22399i	−0.966085	−	0.258224i	$-0.916863\pi$
$317$	−224.015	−	388.005i	−0.706671	−	1.22399i	0.259414	−	0.965766i	$-0.416471\pi$
$318$		0			0
$319$	135.640	−	234.935i	0.425203	−	0.736472i
$320$	21.9411	−	12.6677i	0.0685660	−	0.0395866i
$321$		0			0
$322$		0			0
$323$	−9.72792			−0.0301174
$324$		0			0
$325$	71.2203	+	41.1191i	0.219140	+	0.126520i
$326$	65.0381	−	112.649i	0.199503	−	0.345550i
$327$		0			0
$328$			59.4841i			0.181354i
$329$		0			0
$330$		0			0
$331$	27.5036	+	47.6376i	0.0830924	+	0.143920i	0.904577	−	0.426311i	$-0.140187\pi$
$331$	27.5036	+	47.6376i	0.0830924	+	0.143920i	−0.821484	+	0.570231i	$0.806854\pi$
$332$	187.029	+	107.981i	0.563342	+	0.325245i
$333$		0			0
$334$	−249.213	+	143.883i	−0.746147	+	0.430788i
$335$			293.383i			0.875770i
$336$		0			0
$337$	−111.632			−0.331254			−0.165627	−	0.986189i	$-0.552965\pi$
$337$	−111.632			−0.331254			−0.165627	+	0.986189i	$0.552965\pi$
$338$	−98.1630	−	170.023i	−0.290423	−	0.503027i
$339$		0			0
$340$	42.9411	−	74.3762i	0.126297	−	0.218754i
$341$	282.331	−	163.004i	0.827949	−	0.478016i
$342$		0			0
$343$		0			0
$344$	18.3431			0.0533231
$345$		0			0
$346$	−86.7244	−	50.0703i	−0.250648	−	0.144712i
$347$	188.628	−	326.714i	0.543598	−	0.941539i	−0.455096	−	0.890442i	$-0.650395\pi$
$347$	188.628	−	326.714i	0.543598	−	0.941539i	0.998694	−	0.0510967i	$-0.0162717\pi$
$348$		0			0
$349$		−	204.034i		−	0.584624i	−0.956323	−	0.292312i	$-0.905575\pi$
$349$		−	204.034i		−	0.584624i	0.956323	−	0.292312i	$-0.0944246\pi$
$350$		0			0
$351$		0			0
$352$	−37.4558	−	64.8754i	−0.106409	−	0.184305i
$353$	−361.198	−	208.538i	−1.02323	−	0.590759i	−0.108189	−	0.994130i	$-0.534505\pi$
$353$	−361.198	−	208.538i	−1.02323	−	0.590759i	−0.915036	+	0.403371i	$0.867838\pi$
$354$		0			0
$355$	132.816	−	76.6815i	0.374130	−	0.216004i
$356$		−	335.814i		−	0.943297i
$357$		0			0
$358$	−153.889			−0.429859
$359$	−89.4153	−	154.872i	−0.249068	−	0.431398i	0.714200	−	0.699942i	$-0.246791\pi$
$359$	−89.4153	−	154.872i	−0.249068	−	0.431398i	−0.963267	+	0.268544i	$0.913457\pi$
$360$		0			0
$361$	−180.243	+	312.189i	−0.499287	+	0.864791i
$362$	−122.059	+	70.4707i	−0.337179	+	0.194671i
$363$		0			0
$364$		0			0
$365$	−414.838			−1.13654
$366$		0			0
$367$	544.724	+	314.497i	1.48426	+	0.856939i	0.999840	−	0.0178960i	$-0.00569679\pi$
$367$	544.724	+	314.497i	1.48426	+	0.856939i	0.484422	+	0.874835i	$0.339030\pi$
$368$	−4.54416	+	7.87071i	−0.0123482	+	0.0213878i
$369$		0			0
$370$			290.853i			0.786088i
$371$		0			0
$372$		0			0
$373$	127.779	+	221.320i	0.342572	+	0.593351i	0.984910	−	0.173070i	$-0.0553687\pi$
$373$	127.779	+	221.320i	0.342572	+	0.593351i	−0.642338	+	0.766422i	$0.722035\pi$
$374$	−219.915	−	126.968i	−0.588009	−	0.339487i
$375$		0			0
$376$	117.037	−	67.5711i	0.311267	−	0.179710i
$377$			112.532i			0.298494i
$378$		0			0
$379$	219.750			0.579816			0.289908	−	0.957055i	$-0.406375\pi$
$379$	219.750			0.579816			0.289908	+	0.957055i	$0.406375\pi$
$380$	2.27208	+	3.93535i	0.00597915	+	0.0103562i
$381$		0			0
$382$	49.4300	−	85.6152i	0.129398	−	0.224124i
$383$	−14.7534	+	8.51785i	−0.0385205	+	0.0222398i	−0.519137	−	0.854691i	$-0.673746\pi$
$383$	−14.7534	+	8.51785i	−0.0385205	+	0.0222398i	0.480616	+	0.876931i	$0.340413\pi$
$384$		0			0
$385$		0			0
$386$	−45.7330			−0.118479
$387$		0			0
$388$	−44.3087	−	25.5816i	−0.114198	−	0.0659320i
$389$	−76.1102	+	131.827i	−0.195656	+	0.338886i	−0.947115	−	0.320893i	$-0.896017\pi$
$389$	−76.1102	+	131.827i	−0.195656	+	0.338886i	0.751459	+	0.659779i	$0.229350\pi$
$390$		0			0
$391$			30.8076i			0.0787919i
$392$		0			0
$393$		0			0
$394$	195.941	+	339.380i	0.497313	+	0.861371i
$395$	209.025	+	120.681i	0.529178	+	0.305521i
$396$		0			0
$397$	322.786	−	186.361i	0.813064	−	0.469423i	−0.0349549	−	0.999389i	$-0.511129\pi$
$397$	322.786	−	186.361i	0.813064	−	0.469423i	0.848019	+	0.529966i	$0.177795\pi$
$398$			236.802i			0.594980i
$399$		0			0
$400$	59.8823			0.149706
$401$	325.786	+	564.279i	0.812435	+	1.40718i	0.911155	+	0.412063i	$0.135192\pi$
$401$	325.786	+	564.279i	0.812435	+	1.40718i	−0.0987205	+	0.995115i	$0.531475\pi$
$402$		0			0
$403$	−67.6173	+	117.117i	−0.167785	+	0.290612i
$404$	−49.3675	+	28.5024i	−0.122197	+	0.0705504i
$405$		0			0
$406$		0			0
$407$	859.992			2.11300
$408$		0			0
$409$	−462.081	−	266.782i	−1.12978	−	0.652280i	−0.185902	−	0.982568i	$-0.559521\pi$
$409$	−462.081	−	266.782i	−1.12978	−	0.652280i	−0.943880	+	0.330289i	$0.892854\pi$
$410$	47.0955	−	81.5717i	0.114867	−	0.198955i
$411$		0			0
$412$		−	112.982i		−	0.274229i
$413$		0			0
$414$		0			0
$415$	−170.985	−	296.154i	−0.412012	−	0.713625i
$416$	26.9117	+	15.5375i	0.0646916	+	0.0373497i
$417$		0			0
$418$	11.6360	−	6.71807i	0.0278374	−	0.0160719i
$419$		−	534.252i		−	1.27507i	−0.770423	−	0.637533i	$-0.779955\pi$
$419$		−	534.252i		−	1.27507i	0.770423	−	0.637533i	$-0.220045\pi$
$420$		0			0
$421$	157.220			0.373445			0.186723	−	0.982413i	$-0.440213\pi$
$421$	157.220			0.373445			0.186723	+	0.982413i	$0.440213\pi$
$422$	90.5614	+	156.857i	0.214600	+	0.371699i
$423$		0			0
$424$	31.1543	−	53.9609i	0.0734772	−	0.127266i
$425$	175.794	−	101.495i	0.413633	−	0.238811i
$426$		0			0
$427$		0			0
$428$	−95.2203			−0.222477
$429$		0			0
$430$	−25.1543	−	14.5229i	−0.0584984	−	0.0337741i
$431$	−114.268	+	197.918i	−0.265123	+	0.459207i	−0.967596	−	0.252504i	$-0.918746\pi$
$431$	−114.268	+	197.918i	−0.265123	+	0.459207i	0.702473	+	0.711711i	$0.252079\pi$
$432$		0			0
$433$		−	47.5549i		−	0.109827i	−0.998491	−	0.0549133i	$-0.982512\pi$
$433$		−	47.5549i		−	0.109827i	0.998491	−	0.0549133i	$-0.0174882\pi$
$434$		0			0
$435$		0			0
$436$	−75.3087	−	130.438i	−0.172726	−	0.299171i
$437$	−1.41169	−	0.815039i	−0.00323041	−	0.00186508i
$438$		0			0
$439$	63.9594	−	36.9270i	0.145693	−	0.0841161i	−0.425381	−	0.905014i	$-0.639860\pi$
$439$	63.9594	−	36.9270i	0.145693	−	0.0841161i	0.571075	+	0.820898i	$0.306527\pi$
$440$			118.620i			0.269591i
$441$		0			0
$442$	105.338			0.238321
$443$	117.320	+	203.204i	0.264830	+	0.458699i	0.967519	−	0.252798i	$-0.0813507\pi$
$443$	117.320	+	203.204i	0.264830	+	0.458699i	−0.702689	+	0.711497i	$0.748017\pi$
$444$		0			0
$445$	−265.875	+	460.508i	−0.597471	+	1.03485i
$446$	−510.926	+	294.983i	−1.14557	+	0.661397i
$447$		0			0
$448$		0			0
$449$	255.161			0.568288			0.284144	−	0.958782i	$-0.408291\pi$
$449$	255.161			0.568288			0.284144	+	0.958782i	$0.408291\pi$
$450$		0			0
$451$	−241.191	−	139.252i	−0.534791	−	0.308762i
$452$	85.4558	−	148.014i	0.189062	−	0.327464i
$453$		0			0
$454$		−	328.465i		−	0.723492i
$455$		0			0
$456$		0			0
$457$	72.8675	+	126.210i	0.159448	+	0.276171i	0.934670	−	0.355518i	$-0.115695\pi$
$457$	72.8675	+	126.210i	0.159448	+	0.276171i	−0.775222	+	0.631689i	$0.782362\pi$
$458$	−102.416	−	59.1297i	−0.223615	−	0.129104i
$459$		0			0
$460$	12.4630	−	7.19551i	0.0270934	−	0.0156424i
$461$			888.329i			1.92696i	0.267777	+	0.963481i	$0.413711\pi$
$461$			888.329i			1.92696i	−0.267777	+	0.963481i	$0.586289\pi$
$462$		0			0
$463$	234.014			0.505430			0.252715	−	0.967541i	$-0.418676\pi$
$463$	234.014			0.505430			0.252715	+	0.967541i	$0.418676\pi$
$464$	40.9706	+	70.9631i	0.0882986	+	0.152938i
$465$		0			0
$466$	154.908	−	268.309i	0.332421	−	0.575770i
$467$	681.231	−	393.309i	1.45874	−	0.842204i	0.459790	−	0.888028i	$-0.347925\pi$
$467$	681.231	−	393.309i	1.45874	−	0.842204i	0.998950	+	0.0458237i	$0.0145912\pi$
$468$		0			0
$469$		0			0
$470$	−213.993			−0.455304
$471$		0			0
$472$	−205.154	−	118.446i	−0.434649	−	0.250945i
$473$	−42.9411	+	74.3762i	−0.0907846	+	0.157244i
$474$		0			0
$475$			10.7405i			0.0226115i
$476$		0			0
$477$		0			0
$478$	136.544	+	236.501i	0.285657	+	0.494773i
$479$	638.202	+	368.466i	1.33236	+	0.769240i	0.985661	−	0.168735i	$-0.0539682\pi$
$479$	638.202	+	368.466i	1.33236	+	0.769240i	0.346702	+	0.937975i	$0.387302\pi$
$480$		0			0
$481$	−308.948	+	178.371i	−0.642304	+	0.370834i
$482$			70.0505i			0.145333i
$483$		0			0
$484$	108.735			0.224659
$485$	40.5076	+	70.1612i	0.0835208	+	0.144662i
$486$		0			0
$487$	−135.349	+	234.432i	−0.277925	+	0.481379i	−0.970869	−	0.239612i	$-0.922980\pi$
$487$	−135.349	+	234.432i	−0.277925	+	0.481379i	0.692944	+	0.720991i	$0.256313\pi$
$488$	−162.302	+	93.7048i	−0.332585	+	0.192018i
$489$		0			0
$490$		0			0
$491$	−760.161			−1.54819			−0.774094	−	0.633070i	$-0.781794\pi$
$491$	−760.161			−1.54819			−0.774094	+	0.633070i	$0.781794\pi$
$492$		0			0
$493$	240.551	+	138.882i	0.487934	+	0.281709i
$494$	−2.78680	+	4.82687i	−0.00564129	+	0.00977100i
$495$		0			0
$496$			98.4720i			0.198532i
$497$		0			0
$498$		0			0
$499$	−62.7462	−	108.680i	−0.125744	−	0.217795i	0.796280	−	0.604929i	$-0.206798\pi$
$499$	−62.7462	−	108.680i	−0.125744	−	0.217795i	−0.922023	+	0.387134i	$0.873465\pi$
$500$	−219.250	−	126.584i	−0.438500	−	0.253168i
$501$		0			0
$502$	−199.051	+	114.922i	−0.396516	+	0.228928i
$503$			117.083i			0.232770i	0.993204	+	0.116385i	$0.0371306\pi$
$503$			117.083i			0.232770i	−0.993204	+	0.116385i	$0.962869\pi$
$504$		0			0
$505$	90.2649			0.178742
$506$	−21.2756	−	36.8505i	−0.0420467	−	0.0728271i
$507$		0			0
$508$	60.6619	−	105.070i	0.119413	−	0.206830i
$509$	−574.110	+	331.463i	−1.12792	+	0.651204i	−0.943410	−	0.331627i	$-0.892402\pi$
$509$	−574.110	+	331.463i	−1.12792	+	0.651204i	−0.184507	+	0.982831i	$0.559069\pi$
$510$		0			0
$511$		0			0
$512$	22.6274			0.0441942
$513$		0			0
$514$	121.445	+	70.1164i	0.236275	+	0.136413i
$515$	−89.4518	+	154.935i	−0.173693	+	0.300845i
$516$		0			0
$517$			632.733i			1.22386i
$518$		0			0
$519$		0			0
$520$	−24.6030	−	42.6137i	−0.0473135	−	0.0819494i
$521$	−40.8229	−	23.5691i	−0.0783550	−	0.0452383i	0.460311	−	0.887758i	$-0.347738\pi$
$521$	−40.8229	−	23.5691i	−0.0783550	−	0.0452383i	−0.538666	+	0.842520i	$0.681071\pi$
$522$		0			0
$523$	−432.554	+	249.735i	−0.827064	+	0.477506i	−0.852846	−	0.522162i	$-0.825126\pi$
$523$	−432.554	+	249.735i	−0.827064	+	0.477506i	0.0257824	+	0.999668i	$0.491792\pi$
$524$		−	265.895i		−	0.507434i
$525$		0			0
$526$	−614.257			−1.16779
$527$	166.901	+	289.080i	0.316699	+	0.548539i
$528$		0			0
$529$	261.919	−	453.657i	0.495121	−	0.857574i
$530$	−85.4451	+	49.3318i	−0.161217	+	0.0930788i
$531$		0			0
$532$		0			0
$533$	115.529			0.216752
$534$		0			0
$535$	130.578	+	75.3890i	0.244070	+	0.140914i
$536$	−131.012	+	226.920i	−0.244426	+	0.423358i
$537$		0			0
$538$			129.271i			0.240280i
$539$		0			0
$540$		0			0
$541$	−249.405	−	431.981i	−0.461007	−	0.798487i	0.538005	−	0.842942i	$-0.319178\pi$
$541$	−249.405	−	431.981i	−0.461007	−	0.798487i	−0.999011	+	0.0444550i	$0.985845\pi$
$542$	20.9376	+	12.0883i	0.0386302	+	0.0223031i
$543$		0			0
$544$	66.4264	−	38.3513i	0.122107	−	0.0704987i
$545$			238.497i			0.437609i
$546$		0			0
$547$	−279.897			−0.511694			−0.255847	−	0.966717i	$-0.582354\pi$
$547$	−279.897			−0.511694			−0.255847	+	0.966717i	$0.582354\pi$
$548$	−117.426	−	203.389i	−0.214282	−	0.371147i
$549$		0			0
$550$	−140.184	+	242.805i	−0.254880	+	0.441464i
$551$	−12.7279	+	7.34847i	−0.0230997	+	0.0133366i
$552$		0			0
$553$		0			0
$554$	−566.267			−1.02214
$555$		0			0
$556$	−118.794	−	68.5857i	−0.213658	−	0.123356i
$557$	−130.890	+	226.708i	−0.234991	+	0.407016i	−0.959270	−	0.282491i	$-0.908839\pi$
$557$	−130.890	+	226.708i	−0.234991	+	0.407016i	0.724279	+	0.689507i	$0.242173\pi$
$558$		0			0
$559$		−	35.6258i		−	0.0637312i
$560$		0			0
$561$		0			0
$562$	−380.912	−	659.758i	−0.677779	−	1.17395i
$563$	−420.076	−	242.531i	−0.746139	−	0.430784i	0.0781581	−	0.996941i	$-0.475096\pi$
$563$	−420.076	−	242.531i	−0.746139	−	0.430784i	−0.824297	+	0.566157i	$0.808429\pi$
$564$		0			0
$565$	−234.375	+	135.316i	−0.414822	+	0.239498i
$566$		−	437.287i		−	0.772593i
$567$		0			0
$568$	136.971			0.241145
$569$	−227.000	−	393.175i	−0.398945	−	0.690993i	0.594651	−	0.803984i	$-0.297290\pi$
$569$	−227.000	−	393.175i	−0.398945	−	0.690993i	−0.993596	+	0.112991i	$0.963957\pi$
$570$		0			0
$571$	115.769	−	200.517i	0.202747	−	0.351168i	−0.746666	−	0.665200i	$-0.768346\pi$
$571$	115.769	−	200.517i	0.202747	−	0.351168i	0.949413	+	0.314032i	$0.101680\pi$
$572$	−126.000	+	72.7461i	−0.220280	+	0.127179i
$573$		0			0
$574$		0			0
$575$	34.0143			0.0591553
$576$		0			0
$577$	−564.014	−	325.634i	−0.977494	−	0.564356i	−0.0759812	−	0.997109i	$-0.524209\pi$
$577$	−564.014	−	325.634i	−0.977494	−	0.564356i	−0.901513	+	0.432753i	$0.857542\pi$
$578$	−74.3503	+	128.778i	−0.128634	+	0.222800i
$579$		0			0
$580$		−	129.751i		−	0.223708i
$581$		0			0
$582$		0			0
$583$	145.864	+	252.644i	0.250195	+	0.433351i
$584$	−320.860	−	185.249i	−0.549418	−	0.317206i
$585$		0			0
$586$	−400.971	+	231.500i	−0.684250	+	0.395052i
$587$			823.029i			1.40209i	0.713116	+	0.701046i	$0.247283\pi$
$587$			823.029i			1.40209i	−0.713116	+	0.701046i	$0.752717\pi$
$588$		0			0
$589$	−17.6619			−0.0299863
$590$	187.555	+	324.855i	0.317890	+	0.550601i
$591$		0			0
$592$	−129.882	+	224.963i	−0.219396	+	0.380004i
$593$	−700.110	+	404.209i	−1.18062	+	0.681634i	−0.956159	−	0.292848i	$-0.905397\pi$
$593$	−700.110	+	404.209i	−1.18062	+	0.681634i	−0.224465	+	0.974482i	$0.572064\pi$
$594$		0			0
$595$		0			0
$596$	52.7939			0.0885804
$597$		0			0
$598$	15.2864	+	8.82559i	0.0255625	+	0.0147585i
$599$	265.422	−	459.725i	0.443109	−	0.767488i	−0.554809	−	0.831978i	$-0.687209\pi$
$599$	265.422	−	459.725i	0.443109	−	0.767488i	0.997918	+	0.0644900i	$0.0205421\pi$
$600$		0			0
$601$			936.503i			1.55824i	0.626874	+	0.779121i	$0.284334\pi$
$601$			936.503i			1.55824i	−0.626874	+	0.779121i	$0.715666\pi$
$602$		0			0
$603$		0			0
$604$	134.213	+	232.464i	0.222207	+	0.384874i
$605$	−149.111	−	86.0890i	−0.246464	−	0.142296i
$606$		0			0
$607$	−521.452	+	301.060i	−0.859064	+	0.495981i	−0.863699	−	0.504008i	$-0.831858\pi$
$607$	−521.452	+	301.060i	−0.859064	+	0.495981i	0.00463474	+	0.999989i	$0.498525\pi$
$608$			4.05845i			0.00667508i
$609$		0			0
$610$	296.756			0.486486
$611$	−131.235	−	227.307i	−0.214788	−	0.372024i
$612$		0			0
$613$	−548.448	+	949.940i	−0.894695	+	1.54966i	−0.0605142	+	0.998167i	$0.519274\pi$
$613$	−548.448	+	949.940i	−0.894695	+	1.54966i	−0.834181	+	0.551491i	$0.814059\pi$
$614$	313.706	−	181.118i	0.510921	−	0.294981i
$615$		0			0
$616$		0			0
$617$	432.956			0.701712			0.350856	−	0.936429i	$-0.385891\pi$
$617$	432.956			0.701712			0.350856	+	0.936429i	$0.385891\pi$
$618$		0			0
$619$	−194.951	−	112.555i	−0.314946	−	0.181834i	0.334192	−	0.942505i	$-0.391537\pi$
$619$	−194.951	−	112.555i	−0.314946	−	0.181834i	−0.649137	+	0.760671i	$0.724870\pi$
$620$	77.9634	−	135.037i	0.125747	−	0.217801i
$621$		0			0
$622$		−	305.940i		−	0.491865i
$623$		0			0
$624$		0			0
$625$	13.3091	+	23.0520i	0.0212945	+	0.0368832i
$626$	192.062	+	110.887i	0.306809	+	0.177136i
$627$		0			0
$628$	−392.647	+	226.695i	−0.625234	+	0.360979i
$629$			880.552i			1.39992i
$630$		0			0
$631$	750.514			1.18940			0.594702	−	0.803946i	$-0.297270\pi$
$631$	750.514			1.18940			0.594702	+	0.803946i	$0.297270\pi$
$632$	107.782	+	186.683i	0.170541	+	0.295385i
$633$		0			0
$634$	−316.805	+	548.722i	−0.499692	+	0.865492i
$635$	−166.374	+	96.0560i	−0.262006	+	0.151269i
$636$		0			0
$637$		0			0
$638$	−383.647			−0.601327
$639$		0			0
$640$	−31.0294	−	17.9149i	−0.0484835	−	0.0279920i
$641$	−580.926	+	1006.19i	−0.906281	+	1.56973i	−0.0870937	+	0.996200i	$0.527758\pi$
$641$	−580.926	+	1006.19i	−0.906281	+	1.56973i	−0.819188	+	0.573525i	$0.805575\pi$
$642$		0			0
$643$		−	121.957i		−	0.189669i	−0.995493	−	0.0948347i	$-0.969768\pi$
$643$		−	121.957i		−	0.189669i	0.995493	−	0.0948347i	$-0.0302322\pi$
$644$		0			0
$645$		0			0
$646$	6.87868	+	11.9142i	0.0106481	+	0.0184431i
$647$	−137.504	−	79.3877i	−0.212525	−	0.122701i	0.389959	−	0.920832i	$-0.372489\pi$
$647$	−137.504	−	79.3877i	−0.212525	−	0.122701i	−0.602484	+	0.798131i	$0.705822\pi$
$648$		0			0
$649$	960.529	−	554.561i	1.48001	−	0.854486i
$650$		−	116.302i		−	0.178927i
$651$		0			0
$652$	−183.955			−0.282140
$653$	−195.471	−	338.565i	−0.299342	−	0.518476i	0.676643	−	0.736311i	$-0.263434\pi$
$653$	−195.471	−	338.565i	−0.299342	−	0.518476i	−0.975986	+	0.217835i	$0.930101\pi$
$654$		0			0
$655$	−210.518	+	364.628i	−0.321401	+	0.556683i
$656$	72.8528	−	42.0616i	0.111056	−	0.0641183i
$657$		0			0
$658$		0			0
$659$	331.955			0.503726			0.251863	−	0.967763i	$-0.418957\pi$
$659$	331.955			0.503726			0.251863	+	0.967763i	$0.418957\pi$
$660$		0			0
$661$	−561.029	−	323.910i	−0.848758	−	0.490031i	0.0114736	−	0.999934i	$-0.496348\pi$
$661$	−561.029	−	323.910i	−0.848758	−	0.490031i	−0.860232	+	0.509904i	$0.829681\pi$
$662$	38.8959	−	67.3697i	0.0587552	−	0.101767i
$663$		0			0
$664$		−	305.418i		−	0.459967i
$665$		0			0
$666$		0			0
$667$	23.2721	+	40.3084i	0.0348907	+	0.0604324i
$668$	352.441	+	203.482i	0.527606	+	0.304613i
$669$		0			0
$670$	359.319	−	207.453i	0.536298	−	0.309632i
$671$		−	877.448i		−	1.30767i
$672$		0			0
$673$	100.956			0.150009			0.0750047	−	0.997183i	$-0.476103\pi$
$673$	100.956			0.150009			0.0750047	+	0.997183i	$0.476103\pi$
$674$	78.9361	+	136.721i	0.117116	+	0.202851i
$675$		0			0
$676$	−138.823	+	240.449i	−0.205360	+	0.355694i
$677$	643.610	−	371.588i	0.950679	−	0.548875i	0.0573873	−	0.998352i	$-0.481723\pi$
$677$	643.610	−	371.588i	0.950679	−	0.548875i	0.893292	+	0.449477i	$0.148390\pi$
$678$		0			0
$679$		0			0
$680$	−121.456			−0.178612
$681$		0			0
$682$	−399.276	−	230.522i	−0.585448	−	0.338009i
$683$	2.21721	−	3.84032i	0.00324628	−	0.00562272i	−0.864398	−	0.502809i	$-0.832300\pi$
$683$	2.21721	−	3.84032i	0.00324628	−	0.00562272i	0.867644	+	0.497186i	$0.165633\pi$
$684$		0			0
$685$			371.881i			0.542892i
$686$		0			0
$687$		0			0
$688$	−12.9706	−	22.4657i	−0.0188526	−	0.0326536i
$689$	−104.802	−	60.5074i	−0.152107	−	0.0878192i
$690$		0			0
$691$	846.253	−	488.584i	1.22468	−	0.707069i	0.258767	−	0.965940i	$-0.416684\pi$
$691$	846.253	−	488.584i	1.22468	−	0.707069i	0.965912	+	0.258871i	$0.0833506\pi$
$692$			141.620i			0.204654i
$693$		0			0
$694$	−533.522			−0.768763
$695$	108.603	+	188.106i	0.156263	+	0.270656i
$696$		0			0
$697$	142.581	−	246.957i	0.204563	−	0.354314i
$698$	−249.889	+	144.274i	−0.358008	+	0.206696i
$699$		0			0
$700$		0			0
$701$	840.177			1.19854			0.599270	−	0.800547i	$-0.295458\pi$
$701$	840.177			1.19854			0.599270	+	0.800547i	$0.295458\pi$
$702$		0			0
$703$	−40.3492	−	23.2956i	−0.0573958	−	0.0331375i
$704$	−52.9706	+	91.7477i	−0.0752423	+	0.130323i
$705$		0			0
$706$			589.835i			0.835460i
$707$		0			0
$708$		0			0
$709$	−341.279	−	591.112i	−0.481352	−	0.833727i	0.518419	−	0.855127i	$-0.326521\pi$
$709$	−341.279	−	591.112i	−0.481352	−	0.833727i	−0.999771	+	0.0214003i	$0.993188\pi$
$710$	−187.831	−	108.444i	−0.264550	−	0.152738i
$711$		0			0
$712$	−411.286	+	237.456i	−0.577649	+	0.333506i
$713$			55.9340i			0.0784488i
$714$		0			0
$715$	230.382			0.322212
$716$	108.816	+	188.475i	0.151978	+	0.263234i
$717$		0			0
$718$	−126.452	+	219.022i	−0.176117	+	0.305044i
$719$	119.187	−	68.8126i	0.165768	−	0.0957060i	−0.414821	−	0.909903i	$-0.636156\pi$
$719$	119.187	−	68.8126i	0.165768	−	0.0957060i	0.580589	+	0.814197i	$0.302822\pi$
$720$		0			0
$721$		0			0
$722$	509.803			0.706099
$723$		0			0
$724$	172.617	+	99.6607i	0.238422	+	0.137653i
$725$	153.338	−	265.589i	0.211501	−	0.366330i
$726$		0			0
$727$		−	264.137i		−	0.363325i	−0.983361	−	0.181662i	$-0.941852\pi$
$727$		−	264.137i		−	0.363325i	0.983361	−	0.181662i	$-0.0581478\pi$
$728$		0			0
$729$		0			0
$730$	293.335	+	508.070i	0.401828	+	0.695987i
$731$	−76.1543	−	43.9677i	−0.104178	−	0.0601474i
$732$		0			0
$733$	−501.705	+	289.660i	−0.684455	+	0.395170i	−0.801531	−	0.597953i	$-0.795981\pi$
$733$	−501.705	+	289.660i	−0.684455	+	0.395170i	0.117077	+	0.993123i	$0.462648\pi$
$734$		−	889.530i		−	1.21189i
$735$		0			0
$736$	12.8528			0.0174631
$737$	−613.397	−	1062.43i	−0.832288	−	1.44157i
$738$		0			0
$739$	99.0477	−	171.556i	0.134029	−	0.232146i	−0.791197	−	0.611562i	$-0.790542\pi$
$739$	99.0477	−	171.556i	0.134029	−	0.232146i	0.925226	+	0.379416i	$0.123875\pi$
$740$	356.220	−	205.664i	0.481379	−	0.277924i
$741$		0			0
$742$		0			0
$743$	−976.690			−1.31452			−0.657261	−	0.753663i	$-0.728285\pi$
$743$	−976.690			−1.31452			−0.657261	+	0.753663i	$0.728285\pi$
$744$		0			0
$745$	−72.3974	−	41.7987i	−0.0971777	−	0.0561056i
$746$	180.707	−	312.994i	0.242235	−	0.419563i
$747$		0			0
$748$			359.120i			0.480107i
$749$		0			0
$750$		0			0
$751$	417.665	+	723.417i	0.556145	+	0.963272i	0.997813	+	0.0660933i	$0.0210535\pi$
$751$	417.665	+	723.417i	0.556145	+	0.963272i	−0.441668	+	0.897178i	$0.645613\pi$
$752$	−165.515	−	95.5600i	−0.220099	−	0.127074i
$753$		0			0
$754$	137.823	−	79.5724i	0.182790	−	0.105534i
$755$		−	425.044i		−	0.562972i
$756$		0			0
$757$	104.221			0.137677			0.0688383	−	0.997628i	$-0.478071\pi$
$757$	104.221			0.137677			0.0688383	+	0.997628i	$0.478071\pi$
$758$	−155.387	−	269.138i	−0.204996	−	0.355063i
$759$		0			0
$760$	3.21320	−	5.56543i	0.00422790	−	0.00732294i
$761$	−473.785	+	273.540i	−0.622583	+	0.359448i	−0.777874	−	0.628420i	$-0.783702\pi$
$761$	−473.785	+	273.540i	−0.622583	+	0.359448i	0.155291	+	0.987869i	$0.450368\pi$
$762$		0			0
$763$		0			0
$764$	−139.809			−0.182996
$765$		0			0
$766$	20.8644	+	12.0461i	0.0272381	+	0.0157259i
$767$	−230.044	+	398.447i	−0.299927	+	0.519488i
$768$		0			0
$769$			341.205i			0.443700i	0.975081	+	0.221850i	$0.0712095\pi$
$769$			341.205i			0.443700i	−0.975081	+	0.221850i	$0.928790\pi$
$770$		0			0
$771$		0			0
$772$	32.3381	+	56.0112i	0.0418887	+	0.0725534i
$773$	−425.213	−	245.497i	−0.550081	−	0.317590i	0.199074	−	0.979985i	$-0.436207\pi$
$773$	−425.213	−	245.497i	−0.550081	−	0.317590i	−0.749155	+	0.662395i	$0.769540\pi$
$774$		0			0
$775$	319.169	−	184.273i	0.411832	−	0.237771i
$776$			72.3557i			0.0932419i
$777$		0			0
$778$	215.272			0.276699
$779$	7.54416	+	13.0669i	0.00968441	+	0.0167739i
$780$		0			0
$781$	−320.647	+	555.376i	−0.410559	+	0.711109i
$782$	37.7315	−	21.7843i	0.0482500	−	0.0278571i
$783$		0			0
$784$		0			0
$785$	717.926			0.914555
$786$		0			0
$787$	−260.202	−	150.228i	−0.330625	−	0.190887i	0.325493	−	0.945544i	$-0.394470\pi$
$787$	−260.202	−	150.228i	−0.330625	−	0.190887i	−0.656119	+	0.754658i	$0.727803\pi$
$788$	277.103	−	479.956i	0.351653	−	0.609081i
$789$		0			0
$790$		−	341.337i		−	0.432072i
$791$		0			0
$792$		0			0
$793$	181.992	+	315.219i	0.229498	+	0.397502i
$794$	−456.489	−	263.554i	−0.574923	−	0.331932i
$795$		0			0
$796$	290.022	−	167.444i	0.364350	−	0.210357i
$797$		−	370.072i		−	0.464331i	−0.972676	−	0.232165i	$-0.925419\pi$
$797$		−	370.072i		−	0.464331i	0.972676	−	0.232165i	$-0.0745811\pi$
$798$		0			0
$799$	−647.860			−0.810838
$800$	−42.3431	−	73.3405i	−0.0529289	−	0.0916756i
$801$		0			0
$802$	460.731	−	798.010i	0.574478	−	0.995025i
$803$	1502.26	−	867.330i	1.87081	−	1.08011i
$804$		0			0
$805$		0			0
$806$	191.251			0.237284
$807$		0			0
$808$	69.8162	+	40.3084i	0.0864062	+	0.0498867i
$809$	245.618	−	425.422i	0.303607	−	0.525862i	−0.673344	−	0.739330i	$-0.735142\pi$
$809$	245.618	−	425.422i	0.303607	−	0.525862i	0.976950	+	0.213468i	$0.0684758\pi$
$810$		0			0
$811$		−	156.802i		−	0.193344i	−0.995316	−	0.0966722i	$-0.969180\pi$
$811$		−	156.802i		−	0.193344i	0.995316	−	0.0966722i	$-0.0308199\pi$
$812$		0			0
$813$		0			0
$814$	−608.106	−	1053.27i	−0.747059	−	1.29394i
$815$	252.262	+	145.643i	0.309524	+	0.178704i
$816$		0			0
$817$	4.02944	−	2.32640i	0.00493199	−	0.00284749i
$818$			754.575i			0.922463i
$819$		0			0
$820$	−133.206			−0.162446
$821$	−215.316	−	372.939i	−0.262261	−	0.454249i	0.704581	−	0.709623i	$-0.251135\pi$
$821$	−215.316	−	372.939i	−0.262261	−	0.454249i	−0.966842	+	0.255374i	$0.917801\pi$
$822$		0			0
$823$	354.371	−	613.788i	0.430584	−	0.745793i	−0.566340	−	0.824172i	$-0.691641\pi$
$823$	354.371	−	613.788i	0.430584	−	0.745793i	0.996924	+	0.0783785i	$0.0249743\pi$
$824$	−138.375	+	79.8907i	−0.167930	+	0.0969547i
$825$		0			0
$826$		0			0
$827$	1460.10			1.76554			0.882770	−	0.469805i	$-0.155676\pi$
$827$	1460.10			1.76554			0.882770	+	0.469805i	$0.155676\pi$
$828$		0			0
$829$	223.095	+	128.804i	0.269113	+	0.155373i	0.628485	−	0.777822i	$-0.283675\pi$
$829$	223.095	+	128.804i	0.269113	+	0.155373i	−0.359371	+	0.933195i	$0.617009\pi$
$830$	−241.809	+	418.826i	−0.291336	+	0.504609i
$831$		0			0
$832$		−	43.9466i		−	0.0528204i
$833$		0			0
$834$		0			0
$835$	−322.206	−	558.077i	−0.385876	−	0.668356i
$836$	−16.4558	−	9.50079i	−0.0196840	−	0.0113646i
$837$		0			0
$838$	−654.323	+	377.774i	−0.780815	+	0.450804i
$839$		−	213.621i		−	0.254613i	−0.991863	−	0.127307i	$-0.959367\pi$
$839$		−	213.621i		−	0.254613i	0.991863	−	0.127307i	$-0.0406332\pi$
$840$		0			0
$841$	−421.353			−0.501015
$842$	−111.172	−	192.555i	−0.132033	−	0.228687i
$843$		0			0
$844$	128.073	−	221.829i	0.151745	−	0.262831i
$845$	380.743	−	219.822i	0.450583	−	0.260144i
$846$		0			0
$847$		0			0
$848$	−88.1177			−0.103912
$849$		0			0
$850$	−248.610	−	143.535i	−0.292483	−	0.168865i
$851$	−73.7756	+	127.783i	−0.0866929	+	0.150156i
$852$		0			0
$853$			1127.37i			1.32165i	0.750539	+	0.660826i	$0.229794\pi$
$853$			1127.37i			1.32165i	−0.750539	+	0.660826i	$0.770206\pi$
$854$		0			0
$855$		0			0
$856$	67.3310	+	116.621i	0.0786577	+	0.136239i
$857$	1100.22	+	635.212i	1.28380	+	0.741204i	0.977541	−	0.210744i	$-0.0675885\pi$
$857$	1100.22	+	635.212i	1.28380	+	0.741204i	0.306261	+	0.951947i	$0.400922\pi$
$858$		0			0
$859$	221.488	−	127.876i	0.257844	−	0.148867i	−0.365506	−	0.930809i	$-0.619104\pi$
$859$	221.488	−	127.876i	0.257844	−	0.148867i	0.623351	+	0.781942i	$0.285771\pi$
$860$			41.0768i			0.0477638i
$861$		0			0
$862$	323.199			0.374941
$863$	557.364	+	965.382i	0.645844	+	1.11863i	0.984106	+	0.177583i	$0.0568278\pi$
$863$	557.364	+	965.382i	0.645844	+	1.11863i	−0.338262	+	0.941052i	$0.609839\pi$
$864$		0			0
$865$	112.125	−	194.207i	0.129625	−	0.224516i
$866$	−58.2426	+	33.6264i	−0.0672548	+	0.0388296i
$867$		0			0
$868$		0			0
$869$	−1009.26			−1.16141
$870$		0			0
$871$	440.720	+	254.450i	0.505993	+	0.292135i
$872$	−106.503	+	184.468i	−0.122136	+	0.211546i
$873$		0			0
$874$			2.30528i			0.00263762i
$875$		0			0
$876$		0			0
$877$	550.904	+	954.194i	0.628169	+	1.08802i	0.987919	+	0.154972i	$0.0495286\pi$
$877$	550.904	+	954.194i	0.628169	+	1.08802i	−0.359750	+	0.933049i	$0.617138\pi$
$878$	−90.4523	−	52.2226i	−0.103021	−	0.0594791i
$879$		0			0
$880$	145.279	−	83.8770i	0.165090	−	0.0953148i
$881$			217.067i			0.246387i	0.992383	+	0.123194i	$0.0393136\pi$
$881$			217.067i			0.246387i	−0.992383	+	0.123194i	$0.960686\pi$
$882$		0			0
$883$	−516.544			−0.584988			−0.292494	−	0.956267i	$-0.594485\pi$
$883$	−516.544			−0.584988			−0.292494	+	0.956267i	$0.594485\pi$
$884$	−74.4853	−	129.012i	−0.0842594	−	0.145942i
$885$		0			0
$886$	165.915	−	287.374i	0.187263	−	0.324350i
$887$	−978.445	+	564.905i	−1.10309	+	0.636872i	−0.937032	−	0.349243i	$-0.886439\pi$
$887$	−978.445	+	564.905i	−1.10309	+	0.636872i	−0.166062	+	0.986115i	$0.553105\pi$
$888$		0			0
$889$		0			0
$890$	752.007			0.844952
$891$		0			0
$892$	722.558	+	417.169i	0.810043	+	0.467679i
$893$	17.1396	−	29.6867i	0.0191933	−	0.0332438i
$894$		0			0
$895$		−	344.613i		−	0.385043i
$896$		0			0
$897$		0			0
$898$	−180.426	−	312.508i	−0.200920	−	0.348004i
$899$	436.742	+	252.153i	0.485809	+	0.280482i
$900$		0			0
$901$	−258.684	+	149.351i	−0.287107	+	0.165762i
$902$			393.863i			0.436655i
$903$		0			0
$904$	−241.706			−0.267373
$905$	−157.809	−	273.333i	−0.174375	−	0.302026i
$906$		0			0
$907$	−30.0111	+	51.9808i	−0.0330884	+	0.0573107i	−0.882095	−	0.471071i	$-0.843868\pi$
$907$	−30.0111	+	51.9808i	−0.0330884	+	0.0573107i	0.849007	+	0.528382i	$0.177201\pi$
$908$	−402.286	+	232.260i	−0.443047	+	0.255793i
$909$		0			0
$910$		0			0
$911$	−1422.25			−1.56120			−0.780598	−	0.625033i	$-0.785085\pi$
$911$	−1422.25			−1.56120			−0.780598	+	0.625033i	$0.785085\pi$
$912$		0			0
$913$	1238.38	+	714.980i	1.35639	+	0.783111i
$914$	103.050	−	178.488i	0.112746	−	0.195283i
$915$		0			0
$916$			167.244i			0.182581i
$917$		0			0
$918$		0			0
$919$	−834.849	−	1446.00i	−0.908432	−	1.57345i	−0.816243	−	0.577708i	$-0.803947\pi$
$919$	−834.849	−	1446.00i	−0.908432	−	1.57345i	−0.0921886	−	0.995742i	$-0.529386\pi$
$920$	−17.6253	−	10.1760i	−0.0191580	−	0.0110609i
$921$		0			0
$922$	1087.98	−	628.144i	1.18002	−	0.681284i
$923$		−	266.022i		−	0.288215i
$924$		0			0
$925$	972.205			1.05103
$926$	−165.473	−	286.608i	−0.178697	−	0.309512i
$927$		0			0
$928$	57.9411	−	100.357i	0.0624366	−	0.108143i
$929$	839.058	−	484.430i	0.903184	−	0.521453i	0.0249519	−	0.999689i	$-0.492057\pi$
$929$	839.058	−	484.430i	0.903184	−	0.521453i	0.878232	+	0.478235i	$0.158723\pi$
$930$		0			0
$931$		0			0
$932$	−438.146			−0.470114
$933$		0			0
$934$	−963.407	−	556.223i	−1.03148	−	0.595528i
$935$	284.327	−	492.469i	0.304093	−	0.526705i
$936$		0			0
$937$		−	1212.57i		−	1.29410i	−0.762449	−	0.647049i	$-0.776003\pi$
$937$		−	1212.57i		−	1.29410i	0.762449	−	0.647049i	$-0.223997\pi$
$938$		0			0
$939$		0			0
$940$	151.316	+	262.087i	0.160974	+	0.278816i
$941$	−1293.90	−	747.032i	−1.37502	−	0.793870i	−0.383468	−	0.923554i	$-0.625270\pi$
$941$	−1293.90	−	747.032i	−1.37502	−	0.793870i	−0.991555	+	0.129684i	$0.958604\pi$
$942$		0			0
$943$	41.3818	−	23.8918i	0.0438832	−	0.0253360i
$944$			335.016i			0.354889i
$945$		0			0
$946$	121.456			0.128389
$947$	387.731	+	671.570i	0.409431	+	0.709155i	0.994826	−	0.101593i	$-0.0323939\pi$
$947$	387.731	+	671.570i	0.409431	+	0.709155i	−0.585395	+	0.810748i	$0.699061\pi$
$948$		0			0
$949$	−359.787	+	623.169i	−0.379122	+	0.656659i
$950$	13.1543	−	7.59466i	0.0138467	−	0.00799437i
$951$		0			0
$952$		0			0
$953$	−1055.40			−1.10745			−0.553723	−	0.832701i	$-0.686794\pi$
$953$	−1055.40			−1.10745			−0.553723	+	0.832701i	$0.686794\pi$
$954$		0			0
$955$	191.723	+	110.691i	0.200757	+	0.115907i
$956$	193.103	−	334.464i	0.201990	−	0.349857i
$957$		0			0
$958$		−	1042.18i		−	1.08787i
$959$		0			0
$960$		0			0
$961$	−177.477	−	307.400i	−0.184680	−	0.319875i
$962$	436.919	+	252.255i	0.454178	+	0.262220i
$963$		0			0
$964$	85.7939	−	49.5332i	0.0889979	−	0.0513829i
$965$		−	102.412i		−	0.106127i
$966$		0			0
$967$	1221.63			1.26332			0.631661	−	0.775245i	$-0.282373\pi$
$967$	1221.63			1.26332			0.631661	+	0.775245i	$0.282373\pi$
$968$	−76.8873	−	133.173i	−0.0794290	−	0.137575i
$969$		0			0
$970$	57.2864	−	99.2229i	0.0590581	−	0.102292i
$971$	−455.753	+	263.129i	−0.469365	+	0.270988i	−0.715974	−	0.698127i	$-0.754017\pi$
$971$	−455.753	+	263.129i	−0.469365	+	0.270988i	0.246609	+	0.969115i	$0.420684\pi$
$972$		0			0
$973$		0			0
$974$	382.825			0.393045
$975$		0			0
$976$	229.529	+	132.519i	0.235173	+	0.135777i
$977$	−500.051	+	866.114i	−0.511823	+	0.886504i	0.488083	+	0.872797i	$0.337696\pi$
$977$	−500.051	+	866.114i	−0.511823	+	0.886504i	−0.999906	+	0.0137065i	$0.995637\pi$
$978$		0			0
$979$		−	2223.53i		−	2.27123i
$980$		0			0
$981$		0			0
$982$	537.515	+	931.003i	0.547367	+	0.948068i
$983$	931.584	+	537.850i	0.947695	+	0.547152i	0.892364	−	0.451316i	$-0.149045\pi$
$983$	931.584	+	537.850i	0.947695	+	0.547152i	0.0553306	+	0.998468i	$0.482379\pi$
$984$		0			0
$985$	−759.993	+	438.782i	−0.771566	+	0.445464i
$986$		−	392.819i		−	0.398396i
$987$		0			0
$988$	7.88225			0.00797799
$989$	−7.36753	−	12.7609i	−0.00744948	−	0.0129029i
$990$		0			0
$991$	938.017	−	1624.69i	0.946536	−	1.63945i	0.193891	−	0.981023i	$-0.437889\pi$
$991$	938.017	−	1624.69i	0.946536	−	1.63945i	0.752646	−	0.658426i	$-0.228777\pi$
$992$	120.603	−	69.6302i	0.121576	−	0.0701917i
$993$		0			0
$994$		0			0
$995$	−530.285			−0.532949
$996$		0			0
$997$	−504.221	−	291.112i	−0.505738	−	0.291988i	0.225342	−	0.974280i	$-0.427650\pi$
$997$	−504.221	−	291.112i	−0.505738	−	0.291988i	−0.731080	+	0.682292i	$0.760983\pi$
$998$	−88.7365	+	153.696i	−0.0889144	+	0.154004i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.3.n.b.325.1		4
3.2	odd	2		98.3.d.a.31.2		4
7.2	even	3		126.3.n.c.19.1		4
7.3	odd	6		882.3.c.f.685.3		4
7.4	even	3		882.3.c.f.685.4		4
7.5	odd	6	inner	882.3.n.b.19.1		4
7.6	odd	2		126.3.n.c.73.1		4
12.11	even	2		784.3.s.c.129.1		4
21.2	odd	6		14.3.d.a.5.2	yes	4
21.5	even	6		98.3.d.a.19.2		4
21.11	odd	6		98.3.b.b.97.1		4
21.17	even	6		98.3.b.b.97.2		4
21.20	even	2		14.3.d.a.3.2	✓	4
28.23	odd	6		1008.3.cg.l.145.1		4
28.27	even	2		1008.3.cg.l.577.1		4
84.11	even	6		784.3.c.e.97.4		4
84.23	even	6		112.3.s.b.33.2		4
84.47	odd	6		784.3.s.c.705.1		4
84.59	odd	6		784.3.c.e.97.1		4
84.83	odd	2		112.3.s.b.17.2		4
105.2	even	12		350.3.i.a.299.4		8
105.23	even	12		350.3.i.a.299.1		8
105.44	odd	6		350.3.k.a.201.1		4
105.62	odd	4		350.3.i.a.199.1		8
105.83	odd	4		350.3.i.a.199.4		8
105.104	even	2		350.3.k.a.101.1		4
168.83	odd	2		448.3.s.c.129.1		4
168.107	even	6		448.3.s.c.257.1		4
168.125	even	2		448.3.s.d.129.2		4
168.149	odd	6		448.3.s.d.257.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.3.d.a.3.2	✓	4	21.20	even	2
14.3.d.a.5.2	yes	4	21.2	odd	6
98.3.b.b.97.1		4	21.11	odd	6
98.3.b.b.97.2		4	21.17	even	6
98.3.d.a.19.2		4	21.5	even	6
98.3.d.a.31.2		4	3.2	odd	2
112.3.s.b.17.2		4	84.83	odd	2
112.3.s.b.33.2		4	84.23	even	6
126.3.n.c.19.1		4	7.2	even	3
126.3.n.c.73.1		4	7.6	odd	2
350.3.i.a.199.1		8	105.62	odd	4
350.3.i.a.199.4		8	105.83	odd	4
350.3.i.a.299.1		8	105.23	even	12
350.3.i.a.299.4		8	105.2	even	12
350.3.k.a.101.1		4	105.104	even	2
350.3.k.a.201.1		4	105.44	odd	6
448.3.s.c.129.1		4	168.83	odd	2
448.3.s.c.257.1		4	168.107	even	6
448.3.s.d.129.2		4	168.125	even	2
448.3.s.d.257.2		4	168.149	odd	6
784.3.c.e.97.1		4	84.59	odd	6
784.3.c.e.97.4		4	84.11	even	6
784.3.s.c.129.1		4	12.11	even	2
784.3.s.c.705.1		4	84.47	odd	6
882.3.c.f.685.3		4	7.3	odd	6
882.3.c.f.685.4		4	7.4	even	3
882.3.n.b.19.1		4	7.5	odd	6	inner
882.3.n.b.325.1		4	1.1	even	1	trivial
1008.3.cg.l.145.1		4	28.23	odd	6
1008.3.cg.l.577.1		4	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	882.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(2.74264 - 1.58346i) q^{5} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(2.74264 - 1.58346i) q^{5} +2.82843 q^{8} +(-3.87868 - 2.23936i) q^{10} +(-6.62132 + 11.4685i) q^{11} -5.49333i q^{13} +(-2.00000 - 3.46410i) q^{16} +(-11.7426 - 6.77962i) q^{17} +(0.621320 - 0.358719i) q^{19} +6.33386i q^{20} +18.7279 q^{22} +(-1.13604 - 1.96768i) q^{23} +(-7.48528 + 12.9649i) q^{25} +(-6.72792 + 3.88437i) q^{26} -20.4853 q^{29} +(-21.3198 - 12.3090i) q^{31} +(-2.82843 + 4.89898i) q^{32} +19.1757i q^{34} +(-32.4706 - 56.2407i) q^{37} +(-0.878680 - 0.507306i) q^{38} +(7.75736 - 4.47871i) q^{40} +21.0308i q^{41} +6.48528 q^{43} +(-13.2426 - 22.9369i) q^{44} +(-1.60660 + 2.78272i) q^{46} +(41.3787 - 23.8900i) q^{47} +21.1716 q^{50} +(9.51472 + 5.49333i) q^{52} +(11.0147 - 19.0781i) q^{53} +41.9385i q^{55} +(14.4853 + 25.0892i) q^{58} +(-72.5330 - 41.8770i) q^{59} +(-57.3823 + 33.1297i) q^{61} +34.8151i q^{62} +8.00000 q^{64} +(-8.69848 - 15.0662i) q^{65} +(-46.3198 + 80.2283i) q^{67} +(23.4853 - 13.5592i) q^{68} +48.4264 q^{71} +(-113.441 - 65.4953i) q^{73} +(-45.9203 + 79.5363i) q^{74} +1.43488i q^{76} +(38.1066 + 66.0026i) q^{79} +(-10.9706 - 6.33386i) q^{80} +(25.7574 - 14.8710i) q^{82} -107.981i q^{83} -42.9411 q^{85} +(-4.58579 - 7.94282i) q^{86} +(-18.7279 + 32.4377i) q^{88} +(-145.412 + 83.9535i) q^{89} +4.54416 q^{92} +(-58.5183 - 33.7856i) q^{94} +(1.13604 - 1.96768i) q^{95} +25.5816i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 6 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 - 6 * q^5	\( 4 q - 4 q^{4} - 6 q^{5} - 24 q^{10} - 18 q^{11} - 8 q^{16} - 30 q^{17} - 6 q^{19} + 24 q^{22} - 30 q^{23} + 4 q^{25} + 24 q^{26} - 48 q^{29} + 42 q^{31} - 62 q^{37} - 12 q^{38} + 48 q^{40} - 8 q^{43} - 36 q^{44} + 36 q^{46} + 174 q^{47} + 96 q^{50} + 72 q^{52} + 78 q^{53} + 24 q^{58} - 78 q^{59} + 42 q^{61} + 32 q^{64} + 84 q^{65} - 58 q^{67} + 60 q^{68} + 24 q^{71} - 318 q^{73} - 96 q^{74} + 110 q^{79} + 24 q^{80} + 120 q^{82} - 36 q^{85} - 24 q^{86} - 24 q^{88} - 378 q^{89} + 120 q^{92} + 12 q^{94} + 30 q^{95}+O(q^{100}) \) 4 * q - 4 * q^4 - 6 * q^5 - 24 * q^10 - 18 * q^11 - 8 * q^16 - 30 * q^17 - 6 * q^19 + 24 * q^22 - 30 * q^23 + 4 * q^25 + 24 * q^26 - 48 * q^29 + 42 * q^31 - 62 * q^37 - 12 * q^38 + 48 * q^40 - 8 * q^43 - 36 * q^44 + 36 * q^46 + 174 * q^47 + 96 * q^50 + 72 * q^52 + 78 * q^53 + 24 * q^58 - 78 * q^59 + 42 * q^61 + 32 * q^64 + 84 * q^65 - 58 * q^67 + 60 * q^68 + 24 * q^71 - 318 * q^73 - 96 * q^74 + 110 * q^79 + 24 * q^80 + 120 * q^82 - 36 * q^85 - 24 * q^86 - 24 * q^88 - 378 * q^89 + 120 * q^92 + 12 * q^94 + 30 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more