LMFDB - Embedded newform 441.3.k.a.313.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,3,Mod(31,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("441.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	441.k (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:	$12.0163796583$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			313.1
Character	$\chi$	$=$	441.313
Dual form			441.3.k.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85100 - 3.20603i) q^{2} +(-2.30657 + 1.91826i) q^{3} +(-4.85242 + 8.40464i) q^{4} +5.48291i q^{5} +(10.4195 + 3.84424i) q^{6} +21.1194 q^{8} +(1.64056 - 8.84921i) q^{9} +O(q^{10})$	\(q+(-1.85100 - 3.20603i) q^{2} +(-2.30657 + 1.91826i) q^{3} +(-4.85242 + 8.40464i) q^{4} +5.48291i q^{5} +(10.4195 + 3.84424i) q^{6} +21.1194 q^{8} +(1.64056 - 8.84921i) q^{9} +(17.5784 - 10.1489i) q^{10} -2.38890 q^{11} +(-4.92983 - 28.6941i) q^{12} +(9.84037 - 5.68134i) q^{13} +(-10.5176 - 12.6467i) q^{15} +(-19.6823 - 34.0908i) q^{16} +(1.48995 - 0.860221i) q^{17} +(-31.4075 + 11.1202i) q^{18} +(24.0929 + 13.9100i) q^{19} +(-46.0819 - 26.6054i) q^{20} +(4.42186 + 7.65888i) q^{22} -7.21566 q^{23} +(-48.7134 + 40.5124i) q^{24} -5.06228 q^{25} +(-36.4291 - 21.0324i) q^{26} +(13.1910 + 23.5584i) q^{27} +(-13.1522 + 22.7804i) q^{29} +(-21.0776 + 57.1290i) q^{30} +(13.0212 + 7.51777i) q^{31} +(-30.6253 + 53.0446i) q^{32} +(5.51017 - 4.58253i) q^{33} +(-5.51579 - 3.18454i) q^{34} +(66.4138 + 56.7284i) q^{36} +(-33.8598 + 58.6469i) q^{37} -102.990i q^{38} +(-11.7992 + 31.9808i) q^{39} +115.796i q^{40} +(-32.1822 + 18.5804i) q^{41} +(5.46479 - 9.46530i) q^{43} +(11.5919 - 20.0778i) q^{44} +(48.5194 + 8.99502i) q^{45} +(13.3562 + 23.1336i) q^{46} +(-0.847241 + 0.489155i) q^{47} +(110.794 + 40.8770i) q^{48} +(9.37029 + 16.2298i) q^{50} +(-1.78654 + 4.84226i) q^{51} +110.273i q^{52} +(-34.6044 - 59.9366i) q^{53} +(51.1122 - 85.8975i) q^{54} -13.0981i q^{55} +(-82.2551 + 14.1319i) q^{57} +97.3794 q^{58} +(-40.0948 - 23.1487i) q^{59} +(157.327 - 27.0298i) q^{60} +(-44.2780 + 25.5639i) q^{61} -55.6616i q^{62} +69.2916 q^{64} +(31.1503 + 53.9539i) q^{65} +(-24.8911 - 9.18349i) q^{66} +(20.5315 - 35.5615i) q^{67} +16.6966i q^{68} +(16.6434 - 13.8415i) q^{69} -6.30166 q^{71} +(34.6475 - 186.890i) q^{72} +(-56.9373 + 32.8728i) q^{73} +250.698 q^{74} +(11.6765 - 9.71077i) q^{75} +(-233.818 + 134.995i) q^{76} +(124.372 - 21.3679i) q^{78} +(18.0441 + 31.2532i) q^{79} +(186.917 - 107.916i) q^{80} +(-75.6172 - 29.0353i) q^{81} +(119.139 + 68.7847i) q^{82} +(17.7570 + 10.2520i) q^{83} +(4.71651 + 8.16923i) q^{85} -40.4614 q^{86} +(-13.3620 - 77.7740i) q^{87} -50.4520 q^{88} +(-79.1776 - 45.7132i) q^{89} +(-60.9713 - 172.205i) q^{90} +(35.0134 - 60.6450i) q^{92} +(-44.4553 + 7.63769i) q^{93} +(3.13649 + 1.81085i) q^{94} +(-76.2675 + 132.099i) q^{95} +(-31.1138 - 181.099i) q^{96} +(122.345 + 70.6360i) q^{97} +(-3.91912 + 21.1399i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9	$ 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9} - 8 q^{11} - 54 q^{15} - 42 q^{16} - 138 q^{18} + 14 q^{22} - 8 q^{23} - 56 q^{25} - 38 q^{29} - 294 q^{30} - 168 q^{32} + 234 q^{36} - 18 q^{37} + 84 q^{39} - 66 q^{43} - 54 q^{44} + 20 q^{46} + 196 q^{50} + 318 q^{51} - 260 q^{53} - 198 q^{57} + 68 q^{58} + 366 q^{60} + 72 q^{64} - 102 q^{65} + 68 q^{67} - 332 q^{71} + 714 q^{72} + 1232 q^{74} - 168 q^{78} + 146 q^{79} - 516 q^{81} + 78 q^{85} + 680 q^{86} + 148 q^{88} + 606 q^{92} - 1146 q^{93} - 360 q^{95} + 900 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9 - 8 * q^11 - 54 * q^15 - 42 * q^16 - 138 * q^18 + 14 * q^22 - 8 * q^23 - 56 * q^25 - 38 * q^29 - 294 * q^30 - 168 * q^32 + 234 * q^36 - 18 * q^37 + 84 * q^39 - 66 * q^43 - 54 * q^44 + 20 * q^46 + 196 * q^50 + 318 * q^51 - 260 * q^53 - 198 * q^57 + 68 * q^58 + 366 * q^60 + 72 * q^64 - 102 * q^65 + 68 * q^67 - 332 * q^71 + 714 * q^72 + 1232 * q^74 - 168 * q^78 + 146 * q^79 - 516 * q^81 + 78 * q^85 + 680 * q^86 + 148 * q^88 + 606 * q^92 - 1146 * q^93 - 360 * q^95 + 900 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.85100	−	3.20603i	−0.925501	−	1.60302i	−0.790753	−	0.612136i	$-0.790311\pi$
$2$	−1.85100	−	3.20603i	−0.925501	−	1.60302i	−0.134749	−	0.990880i	$-0.543023\pi$
$3$	−2.30657	+	1.91826i	−0.768858	+	0.639420i
$3$	−2.30657	+	1.91826i	−0.768858	+	0.639420i
$4$	−4.85242	+	8.40464i	−1.21311	+	2.10116i
$5$			5.48291i			1.09658i	0.836288	+	0.548291i	$0.184721\pi$
$5$			5.48291i			1.09658i	−0.836288	+	0.548291i	$0.815279\pi$
$6$	10.4195	+	3.84424i	1.73658	+	0.640706i
$7$		0			0
$7$		0			0
$8$	21.1194			2.63992
$9$	1.64056	−	8.84921i	0.182284	−	0.983246i
$10$	17.5784	−	10.1489i	1.75784	−	1.01489i
$11$	−2.38890			−0.217173			−0.108586	−	0.994087i	$-0.534632\pi$
$11$	−2.38890			−0.217173			−0.108586	+	0.994087i	$0.534632\pi$
$12$	−4.92983	−	28.6941i	−0.410819	−	2.39118i
$13$	9.84037	−	5.68134i	0.756952	−	0.437026i	−0.0712485	−	0.997459i	$-0.522698\pi$
$13$	9.84037	−	5.68134i	0.756952	−	0.437026i	0.828200	+	0.560432i	$0.189365\pi$
$14$		0			0
$15$	−10.5176	−	12.6467i	−0.701176	−	0.843115i
$16$	−19.6823	−	34.0908i	−1.23014	−	2.13067i
$17$	1.48995	−	0.860221i	0.0876439	−	0.0506012i	−0.455538	−	0.890217i	$-0.650553\pi$
$17$	1.48995	−	0.860221i	0.0876439	−	0.0506012i	0.543181	+	0.839615i	$0.317220\pi$
$18$	−31.4075	+	11.1202i	−1.74486	+	0.617791i
$19$	24.0929	+	13.9100i	1.26805	+	0.732108i	0.974618	−	0.223873i	$-0.0718701\pi$
$19$	24.0929	+	13.9100i	1.26805	+	0.732108i	0.293429	+	0.955981i	$0.405203\pi$
$20$	−46.0819	−	26.6054i	−2.30409	−	1.33027i
$21$		0			0
$22$	4.42186	+	7.65888i	0.200993	+	0.348131i
$23$	−7.21566			−0.313724			−0.156862	−	0.987621i	$-0.550138\pi$
$23$	−7.21566			−0.313724			−0.156862	+	0.987621i	$0.550138\pi$
$24$	−48.7134	+	40.5124i	−2.02972	+	1.68802i
$25$	−5.06228			−0.202491
$26$	−36.4291	−	21.0324i	−1.40112	−	0.808937i
$27$	13.1910	+	23.5584i	0.488557	+	0.872532i
$28$		0			0
$29$	−13.1522	+	22.7804i	−0.453526	+	0.785530i	−0.998602	−	0.0528567i	$-0.983167\pi$
$29$	−13.1522	+	22.7804i	−0.453526	+	0.785530i	0.545076	+	0.838386i	$0.316501\pi$
$30$	−21.0776	+	57.1290i	−0.702587	+	1.90430i
$31$	13.0212	+	7.51777i	0.420037	+	0.242509i	0.695093	−	0.718920i	$-0.255363\pi$
$31$	13.0212	+	7.51777i	0.420037	+	0.242509i	−0.275056	+	0.961428i	$0.588696\pi$
$32$	−30.6253	+	53.0446i	−0.957041	+	1.65764i
$33$	5.51017	−	4.58253i	0.166975	−	0.138864i
$34$	−5.51579	−	3.18454i	−0.162229	−	0.0936630i
$35$		0			0
$36$	66.4138	+	56.7284i	1.84483	+	1.57579i
$37$	−33.8598	+	58.6469i	−0.915130	+	1.58505i	−0.108419	+	0.994105i	$0.534579\pi$
$37$	−33.8598	+	58.6469i	−0.915130	+	1.58505i	−0.806711	+	0.590946i	$0.798755\pi$
$38$		−	102.990i		−	2.71027i
$39$	−11.7992	+	31.9808i	−0.302545	+	0.820021i
$40$			115.796i			2.89489i
$41$	−32.1822	+	18.5804i	−0.784931	+	0.453180i	−0.838175	−	0.545401i	$-0.816377\pi$
$41$	−32.1822	+	18.5804i	−0.784931	+	0.453180i	0.0532441	+	0.998582i	$0.483044\pi$
$42$		0			0
$43$	5.46479	−	9.46530i	0.127088	−	0.220123i	−0.795459	−	0.606007i	$-0.792770\pi$
$43$	5.46479	−	9.46530i	0.127088	−	0.220123i	0.922547	+	0.385884i	$0.126104\pi$
$44$	11.5919	−	20.0778i	0.263453	−	0.456314i
$45$	48.5194	+	8.99502i	1.07821	+	0.199889i
$46$	13.3562	+	23.1336i	0.290352	+	0.502905i
$47$	−0.847241	+	0.489155i	−0.0180264	+	0.0104076i	−0.508986	−	0.860775i	$-0.669980\pi$
$47$	−0.847241	+	0.489155i	−0.0180264	+	0.0104076i	0.490960	+	0.871182i	$0.336646\pi$
$48$	110.794	+	40.8770i	2.30820	+	0.851605i
$49$		0			0
$50$	9.37029	+	16.2298i	0.187406	+	0.324596i
$51$	−1.78654	+	4.84226i	−0.0350302	+	0.0949464i
$52$			110.273i			2.12064i
$53$	−34.6044	−	59.9366i	−0.652913	−	1.13088i	−0.982413	−	0.186723i	$-0.940213\pi$
$53$	−34.6044	−	59.9366i	−0.652913	−	1.13088i	0.329499	−	0.944156i	$-0.393120\pi$
$54$	51.1122	−	85.8975i	0.946522	−	1.59069i
$55$		−	13.0981i		−	0.238147i
$56$		0			0
$57$	−82.2551	+	14.1319i	−1.44307	+	0.247929i
$58$	97.3794			1.67896
$59$	−40.0948	−	23.1487i	−0.679572	−	0.392351i	0.120122	−	0.992759i	$-0.461672\pi$
$59$	−40.0948	−	23.1487i	−0.679572	−	0.392351i	−0.799694	+	0.600408i	$0.795005\pi$
$60$	157.327	−	27.0298i	2.62212	−	0.450496i
$61$	−44.2780	+	25.5639i	−0.725869	+	0.419081i	−0.816909	−	0.576766i	$-0.804314\pi$
$61$	−44.2780	+	25.5639i	−0.725869	+	0.419081i	0.0910399	+	0.995847i	$0.470981\pi$
$62$		−	55.6616i		−	0.897768i
$63$		0			0
$64$	69.2916			1.08268
$65$	31.1503	+	53.9539i	0.479235	+	0.830059i
$66$	−24.8911	−	9.18349i	−0.377137	−	0.139144i
$67$	20.5315	−	35.5615i	0.306440	−	0.530769i	−0.671141	−	0.741330i	$-0.734196\pi$
$67$	20.5315	−	35.5615i	0.306440	−	0.530769i	0.977581	+	0.210560i	$0.0675289\pi$
$68$			16.6966i			0.245538i
$69$	16.6434	−	13.8415i	0.241209	−	0.200602i
$70$		0			0
$71$	−6.30166			−0.0887557			−0.0443779	−	0.999015i	$-0.514131\pi$
$71$	−6.30166			−0.0887557			−0.0443779	+	0.999015i	$0.514131\pi$
$72$	34.6475	−	186.890i	0.481215	−	2.59569i
$73$	−56.9373	+	32.8728i	−0.779963	+	0.450312i	−0.836417	−	0.548093i	$-0.815354\pi$
$73$	−56.9373	+	32.8728i	−0.779963	+	0.450312i	0.0564539	+	0.998405i	$0.482021\pi$
$74$	250.698			3.38782
$75$	11.6765	−	9.71077i	0.155687	−	0.129477i
$76$	−233.818	+	134.995i	−3.07655	+	1.77625i
$77$		0			0
$78$	124.372	−	21.3679i	1.59451	−	0.273947i
$79$	18.0441	+	31.2532i	0.228406	+	0.395611i	0.957336	−	0.288978i	$-0.0933153\pi$
$79$	18.0441	+	31.2532i	0.228406	+	0.395611i	−0.728930	+	0.684588i	$0.759982\pi$
$80$	186.917	−	107.916i	2.33646	−	1.34895i
$81$	−75.6172	−	29.0353i	−0.933545	−	0.358460i
$82$	119.139	+	68.7847i	1.45291	+	0.838837i
$83$	17.7570	+	10.2520i	0.213940	+	0.123518i	0.603141	−	0.797635i	$-0.293916\pi$
$83$	17.7570	+	10.2520i	0.213940	+	0.123518i	−0.389201	+	0.921153i	$0.627249\pi$
$84$		0			0
$85$	4.71651	+	8.16923i	0.0554884	+	0.0961086i
$86$	−40.4614			−0.470481
$87$	−13.3620	−	77.7740i	−0.153587	−	0.893954i
$88$	−50.4520			−0.573318
$89$	−79.1776	−	45.7132i	−0.889636	−	0.513631i	−0.0158125	−	0.999875i	$-0.505033\pi$
$89$	−79.1776	−	45.7132i	−0.889636	−	0.513631i	−0.873823	+	0.486243i	$0.838367\pi$
$90$	−60.9713	−	172.205i	−0.677459	−	1.91338i
$91$		0			0
$92$	35.0134	−	60.6450i	0.380581	−	0.659185i
$93$	−44.4553	+	7.63769i	−0.478014	+	0.0821257i
$94$	3.13649	+	1.81085i	0.0333669	+	0.0192644i
$95$	−76.2675	+	132.099i	−0.802816	+	1.39052i
$96$	−31.1138	−	181.099i	−0.324102	−	1.88644i
$97$	122.345	+	70.6360i	1.26129	+	0.728206i	0.973324	−	0.229434i	$-0.0736876\pi$
$97$	122.345	+	70.6360i	1.26129	+	0.728206i	0.287966	+	0.957641i	$0.407021\pi$
$98$		0			0
$99$	−3.91912	+	21.1399i	−0.0395871	+	0.213534i
$100$	24.5643	−	42.5466i	0.245643	−	0.425466i
$101$			165.870i			1.64228i	0.570729	+	0.821138i	$0.306661\pi$
$101$			165.870i			1.64228i	−0.570729	+	0.821138i	$0.693339\pi$
$102$	18.8313	−	3.23534i	0.184621	−	0.0317190i
$103$		−	4.76731i		−	0.0462846i	−0.999732	−	0.0231423i	$-0.992633\pi$
$103$		−	4.76731i		−	0.0462846i	0.999732	−	0.0231423i	$-0.00736708\pi$
$104$	207.822	−	119.986i	1.99829	−	1.15371i
$105$		0			0
$106$	−128.106	+	221.886i	−1.20854	+	2.09326i
$107$	−8.06624	+	13.9711i	−0.0753854	+	0.130571i	−0.901254	−	0.433292i	$-0.857352\pi$
$107$	−8.06624	+	13.9711i	−0.0753854	+	0.130571i	0.825868	+	0.563863i	$0.190685\pi$
$108$	−262.008	−	3.44924i	−2.42600	−	0.0319374i
$109$	53.1099	+	91.9890i	0.487247	+	0.843936i	0.999892	−	0.0146642i	$-0.00466792\pi$
$109$	53.1099	+	91.9890i	0.487247	+	0.843936i	−0.512646	+	0.858600i	$0.671335\pi$
$110$	−41.9929	+	24.2446i	−0.381754	+	0.220406i
$111$	−34.3999	−	200.225i	−0.309909	−	1.80383i
$112$		0			0
$113$	−36.9415	−	63.9845i	−0.326916	−	0.566235i	0.654982	−	0.755644i	$-0.272676\pi$
$113$	−36.9415	−	63.9845i	−0.326916	−	0.566235i	−0.981898	+	0.189409i	$0.939343\pi$
$114$	197.562	+	237.554i	1.73300	+	2.08381i
$115$		−	39.5628i		−	0.344024i
$116$	−127.641	−	221.080i	−1.10035	−	1.90586i
$117$	−34.1317	−	96.4001i	−0.291724	−	0.823933i
$118$			171.393i			1.45249i
$119$		0			0
$120$	−222.126	−	267.091i	−1.85105	−	2.22576i
$121$	−115.293			−0.952836
$122$	163.917	+	94.6378i	1.34359	+	0.775720i
$123$	38.5885	−	104.591i	0.313728	−	0.850331i
$124$	−126.368	+	72.9588i	−1.01910	+	0.588377i
$125$			109.317i			0.874534i
$126$		0			0
$127$	41.1373			0.323916			0.161958	−	0.986798i	$-0.448219\pi$
$127$	41.1373			0.323916			0.161958	+	0.986798i	$0.448219\pi$
$128$	−5.75772	−	9.97266i	−0.0449822	−	0.0779114i
$129$	5.55196	+	32.3153i	0.0430385	+	0.250506i
$130$	115.318	−	199.737i	0.887065	−	1.53644i
$131$			80.7864i			0.616690i	0.951275	+	0.308345i	$0.0997751\pi$
$131$			80.7864i			0.616690i	−0.951275	+	0.308345i	$0.900225\pi$
$132$	11.7768	+	68.5473i	0.0892186	+	0.519298i
$133$		0			0
$134$	−152.015			−1.13444
$135$	−129.168	+	72.3252i	−0.956803	+	0.535742i
$136$	31.4667	−	18.1673i	0.231373	−	0.133583i
$137$	−158.186			−1.15464			−0.577319	−	0.816518i	$-0.695901\pi$
$137$	−158.186			−1.15464			−0.577319	+	0.816518i	$0.695901\pi$
$138$	−75.1834	−	27.7387i	−0.544807	−	0.201005i
$139$	45.2826	−	26.1439i	0.325774	−	0.188086i	−0.328189	−	0.944612i	$-0.606438\pi$
$139$	45.2826	−	26.1439i	0.325774	−	0.188086i	0.653963	+	0.756526i	$0.273105\pi$
$140$		0			0
$141$	1.01590	−	2.75350i	0.00720494	−	0.0195284i
$142$	11.6644	+	20.2033i	0.0821435	+	0.142277i
$143$	−23.5076	+	13.5721i	−0.164389	+	0.0949101i
$144$	−333.966	+	118.245i	−2.31921	+	0.821147i
$145$	−124.903	−	72.1126i	−0.861397	−	0.497328i
$146$	210.782	+	121.695i	1.44371	+	0.833529i
$147$		0			0
$148$	−328.604	−	569.159i	−2.22030	−	3.84567i
$149$	−93.6920			−0.628805			−0.314403	−	0.949290i	$-0.601804\pi$
$149$	−93.6920			−0.628805			−0.314403	+	0.949290i	$0.601804\pi$
$150$	−52.7463	−	19.4606i	−0.351642	−	0.129737i
$151$	−272.108			−1.80204			−0.901020	−	0.433779i	$-0.857180\pi$
$151$	−272.108			−1.80204			−0.901020	+	0.433779i	$0.857180\pi$
$152$	508.827	+	293.771i	3.34755	+	1.93271i
$153$	−5.16794	−	14.5961i	−0.0337774	−	0.0953993i
$154$		0			0
$155$	−41.2192	+	71.3938i	−0.265930	+	0.460605i
$156$	−211.532	−	254.353i	−1.35598	−	1.63047i
$157$	176.758	+	102.051i	1.12584	+	0.650007i	0.942886	−	0.333114i	$-0.108099\pi$
$157$	176.758	+	102.051i	1.12584	+	0.650007i	0.182958	+	0.983121i	$0.441433\pi$
$158$	66.7993	−	115.700i	0.422780	−	0.732277i
$159$	194.792	+	71.8679i	1.22510	+	0.451999i
$160$	−290.839	−	167.916i	−1.81774	−	1.04947i
$161$		0			0
$162$	46.8796	+	296.175i	0.289381	+	1.82824i
$163$	93.1505	−	161.341i	0.571476	−	0.989825i	−0.424939	−	0.905222i	$-0.639705\pi$
$163$	93.1505	−	161.341i	0.571476	−	0.989825i	0.996415	−	0.0846029i	$-0.0269622\pi$
$164$		−	360.639i		−	2.19902i
$165$	25.1256	+	30.2117i	0.152276	+	0.183101i
$166$		−	75.9060i		−	0.457265i
$167$	−258.022	+	148.969i	−1.54504	+	0.892030i	−0.546532	+	0.837438i	$0.684052\pi$
$167$	−258.022	+	148.969i	−1.54504	+	0.892030i	−0.998509	+	0.0545920i	$0.982614\pi$
$168$		0			0
$169$	−19.9447	+	34.5453i	−0.118016	+	0.204410i
$170$	17.4605	−	30.2426i	0.102709	−	0.177897i
$171$	162.619	−	190.383i	0.950987	−	1.11335i
$172$	53.0350	+	91.8593i	0.308343	+	0.534065i
$173$	193.032	−	111.447i	1.11579	−	0.644203i	0.175469	−	0.984485i	$-0.443856\pi$
$173$	193.032	−	111.447i	1.11579	−	0.644203i	0.940323	+	0.340282i	$0.110523\pi$
$174$	−224.613	+	186.799i	−1.29088	+	1.07356i
$175$		0			0
$176$	47.0190	+	81.4394i	0.267154	+	0.462724i
$177$	136.887	−	23.5180i	0.773372	−	0.132870i
$178$			338.461i			1.90147i
$179$	82.8923	+	143.574i	0.463086	+	0.802088i	0.999113	−	0.0421128i	$-0.0134089\pi$
$179$	82.8923	+	143.574i	0.463086	+	0.802088i	−0.536027	+	0.844201i	$0.680076\pi$
$180$	−311.037	+	364.141i	−1.72798	+	2.02300i
$181$		−	219.158i		−	1.21082i	−0.795915	−	0.605408i	$-0.793010\pi$
$181$		−	219.158i		−	1.21082i	0.795915	−	0.605408i	$-0.206990\pi$
$182$		0			0
$183$	53.0922	−	143.902i	0.290121	−	0.786349i
$184$	−152.390			−0.828207
$185$	−321.556	−	185.650i	−1.73814	−	1.00351i
$186$	106.773	+	128.388i	0.574051	+	0.690256i
$187$	−3.55933	+	2.05498i	−0.0190338	+	0.0109892i
$188$		−	9.49435i		−	0.0505018i
$189$		0			0
$190$	564.685			2.97203
$191$	−128.065	−	221.815i	−0.670497	−	1.16133i	−0.977763	−	0.209711i	$-0.932748\pi$
$191$	−128.065	−	221.815i	−0.670497	−	1.16133i	0.307267	−	0.951623i	$-0.400586\pi$
$192$	−159.826	+	132.919i	−0.832428	+	0.692288i
$193$	−0.196120	+	0.339689i	−0.00101616	+	0.00176005i	−0.866533	−	0.499120i	$-0.833657\pi$
$193$	−0.196120	+	0.339689i	−0.00101616	+	0.00176005i	0.865517	+	0.500880i	$0.166990\pi$
$194$		−	522.990i		−	2.69582i
$195$	−175.348	−	64.6942i	−0.899220	−	0.331765i
$196$		0			0
$197$	155.648			0.790092			0.395046	−	0.918661i	$-0.370729\pi$
$197$	155.648			0.790092			0.395046	+	0.918661i	$0.370729\pi$
$198$	75.0294	−	26.5651i	0.378936	−	0.134167i
$199$	34.5080	−	19.9232i	0.173407	−	0.100117i	−0.410784	−	0.911733i	$-0.634745\pi$
$199$	34.5080	−	19.9232i	0.173407	−	0.100117i	0.584191	+	0.811616i	$0.301412\pi$
$200$	−106.912			−0.534561
$201$	20.8590	+	121.410i	0.103776	+	0.604030i
$202$	531.784	−	307.026i	2.63259	−	1.51993i
$203$		0			0
$204$	−32.0284	−	38.5120i	−0.157002	−	0.188784i
$205$	−101.875	−	176.452i	−0.496949	−	0.860741i
$206$	−15.2841	+	8.82431i	−0.0741949	+	0.0428364i
$207$	−11.8377	+	63.8529i	−0.0571869	+	0.308468i
$208$	−387.363	−	223.644i	−1.86232	−	1.07521i
$209$	−57.5555	−	33.2297i	−0.275385	−	0.158994i
$210$		0			0
$211$	−66.8190	−	115.734i	−0.316678	−	0.548502i	0.663115	−	0.748518i	$-0.269234\pi$
$211$	−66.8190	−	115.734i	−0.316678	−	0.548502i	−0.979793	+	0.200016i	$0.935901\pi$
$212$	671.661			3.16821
$213$	14.5352	−	12.0882i	0.0682405	−	0.0567522i
$214$	59.7225			0.279077
$215$	51.8974	+	29.9630i	0.241383	+	0.139363i
$216$	278.586	+	497.538i	1.28975	+	2.30342i
$217$		0			0
$218$	196.613	−	340.544i	0.901895	−	1.56213i
$219$	68.2715	−	185.044i	0.311742	−	0.844950i
$220$	110.085	+	63.5575i	0.500386	+	0.288898i
$221$	9.77441	−	16.9298i	0.0442281	−	0.0766053i
$222$	−578.254	+	480.905i	−2.60475	+	2.16624i
$223$	27.4922	+	15.8727i	0.123284	+	0.0711778i	0.560374	−	0.828240i	$-0.310658\pi$
$223$	27.4922	+	15.8727i	0.123284	+	0.0711778i	−0.437090	+	0.899418i	$0.643991\pi$
$224$		0			0
$225$	−8.30495	+	44.7972i	−0.0369109	+	0.199099i
$226$	−136.758	+	236.871i	−0.605122	+	1.04810i
$227$		−	251.807i		−	1.10928i	−0.832090	−	0.554641i	$-0.812856\pi$
$227$		−	251.807i		−	1.10928i	0.832090	−	0.554641i	$-0.187144\pi$
$228$	280.363	−	759.899i	1.22966	−	3.33289i
$229$			153.863i			0.671893i	0.941881	+	0.335946i	$0.109056\pi$
$229$			153.863i			0.671893i	−0.941881	+	0.335946i	$0.890944\pi$
$230$	−126.840	+	73.2308i	−0.551476	+	0.318395i
$231$		0			0
$232$	−277.767	+	481.107i	−1.19727	+	2.07374i
$233$	−29.5866	+	51.2455i	−0.126981	+	0.219938i	−0.922506	−	0.385984i	$-0.873862\pi$
$233$	−29.5866	+	51.2455i	−0.126981	+	0.219938i	0.795524	+	0.605922i	$0.207195\pi$
$234$	−245.884	+	287.864i	−1.05079	+	1.23019i
$235$	−2.68199	−	4.64535i	−0.0114127	−	0.0197674i
$236$	389.113	−	224.655i	1.64879	−	0.951927i
$237$	−101.572	−	37.4747i	−0.428573	−	0.158121i
$238$		0			0
$239$	36.0066	+	62.3653i	0.150655	+	0.260943i	0.931469	−	0.363822i	$-0.118528\pi$
$239$	36.0066	+	62.3653i	0.150655	+	0.260943i	−0.780813	+	0.624765i	$0.785195\pi$
$240$	−224.125	+	607.471i	−0.933854	+	2.53113i
$241$			1.24115i			0.00515001i	0.999997	+	0.00257500i	$0.000819650\pi$
$241$			1.24115i			0.00515001i	−0.999997	+	0.00257500i	$0.999180\pi$
$242$	213.408	+	369.633i	0.881851	+	1.52741i
$243$	230.114	−	78.0815i	0.946970	−	0.321323i
$244$		−	496.188i		−	2.03356i
$245$		0			0
$246$	−406.749	+	69.8819i	−1.65345	+	0.284073i
$247$	316.111			1.27980
$248$	274.999	+	158.770i	1.10887	+	0.640204i
$249$	−60.6238	+	10.4155i	−0.243469	+	0.0418295i
$250$	350.473	−	202.345i	1.40189	−	0.809382i
$251$			482.474i			1.92221i	0.276189	+	0.961103i	$0.410929\pi$
$251$			482.474i			1.92221i	−0.276189	+	0.961103i	$0.589071\pi$
$252$		0			0
$253$	17.2375			0.0681323
$254$	−76.1453	−	131.888i	−0.299785	−	0.519242i
$255$	−26.5497	−	9.79544i	−0.104116	−	0.0384135i
$256$	117.268	−	203.114i	0.458079	−	0.793415i
$257$			414.867i			1.61427i	0.590368	+	0.807134i	$0.298983\pi$
$257$			414.867i			1.61427i	−0.590368	+	0.807134i	$0.701017\pi$
$258$	93.3271	−	77.6155i	0.361733	−	0.300835i
$259$		0			0
$260$	−604.617			−2.32545
$261$	180.011	+	153.760i	0.689698	+	0.589117i
$262$	259.004	−	149.536i	0.988564	−	0.570748i
$263$	360.427			1.37044			0.685222	−	0.728334i	$-0.259705\pi$
$263$	360.427			1.37044			0.685222	+	0.728334i	$0.259705\pi$
$264$	116.371	−	96.7801i	0.440800	−	0.366591i
$265$	328.627	−	189.733i	1.24010	−	0.715973i
$266$		0			0
$267$	270.319	−	46.4424i	1.01243	−	0.173942i
$268$	199.255	+	345.119i	0.743488	+	1.28776i
$269$	−258.190	+	149.066i	−0.959813	+	0.554148i	−0.896115	−	0.443821i	$-0.853623\pi$
$269$	−258.190	+	149.066i	−0.959813	+	0.554148i	−0.0636972	+	0.997969i	$0.520289\pi$
$270$	470.968	+	280.244i	1.74433	+	1.03794i
$271$	−197.989	−	114.309i	−0.730588	−	0.421805i	0.0880491	−	0.996116i	$-0.471937\pi$
$271$	−197.989	−	114.309i	−0.730588	−	0.421805i	−0.818637	+	0.574311i	$0.805270\pi$
$272$	−58.6512	−	33.8623i	−0.215629	−	0.124494i
$273$		0			0
$274$	292.802	+	507.148i	1.06862	+	1.85090i
$275$	12.0933			0.0439755
$276$	35.5719	+	207.047i	0.128884	+	0.750170i
$277$	−90.4756			−0.326627			−0.163313	−	0.986574i	$-0.552218\pi$
$277$	−90.4756			−0.326627			−0.163313	+	0.986574i	$0.552218\pi$
$278$	−167.637	−	96.7850i	−0.603009	−	0.348147i
$279$	87.8883	−	102.894i	0.315012	−	0.368794i
$280$		0			0
$281$	15.0187	−	26.0131i	0.0534473	−	0.0925734i	−0.838064	−	0.545572i	$-0.816312\pi$
$281$	15.0187	−	26.0131i	0.0534473	−	0.0925734i	0.891511	+	0.452999i	$0.149646\pi$
$282$	−10.7082	+	1.83974i	−0.0379725	+	0.00652390i
$283$	288.349	+	166.479i	1.01890	+	0.588264i	0.913786	−	0.406196i	$-0.133145\pi$
$283$	288.349	+	166.479i	1.01890	+	0.588264i	0.105117	+	0.994460i	$0.466478\pi$
$284$	30.5783	−	52.9632i	0.107670	−	0.186490i
$285$	−77.4841	−	450.997i	−0.271874	−	1.58245i
$286$	87.0254	+	50.2442i	0.304285	+	0.175679i
$287$		0			0
$288$	419.160	+	358.033i	1.45542	+	1.24317i
$289$	−143.020	+	247.718i	−0.494879	+	0.857156i
$290$			533.922i			1.84111i
$291$	−417.696	+	71.7627i	−1.43538	+	0.246607i
$292$		−	638.050i		−	2.18510i
$293$	−218.453	+	126.124i	−0.745573	+	0.430457i	−0.824092	−	0.566456i	$-0.808314\pi$
$293$	−218.453	+	126.124i	−0.745573	+	0.430457i	0.0785193	+	0.996913i	$0.474981\pi$
$294$		0			0
$295$	126.922	−	219.836i	0.430245	−	0.745206i
$296$	−715.098	+	1238.59i	−2.41587	+	4.18441i
$297$	−31.5120	−	56.2785i	−0.106101	−	0.189490i
$298$	173.424	+	300.379i	0.581960	+	1.00798i
$299$	−71.0048	+	40.9946i	−0.237474	+	0.137106i
$300$	24.9562	+	145.258i	0.0831872	+	0.484192i
$301$		0			0
$302$	503.672	+	872.386i	1.66779	+	2.88870i
$303$	−318.182	−	382.591i	−1.05010	−	1.26268i
$304$		−	1095.13i		−	3.60239i
$305$	−140.165	−	242.772i	−0.459556	−	0.795975i
$306$	−37.2296	+	43.5860i	−0.121665	+	0.142438i
$307$			155.519i			0.506576i	0.967391	+	0.253288i	$0.0815120\pi$
$307$			155.519i			0.506576i	−0.967391	+	0.253288i	$0.918488\pi$
$308$		0			0
$309$	9.14494	+	10.9961i	0.0295953	+	0.0355862i
$310$	305.188			0.984476
$311$	107.293	+	61.9455i	0.344993	+	0.199182i	0.662478	−	0.749082i	$-0.269505\pi$
$311$	107.293	+	61.9455i	0.344993	+	0.199182i	−0.317485	+	0.948263i	$0.602838\pi$
$312$	−249.193	+	675.415i	−0.798694	+	2.16479i
$313$	−215.178	+	124.233i	−0.687471	+	0.396911i	−0.802664	−	0.596432i	$-0.796585\pi$
$313$	−215.178	+	124.233i	−0.687471	+	0.396911i	0.115193	+	0.993343i	$0.463251\pi$
$314$		−	755.587i		−	2.40633i
$315$		0			0
$316$	−350.230			−1.10832
$317$	−82.2066	−	142.386i	−0.259327	−	0.449167i	0.706735	−	0.707478i	$-0.250167\pi$
$317$	−82.2066	−	142.386i	−0.259327	−	0.449167i	−0.966062	+	0.258311i	$0.916834\pi$
$318$	−130.149	−	757.535i	−0.409274	−	2.38219i
$319$	31.4194	−	54.4200i	0.0984933	−	0.170595i
$320$			379.920i			1.18725i
$321$	−8.19491	−	47.6986i	−0.0255293	−	0.148594i
$322$		0			0
$323$	47.8628			0.148182
$324$	610.957	−	494.644i	1.88567	−	1.52668i
$325$	−49.8147	+	28.7605i	−0.153276	+	0.0884940i
$326$	−689.688			−2.11561
$327$	−298.961	−	110.301i	−0.914253	−	0.337311i
$328$	−679.667	+	392.406i	−2.07216	+	1.19636i
$329$		0			0
$330$	50.3522	−	136.475i	0.152583	−	0.413562i
$331$	−239.397	−	414.648i	−0.723254	−	1.25271i	−0.959689	−	0.281066i	$-0.909312\pi$
$331$	−239.397	−	414.648i	−0.723254	−	1.25271i	0.236434	−	0.971648i	$-0.424021\pi$
$332$	−172.329	+	99.4942i	−0.519063	+	0.299681i
$333$	463.430	+	395.846i	1.39168	+	1.18873i
$334$	955.198	+	551.484i	2.85988	+	1.65115i
$335$	194.981	+	112.572i	0.582032	+	0.336036i
$336$		0			0
$337$	−10.8833	−	18.8505i	−0.0322947	−	0.0559361i	0.849426	−	0.527707i	$-0.176948\pi$
$337$	−10.8833	−	18.8505i	−0.0322947	−	0.0559361i	−0.881721	+	0.471771i	$0.843615\pi$
$338$	147.671			0.436896
$339$	207.947	+	76.7216i	0.613413	+	0.226317i
$340$	−91.5460			−0.269253
$341$	−31.1062	−	17.9592i	−0.0912206	−	0.0526662i
$342$	−911.382	−	168.961i	−2.66486	−	0.494038i
$343$		0			0
$344$	115.413	−	199.901i	0.335503	−	0.581108i
$345$	75.8917	+	91.2544i	0.219976	+	0.264506i
$346$	−714.606	−	412.578i	−2.06533	−	1.19242i
$347$	317.158	−	549.333i	0.913999	−	1.58309i	0.105639	−	0.994405i	$-0.466311\pi$
$347$	317.158	−	549.333i	0.913999	−	1.58309i	0.808360	−	0.588688i	$-0.200355\pi$
$348$	718.501	+	265.089i	2.06466	+	0.761750i
$349$	12.9494	+	7.47635i	0.0371044	+	0.0214222i	0.518437	−	0.855116i	$-0.326514\pi$
$349$	12.9494	+	7.47635i	0.0371044	+	0.0214222i	−0.481333	+	0.876538i	$0.659847\pi$
$350$		0			0
$351$	263.648	+	156.880i	0.751133	+	0.446953i
$352$	73.1607	−	126.718i	0.207843	−	0.359995i
$353$			166.592i			0.471932i	0.971761	+	0.235966i	$0.0758255\pi$
$353$			166.592i			0.471932i	−0.971761	+	0.235966i	$0.924175\pi$
$354$	−328.777	−	395.331i	−0.928749	−	1.11676i
$355$		−	34.5514i		−	0.0973279i
$356$	768.406	−	443.640i	2.15844	−	1.24618i
$357$		0			0
$358$	306.868	−	531.511i	0.857173	−	1.48467i
$359$	271.513	−	470.274i	0.756303	−	1.30996i	−0.188421	−	0.982088i	$-0.560337\pi$
$359$	271.513	−	470.274i	0.756303	−	1.30996i	0.944724	−	0.327867i	$-0.106330\pi$
$360$	1024.70	+	189.969i	2.84639	+	0.527692i
$361$	206.479	+	357.632i	0.571963	+	0.990670i
$362$	−702.626	+	405.661i	−1.94096	+	1.12061i
$363$	265.932	−	221.162i	0.732595	−	0.609263i
$364$		0			0
$365$	−180.238	−	312.182i	−0.493804	−	0.855293i
$366$	−559.628	+	96.1474i	−1.52904	+	0.262698i
$367$			352.379i			0.960160i	0.877225	+	0.480080i	$0.159392\pi$
$367$			352.379i			0.960160i	−0.877225	+	0.480080i	$0.840608\pi$
$368$	142.021	+	245.987i	0.385926	+	0.668444i
$369$	111.625	+	315.269i	0.302507	+	0.854388i
$370$			1374.56i			3.71502i
$371$		0			0
$372$	151.524	−	410.692i	0.407322	−	1.10401i
$373$	205.804			0.551753			0.275876	−	0.961193i	$-0.411032\pi$
$373$	205.804			0.551753			0.275876	+	0.961193i	$0.411032\pi$
$374$	13.1767	+	7.60754i	0.0352317	+	0.0203410i
$375$	−209.698	−	252.147i	−0.559194	−	0.672392i
$376$	−17.8932	+	10.3306i	−0.0475883	+	0.0274751i
$377$			298.890i			0.792811i
$378$		0			0
$379$	35.5637			0.0938357			0.0469178	−	0.998899i	$-0.485060\pi$
$379$	35.5637			0.0938357			0.0469178	+	0.998899i	$0.485060\pi$
$380$	−740.164	−	1282.00i	−1.94780	−	3.37369i
$381$	−94.8863	+	78.9121i	−0.249045	+	0.207118i
$382$	−474.097	+	821.160i	−1.24109	+	2.14963i
$383$		−	119.295i		−	0.311474i	−0.987799	−	0.155737i	$-0.950225\pi$
$383$		−	119.295i		−	0.311474i	0.987799	−	0.155737i	$-0.0497753\pi$
$384$	32.4107	+	11.9579i	0.0844030	+	0.0311403i
$385$		0			0
$386$	1.45207			0.00376184
$387$	−74.7952	−	63.8875i	−0.193269	−	0.165084i
$388$	−1187.34	+	685.511i	−3.06016	+	1.76678i
$389$	−588.890			−1.51386			−0.756929	−	0.653498i	$-0.773301\pi$
$389$	−588.890			−1.51386			−0.756929	+	0.653498i	$0.773301\pi$
$390$	117.158	+	681.920i	0.300405	+	1.74851i
$391$	−10.7509	+	6.20706i	−0.0274960	+	0.0158748i
$392$		0			0
$393$	−154.969	−	186.340i	−0.394324	−	0.474147i
$394$	−288.105	−	499.013i	−0.731232	−	1.26653i
$395$	−171.359	+	98.9340i	−0.433819	+	0.250466i
$396$	−158.656	−	135.518i	−0.400646	−	0.342218i
$397$	−414.579	−	239.358i	−1.04428	−	0.602916i	−0.123238	−	0.992377i	$-0.539328\pi$
$397$	−414.579	−	239.358i	−1.04428	−	0.602916i	−0.921043	+	0.389461i	$0.872661\pi$
$398$	−127.749	−	73.7557i	−0.320977	−	0.185316i
$399$		0			0
$400$	99.6374	+	172.577i	0.249093	+	0.431443i
$401$	410.539			1.02379			0.511894	−	0.859049i	$-0.328944\pi$
$401$	410.539			1.02379			0.511894	+	0.859049i	$0.328944\pi$
$402$	350.634	−	291.605i	0.872224	−	0.725385i
$403$	170.844			0.423931
$404$	−1394.08	−	804.871i	−3.45069	−	1.99226i
$405$	159.198	−	414.602i	0.393081	−	1.02371i
$406$		0			0
$407$	80.8876	−	140.101i	0.198741	−	0.344230i
$408$	−37.7306	+	102.266i	−0.0924770	+	0.250651i
$409$	−283.857	−	163.885i	−0.694026	−	0.400696i	0.111092	−	0.993810i	$-0.464565\pi$
$409$	−283.857	−	163.885i	−0.694026	−	0.400696i	−0.805119	+	0.593114i	$0.797898\pi$
$410$	−377.140	+	653.226i	−0.919854	+	1.59323i
$411$	364.866	−	303.441i	0.887753	−	0.738299i
$412$	40.0675	+	23.1330i	0.0972513	+	0.0561481i
$413$		0			0
$414$	226.626	−	80.2399i	0.547406	−	0.193816i
$415$	−56.2108	+	97.3600i	−0.135448	+	0.234602i
$416$			695.971i			1.67301i
$417$	−54.2968	+	147.167i	−0.130208	+	0.352918i
$418$			246.033i			0.588596i
$419$	304.035	−	175.535i	0.725622	−	0.418938i	−0.0911967	−	0.995833i	$-0.529069\pi$
$419$	304.035	−	175.535i	0.725622	−	0.418938i	0.816818	+	0.576895i	$0.195736\pi$
$420$		0			0
$421$	−323.054	+	559.546i	−0.767349	+	1.32909i	0.171647	+	0.985158i	$0.445091\pi$
$421$	−323.054	+	559.546i	−0.767349	+	1.32909i	−0.938996	+	0.343928i	$0.888242\pi$
$422$	−247.364	+	428.448i	−0.586172	+	1.01528i
$423$	2.93869	+	8.29991i	0.00694726	+	0.0196215i
$424$	−730.823	−	1265.82i	−1.72364	−	2.98543i
$425$	−7.54252	+	4.35468i	−0.0177471	+	0.0102463i
$426$	−65.6599	−	24.2251i	−0.154131	−	0.0568664i
$427$		0			0
$428$	−78.2816	−	135.588i	−0.182901	−	0.316794i
$429$	28.1872	−	76.3989i	0.0657044	−	0.178086i
$430$		−	221.846i		−	0.515921i
$431$	378.302	+	655.238i	0.877730	+	1.52027i	0.853825	+	0.520559i	$0.174277\pi$
$431$	378.302	+	655.238i	0.877730	+	1.52027i	0.0239050	+	0.999714i	$0.492390\pi$
$432$	543.493	−	913.376i	1.25809	−	2.11430i
$433$		−	143.339i		−	0.331037i	−0.986207	−	0.165518i	$-0.947070\pi$
$433$		−	143.339i		−	0.331037i	0.986207	−	0.165518i	$-0.0529297\pi$
$434$		0			0
$435$	426.428	−	73.2629i	0.980293	−	0.168420i
$436$	−1030.85			−2.36433
$437$	−173.846	−	100.370i	−0.397817	−	0.229680i
$438$	−719.628	+	123.636i	−1.64299	+	0.282275i
$439$	−209.092	+	120.719i	−0.476291	+	0.274987i	−0.718870	−	0.695145i	$-0.755340\pi$
$439$	−209.092	+	120.719i	−0.476291	+	0.274987i	0.242578	+	0.970132i	$0.422007\pi$
$440$		−	276.624i		−	0.628690i
$441$		0			0
$442$	−72.3699			−0.163733
$443$	247.055	+	427.912i	0.557686	+	0.965940i	0.997689	+	0.0679442i	$0.0216440\pi$
$443$	247.055	+	427.912i	0.557686	+	0.965940i	−0.440003	+	0.897996i	$0.645023\pi$
$444$	1849.74	+	682.459i	4.16609	+	1.53707i
$445$	250.641	−	434.123i	0.563239	−	0.975558i
$446$		−	117.521i		−	0.263501i
$447$	216.107	−	179.726i	0.483462	−	0.402071i
$448$		0			0
$449$	320.006			0.712709			0.356355	−	0.934351i	$-0.384020\pi$
$449$	320.006			0.712709			0.356355	+	0.934351i	$0.384020\pi$
$450$	158.994	−	56.2938i	0.353319	−	0.125097i
$451$	76.8799	−	44.3866i	0.170465	−	0.0984183i
$452$	717.023			1.58633
$453$	627.637	−	521.974i	1.38551	−	1.15226i
$454$	−807.301	+	466.096i	−1.77820	+	1.02664i
$455$		0			0
$456$	−1737.18	+	298.457i	−3.80960	+	0.654512i
$457$	73.6310	+	127.533i	0.161118	+	0.279065i	0.935270	−	0.353935i	$-0.115157\pi$
$457$	73.6310	+	127.533i	0.161118	+	0.279065i	−0.774152	+	0.633000i	$0.781823\pi$
$458$	493.291	−	284.802i	1.07705	−	0.621838i
$459$	39.9193	+	23.7535i	0.0869702	+	0.0517505i
$460$	332.511	+	191.975i	0.722850	+	0.417338i
$461$	−608.502	−	351.319i	−1.31996	−	0.762080i	−0.336239	−	0.941777i	$-0.609155\pi$
$461$	−608.502	−	351.319i	−1.31996	−	0.762080i	−0.983722	+	0.179697i	$0.942488\pi$
$462$		0			0
$463$	207.655	+	359.670i	0.448500	+	0.776825i	0.998289	−	0.0584791i	$-0.0186251\pi$
$463$	207.655	+	359.670i	0.448500	+	0.776825i	−0.549789	+	0.835304i	$0.685292\pi$
$464$	1035.47			2.23161
$465$	−41.8767	−	243.744i	−0.0900575	−	0.524181i
$466$	219.060			0.470085
$467$	575.307	+	332.154i	1.23192	+	0.711250i	0.967430	−	0.253139i	$-0.0814628\pi$
$467$	575.307	+	332.154i	1.23192	+	0.711250i	0.264491	+	0.964388i	$0.414796\pi$
$468$	975.830	+	180.909i	2.08511	+	0.386558i
$469$		0			0
$470$	−9.92875	+	17.1971i	−0.0211250	+	0.0365896i
$471$	−603.465	+	103.679i	−1.28124	+	0.220125i
$472$	−846.776	−	488.886i	−1.79402	−	1.03578i
$473$	−13.0548	+	22.6116i	−0.0276001	+	0.0478047i
$474$	67.8648	+	395.008i	0.143175	+	0.833350i
$475$	−121.965	−	70.4165i	−0.256768	−	0.148245i
$476$		0			0
$477$	−587.162	+	207.892i	−1.23095	+	0.435833i
$478$	133.297	−	230.877i	0.278864	−	0.483006i
$479$			80.0410i			0.167100i	0.996504	+	0.0835501i	$0.0266259\pi$
$479$			80.0410i			0.167100i	−0.996504	+	0.0835501i	$0.973374\pi$
$480$	992.947	−	170.594i	2.06864	−	0.355405i
$481$			769.476i			1.59974i
$482$	3.97917	−	2.29738i	0.00825554	−	0.00476634i
$483$		0			0
$484$	559.451	−	968.998i	1.15589	−	2.00206i
$485$	−387.291	+	670.807i	−0.798538	+	1.38311i
$486$	−676.273	−	593.222i	−1.39151	−	1.22062i
$487$	74.9802	+	129.870i	0.153963	+	0.266673i	0.932681	−	0.360702i	$-0.117463\pi$
$487$	74.9802	+	129.870i	0.153963	+	0.266673i	−0.778718	+	0.627375i	$0.784130\pi$
$488$	−935.124	+	539.894i	−1.91624	+	1.10634i
$489$	94.6364	+	550.833i	0.193530	+	1.12645i
$490$		0			0
$491$	−171.208	−	296.541i	−0.348692	−	0.603953i	0.637325	−	0.770595i	$-0.280041\pi$
$491$	−171.208	−	296.541i	−0.348692	−	0.603953i	−0.986017	+	0.166642i	$0.946708\pi$
$492$	691.800	+	831.841i	1.40610	+	1.69073i
$493$			45.2553i			0.0917958i
$494$	−585.122	−	1013.46i	−1.18446	−	2.05154i
$495$	−115.908	−	21.4882i	−0.234157	−	0.0434104i
$496$		−	591.868i		−	1.19328i
$497$		0			0
$498$	145.607	+	175.083i	0.292384	+	0.351572i
$499$	511.125			1.02430			0.512149	−	0.858896i	$-0.328849\pi$
$499$	511.125			1.02430			0.512149	+	0.858896i	$0.328849\pi$
$500$	−918.768	−	530.451i	−1.83754	−	1.06090i
$501$	309.385	−	838.561i	0.617535	−	1.67377i
$502$	1546.83	−	893.061i	3.08133	−	1.77901i
$503$			110.344i			0.219371i	0.993966	+	0.109686i	$0.0349844\pi$
$503$			110.344i			0.219371i	−0.993966	+	0.109686i	$0.965016\pi$
$504$		0			0
$505$	−909.450			−1.80089
$506$	−31.9066	−	55.2639i	−0.0630565	−	0.109217i
$507$	−20.2629	−	117.940i	−0.0399662	−	0.232624i
$508$	−199.616	+	345.745i	−0.392944	+	0.680600i
$509$		−	304.518i		−	0.598267i	−0.954211	−	0.299133i	$-0.903302\pi$
$509$		−	304.518i		−	0.598267i	0.954211	−	0.299133i	$-0.0966976\pi$
$510$	17.7391	+	103.251i	0.0347825	+	0.202452i
$511$		0			0
$512$	−914.316			−1.78577
$513$	−9.88764	+	751.077i	−0.0192742	+	1.46409i
$514$	1330.08	−	767.920i	2.58770	−	1.49401i
$515$	26.1387			0.0507548
$516$	−298.539	−	110.145i	−0.578564	−	0.213460i
$517$	2.02397	−	1.16854i	0.00391484	−	0.00226023i
$518$		0			0
$519$	−231.458	+	627.347i	−0.445969	+	1.20876i
$520$	657.874	+	1139.47i	1.26514	+	2.19129i
$521$	538.992	−	311.187i	1.03453	−	0.597288i	0.116253	−	0.993220i	$-0.462912\pi$
$521$	538.992	−	311.187i	1.03453	−	0.597288i	0.918280	+	0.395932i	$0.129578\pi$
$522$	159.756	−	861.731i	0.306047	−	1.65083i
$523$	−20.7472	−	11.9784i	−0.0396696	−	0.0229032i	0.480034	−	0.877250i	$-0.340624\pi$
$523$	−20.7472	−	11.9784i	−0.0396696	−	0.0229032i	−0.519704	+	0.854347i	$0.673958\pi$
$524$	−678.981	−	392.010i	−1.29577	−	0.748110i
$525$		0			0
$526$	−667.151	−	1155.54i	−1.26835	−	2.19684i
$527$	25.8678			0.0490849
$528$	−264.675	−	97.6511i	−0.501278	−	0.184945i
$529$	−476.934			−0.901577
$530$	−1216.58	−	702.392i	−2.29543	−	1.32527i
$531$	−270.626	+	316.830i	−0.509653	+	0.596667i
$532$		0			0
$533$	−211.123	+	365.676i	−0.396103	+	0.686071i
$534$	−649.256	−	780.685i	−1.21584	−	1.46196i
$535$	−76.6025	−	44.2265i	−0.143182	−	0.0826663i
$536$	433.611	−	751.037i	0.808977	−	1.40119i
$537$	−466.609	−	172.154i	−0.868918	−	0.320585i
$538$	955.819	+	551.843i	1.77662	+	1.02573i
$539$		0			0
$540$	18.9118	−	1436.57i	0.0350219	−	2.66031i
$541$	−383.845	+	664.840i	−0.709511	+	1.22891i	0.255528	+	0.966802i	$0.417751\pi$
$541$	−383.845	+	664.840i	−0.709511	+	1.22891i	−0.965039	+	0.262107i	$0.915583\pi$
$542$			846.347i			1.56153i
$543$	420.401	+	505.503i	0.774220	+	0.930945i
$544$			105.378i			0.193710i
$545$	−504.367	+	291.197i	−0.925445	+	0.534306i
$546$		0			0
$547$	175.373	−	303.756i	0.320610	−	0.555312i	−0.660004	−	0.751262i	$-0.729446\pi$
$547$	175.373	−	303.756i	0.320610	−	0.555312i	0.980614	+	0.195950i	$0.0627789\pi$
$548$	767.583	−	1329.49i	1.40070	−	2.42608i
$549$	153.580	+	433.765i	0.279745	+	0.790100i
$550$	−22.3847	−	38.7714i	−0.0406994	−	0.0704934i
$551$	−633.752	+	365.897i	−1.15018	+	0.664060i
$552$	351.499	−	292.324i	0.636773	−	0.529572i
$553$		0			0
$554$	167.471	+	290.068i	0.302293	+	0.523588i
$555$	1097.82	−	188.612i	1.97805	−	0.339841i
$556$			507.446i			0.912672i
$557$	−77.6449	−	134.485i	−0.139398	−	0.241445i	0.787871	−	0.615841i	$-0.211184\pi$
$557$	−77.6449	−	134.485i	−0.139398	−	0.241445i	−0.927269	+	0.374396i	$0.877850\pi$
$558$	−492.562	−	91.3160i	−0.882727	−	0.163649i
$559$		−	124.189i		−	0.222164i
$560$		0			0
$561$	4.26786	−	11.5677i	0.00760760	−	0.0206197i
$562$	−111.198			−0.197862
$563$	598.264	+	345.408i	1.06264	+	0.613513i	0.926160	−	0.377131i	$-0.123089\pi$
$563$	598.264	+	345.408i	1.06264	+	0.613513i	0.136475	+	0.990643i	$0.456423\pi$
$564$	18.2126	+	21.8994i	0.0322919	+	0.0388287i
$565$	350.821	−	202.547i	0.620922	−	0.358490i
$566$		−	1232.61i		−	2.17776i
$567$		0			0
$568$	−133.087			−0.234308
$569$	194.560	+	336.987i	0.341932	+	0.592244i	0.984792	−	0.173740i	$-0.0555853\pi$
$569$	194.560	+	336.987i	0.341932	+	0.592244i	−0.642859	+	0.765984i	$0.722252\pi$
$570$	−1302.49	+	1083.21i	−2.28507	+	1.90037i
$571$	403.181	−	698.330i	0.706096	−	1.22299i	−0.260198	−	0.965555i	$-0.583788\pi$
$571$	403.181	−	698.330i	0.706096	−	1.22299i	0.966294	−	0.257440i	$-0.0828788\pi$
$572$		−	263.431i		−	0.460544i
$573$	720.890	+	265.970i	1.25810	+	0.464172i
$574$		0			0
$575$	36.5277			0.0635264
$576$	113.677	−	613.176i	0.197355	−	1.06454i
$577$	669.238	−	386.385i	1.15986	−	0.669645i	0.208588	−	0.978004i	$-0.433113\pi$
$577$	669.238	−	386.385i	1.15986	−	0.669645i	0.951270	+	0.308359i	$0.0997798\pi$
$578$	1058.92			1.83204
$579$	−0.199248	−	1.15973i	−0.000344124	−	0.00200298i
$580$	1212.16	−	699.841i	2.08993	−	1.20662i
$581$		0			0
$582$	1003.23	+	1206.31i	1.72376	+	2.07270i
$583$	82.6664	+	143.182i	0.141795	+	0.245596i
$584$	−1202.48	+	694.252i	−2.05904	+	1.18879i
$585$	528.553	−	187.141i	0.903509	−	0.319899i
$586$	808.713	+	466.911i	1.38006	+	0.796776i
$587$	212.938	+	122.940i	0.362757	+	0.209438i	0.670289	−	0.742100i	$-0.266170\pi$
$587$	212.938	+	122.940i	0.362757	+	0.209438i	−0.307533	+	0.951538i	$0.599503\pi$
$588$		0			0
$589$	209.145	+	362.250i	0.355085	+	0.615025i
$590$	−939.734			−1.59277
$591$	−359.014	+	298.574i	−0.607469	+	0.505201i
$592$	2665.76			4.50297
$593$	868.167	+	501.236i	1.46402	+	0.845255i	0.999194	−	0.0401445i	$-0.0127818\pi$
$593$	868.167	+	501.236i	1.46402	+	0.845255i	0.464831	+	0.885400i	$0.346115\pi$
$594$	−122.102	+	205.200i	−0.205559	+	0.345455i
$595$		0			0
$596$	454.633	−	787.448i	0.762807	−	1.32122i
$597$	−41.3773	+	112.150i	−0.0693087	+	0.187855i
$598$	262.860	+	151.762i	0.439565	+	0.253783i
$599$	−181.436	+	314.257i	−0.302899	+	0.524636i	−0.976791	−	0.214193i	$-0.931288\pi$
$599$	−181.436	+	314.257i	−0.302899	+	0.524636i	0.673893	+	0.738829i	$0.264621\pi$
$600$	246.601	−	205.085i	0.411001	−	0.341809i
$601$	−491.710	−	283.889i	−0.818154	−	0.472361i	0.0316257	−	0.999500i	$-0.489932\pi$
$601$	−491.710	−	283.889i	−0.818154	−	0.472361i	−0.849779	+	0.527139i	$0.823265\pi$
$602$		0			0
$603$	−281.009	−	240.028i	−0.466018	−	0.398056i
$604$	1320.38	−	2286.97i	2.18606	−	3.78637i
$605$		−	632.142i		−	1.04486i
$606$	−637.644	+	1728.28i	−1.05222	+	2.85194i
$607$		−	233.388i		−	0.384494i	−0.981347	−	0.192247i	$-0.938422\pi$
$607$		−	233.388i		−	0.384494i	0.981347	−	0.192247i	$-0.0615775\pi$
$608$	−1475.71	+	851.999i	−2.42715	+	1.40131i
$609$		0			0
$610$	−518.890	+	898.744i	−0.850640	+	1.47335i
$611$	−5.55811	+	9.62693i	−0.00909675	+	0.0157560i
$612$	147.752	+	27.3917i	0.241425	+	0.0447577i
$613$	−138.832	−	240.464i	−0.226479	−	0.392274i	0.730283	−	0.683145i	$-0.239388\pi$
$613$	−138.832	−	240.464i	−0.226479	−	0.392274i	−0.956762	+	0.290871i	$0.906055\pi$
$614$	498.598	−	287.866i	0.812049	−	0.468837i
$615$	573.462	+	211.577i	0.932458	+	0.344028i
$616$		0			0
$617$	148.590	+	257.365i	0.240826	+	0.417123i	0.960950	−	0.276723i	$-0.0892483\pi$
$617$	148.590	+	257.365i	0.240826	+	0.417123i	−0.720124	+	0.693846i	$0.755915\pi$
$618$	18.3267	−	49.6729i	0.0296548	−	0.0803768i
$619$		−	888.066i		−	1.43468i	−0.696724	−	0.717339i	$-0.745360\pi$
$619$		−	888.066i		−	1.43468i	0.696724	−	0.717339i	$-0.254640\pi$
$620$	−400.026	−	692.866i	−0.645204	−	1.11753i
$621$	−95.1820	−	169.989i	−0.153272	−	0.273734i
$622$		−	458.645i		−	0.737371i
$623$		0			0
$624$	1322.49	−	227.211i	2.11937	−	0.364121i
$625$	−725.930			−1.16149
$626$	796.592	+	459.912i	1.27251	+	0.734684i
$627$	196.499	−	33.7597i	0.313396	−	0.0538433i
$628$	−1715.40	+	990.389i	−2.73154	+	1.57705i
$629$			116.508i			0.185227i
$630$		0			0
$631$	974.133			1.54379			0.771897	−	0.635748i	$-0.219308\pi$
$631$	974.133			1.54379			0.771897	+	0.635748i	$0.219308\pi$
$632$	381.079	+	660.049i	0.602974	+	1.04438i
$633$	376.131	+	138.772i	0.594203	+	0.219230i
$634$	−304.329	+	527.114i	−0.480015	+	0.831410i
$635$			225.552i			0.355200i
$636$	−1549.23	+	1288.42i	−2.43590	+	2.02582i
$637$		0			0
$638$	−232.629			−0.364623
$639$	−10.3382	+	55.7647i	−0.0161787	+	0.0872687i
$640$	54.6792	−	31.5690i	0.0854362	−	0.0493266i
$641$	647.777			1.01057			0.505286	−	0.862952i	$-0.331387\pi$
$641$	647.777			1.01057			0.505286	+	0.862952i	$0.331387\pi$
$642$	−137.754	+	114.563i	−0.214571	+	0.178448i
$643$	−209.826	+	121.143i	−0.326324	+	0.188403i	−0.654208	−	0.756315i	$-0.726998\pi$
$643$	−209.826	+	121.143i	−0.326324	+	0.188403i	0.327884	+	0.944718i	$0.393664\pi$
$644$		0			0
$645$	−177.182	+	30.4409i	−0.274700	+	0.0471952i
$646$	−88.5942	−	153.450i	−0.137143	−	0.237538i
$647$	−732.768	+	423.064i	−1.13256	+	0.653885i	−0.944578	−	0.328287i	$-0.893529\pi$
$647$	−732.768	+	423.064i	−1.13256	+	0.653885i	−0.187984	+	0.982172i	$0.560195\pi$
$648$	−1596.99	−	613.206i	−2.46449	−	0.946306i
$649$	95.7823	+	55.2999i	0.147584	+	0.0852079i
$650$	184.414	+	106.472i	0.283714	+	0.163803i
$651$		0			0
$652$	904.011	+	1565.79i	1.38652	+	2.40152i
$653$	−438.652			−0.671749			−0.335875	−	0.941907i	$-0.609032\pi$
$653$	−438.652			−0.671749			−0.335875	+	0.941907i	$0.609032\pi$
$654$	199.749	+	1162.64i	0.305427	+	1.77774i
$655$	−442.944			−0.676251
$656$	1266.84	+	731.410i	1.93116	+	1.11495i
$657$	197.489	+	557.780i	0.300593	+	0.848980i
$658$		0			0
$659$	−317.963	+	550.728i	−0.482493	+	0.835703i	−0.999798	−	0.0200985i	$-0.993602\pi$
$659$	−317.963	+	550.728i	−0.482493	+	0.835703i	0.517305	+	0.855801i	$0.326935\pi$
$660$	−375.839	+	64.5714i	−0.569453	+	0.0978354i
$661$	487.140	+	281.250i	0.736975	+	0.425492i	0.820968	−	0.570974i	$-0.193434\pi$
$661$	487.140	+	281.250i	0.736975	+	0.425492i	−0.0839937	+	0.996466i	$0.526768\pi$
$662$	−886.250	+	1535.03i	−1.33875	+	2.31878i
$663$	9.93033	+	57.7996i	0.0149779	+	0.0871789i
$664$	375.017	+	216.516i	0.564784	+	0.326078i
$665$		0			0
$666$	411.285	−	2218.48i	0.617544	−	3.33106i
$667$	94.9021	−	164.375i	0.142282	−	0.246440i
$668$		−	2891.44i		−	4.32851i
$669$	−93.8607	+	16.1258i	−0.140300	+	0.0241044i
$670$		−	833.485i		−	1.24401i
$671$	105.776	−	61.0696i	0.157639	−	0.0910128i
$672$		0			0
$673$	507.452	−	878.932i	0.754014	−	1.30599i	−0.191849	−	0.981424i	$-0.561448\pi$
$673$	507.452	−	878.932i	0.754014	−	1.30599i	0.945863	−	0.324566i	$-0.105218\pi$
$674$	−40.2901	+	69.7845i	−0.0597776	+	0.103538i
$675$	−66.7767	−	119.259i	−0.0989284	−	0.176680i
$676$	−193.560	−	335.257i	−0.286332	−	0.495942i
$677$	138.742	−	80.1026i	0.204936	−	0.118320i	−0.394020	−	0.919102i	$-0.628916\pi$
$677$	138.742	−	80.1026i	0.204936	−	0.118320i	0.598956	+	0.800782i	$0.295582\pi$
$678$	−138.939	−	808.697i	−0.204925	−	1.19277i
$679$		0			0
$680$	99.6097	+	172.529i	0.146485	+	0.253719i
$681$	483.031	+	580.811i	0.709297	+	0.852880i
$682$			132.970i			0.194971i
$683$	−141.605	−	245.267i	−0.207328	−	0.359102i	0.743544	−	0.668687i	$-0.233143\pi$
$683$	−141.605	−	245.267i	−0.207328	−	0.359102i	−0.950872	+	0.309585i	$0.899810\pi$
$684$	811.007	+	2290.57i	1.18568	+	3.34879i
$685$		−	867.317i		−	1.26616i
$686$		0			0
$687$	−295.150	−	354.897i	−0.429622	−	0.516590i
$688$	−430.239			−0.625348
$689$	−681.041	−	393.199i	−0.988448	−	0.570681i
$690$	152.089	−	412.223i	0.220419	−	0.597425i
$691$	−1101.97	+	636.224i	−1.59475	+	0.920729i	−0.602274	+	0.798290i	$0.705738\pi$
$691$	−1101.97	+	636.224i	−1.59475	+	0.920729i	−0.992476	+	0.122440i	$0.960928\pi$
$692$			2163.15i			3.12595i
$693$		0			0
$694$	−2348.24			−3.38363
$695$	143.345	+	248.280i	0.206252	+	0.357238i
$696$	−282.198	−	1642.54i	−0.405457	−	2.35997i
$697$	−31.9665	+	55.3675i	−0.0458629	+	0.0794369i
$698$		−	55.3550i		−	0.0793052i
$699$	−30.0586	−	174.956i	−0.0430022	−	0.250295i
$700$		0			0
$701$	−941.137			−1.34256			−0.671282	−	0.741202i	$-0.734256\pi$
$701$	−941.137			−1.34256			−0.671282	+	0.741202i	$0.734256\pi$
$702$	14.9504	−	1135.65i	0.0212968	−	1.61773i
$703$	−1631.56	+	941.983i	−2.32086	+	1.33995i
$704$	−165.531			−0.235129
$705$	15.0972	+	5.57007i	0.0214145	+	0.00790081i
$706$	534.100	−	308.363i	0.756515	−	0.436774i
$707$		0			0
$708$	−466.572	+	1264.60i	−0.659000	+	1.78616i
$709$	462.522	+	801.111i	0.652358	+	1.12992i	0.982549	+	0.186003i	$0.0595533\pi$
$709$	462.522	+	801.111i	0.652358	+	1.12992i	−0.330192	+	0.943914i	$0.607113\pi$
$710$	−110.773	+	63.9547i	−0.156018	+	0.0900771i
$711$	306.169	−	108.403i	0.430617	−	0.152466i
$712$	−1672.18	−	965.434i	−2.34857	−	1.35595i
$713$	−93.9562	−	54.2456i	−0.131776	−	0.0760808i
$714$		0			0
$715$	−74.4148	−	128.890i	−0.104077	−	0.180266i
$716$	−1608.91			−2.24709
$717$	−202.685	−	74.7801i	−0.282685	−	0.104296i
$718$	−2010.28			−2.79984
$719$	60.0742	+	34.6839i	0.0835525	+	0.0482390i	0.541194	−	0.840898i	$-0.317972\pi$
$719$	60.0742	+	34.6839i	0.0835525	+	0.0482390i	−0.457642	+	0.889137i	$0.651306\pi$
$720$	−648.328	−	1831.11i	−0.900455	−	2.54320i
$721$		0			0
$722$	764.386	−	1323.95i	1.05871	−	1.83373i
$723$	−2.38085	−	2.86281i	−0.00329302	−	0.00395962i
$724$	1841.94	+	1063.45i	2.54412	+	1.46885i
$725$	66.5804	−	115.321i	0.0918350	−	0.159063i
$726$	−1201.29	−	443.214i	−1.65468	−	0.610488i
$727$	−953.931	−	550.752i	−1.31215	−	0.757568i	−0.329695	−	0.944087i	$-0.606946\pi$
$727$	−953.931	−	550.752i	−1.31215	−	0.757568i	−0.982451	+	0.186519i	$0.940279\pi$
$728$		0			0
$729$	−380.993	+	621.518i	−0.522625	+	0.852563i
$730$	−667.244	+	1155.70i	−0.914032	+	1.58315i
$731$		−	18.8037i		−	0.0257233i
$732$	951.818	+	1144.49i	1.30030	+	1.56352i
$733$		−	1212.03i		−	1.65352i	−0.562557	−	0.826759i	$-0.690182\pi$
$733$		−	1212.03i		−	1.65352i	0.562557	−	0.826759i	$-0.309818\pi$
$734$	1129.74	−	652.254i	1.53915	−	0.888629i
$735$		0			0
$736$	220.982	−	382.752i	0.300247	−	0.520043i
$737$	−49.0476	+	84.9529i	−0.0665503	+	0.115268i
$738$	804.144	−	941.437i	1.08963	−	1.27566i
$739$	383.740	+	664.657i	0.519269	+	0.899400i	0.999749	+	0.0223947i	$0.00712904\pi$
$739$	383.740	+	664.657i	0.519269	+	0.899400i	−0.480480	+	0.877006i	$0.659538\pi$
$740$	3120.65	−	1801.71i	4.21709	−	2.43474i
$741$	−729.133	+	606.383i	−0.983985	+	0.818331i
$742$		0			0
$743$	−39.2644	−	68.0079i	−0.0528458	−	0.0915315i	0.838392	−	0.545067i	$-0.183496\pi$
$743$	−39.2644	−	68.0079i	−0.0528458	−	0.0915315i	−0.891238	+	0.453536i	$0.850162\pi$
$744$	−938.867	+	161.303i	−1.26192	+	0.216805i
$745$		−	513.705i		−	0.689536i
$746$	−380.944	−	659.814i	−0.510648	−	0.884469i
$747$	119.854	−	140.317i	0.160447	−	0.187840i
$748$		−	39.8865i		−	0.0533242i
$749$		0			0
$750$	−420.239	+	1139.02i	−0.560319	+	1.51870i
$751$	349.127			0.464883			0.232442	−	0.972610i	$-0.425329\pi$
$751$	349.127			0.464883			0.232442	+	0.972610i	$0.425329\pi$
$752$	33.3513	+	19.2554i	0.0443502	+	0.0256056i
$753$	−925.511	−	1112.86i	−1.22910	−	1.47790i
$754$	958.249	−	553.246i	1.27089	−	0.733747i
$755$		−	1491.94i		−	1.97608i
$756$		0			0
$757$	−523.898			−0.692072			−0.346036	−	0.938221i	$-0.612472\pi$
$757$	−523.898			−0.692072			−0.346036	+	0.938221i	$0.612472\pi$
$758$	−65.8286	−	114.018i	−0.0868451	−	0.150420i
$759$	−39.7595	+	33.0660i	−0.0523840	+	0.0435652i
$760$	−1610.72	+	2789.85i	−2.11937	+	3.67086i
$761$			424.041i			0.557216i	0.960405	+	0.278608i	$0.0898729\pi$
$761$			424.041i			0.557216i	−0.960405	+	0.278608i	$0.910127\pi$
$762$	428.629	+	158.142i	0.562506	+	0.207535i
$763$		0			0
$764$	2485.70			3.25353
$765$	80.0290	−	28.3353i	0.104613	−	0.0370396i
$766$	−382.463	+	220.815i	−0.499298	+	0.288270i
$767$	−526.063			−0.685871
$768$	119.139	+	693.449i	0.155129	+	0.902928i
$769$	−1109.15	+	640.365i	−1.44232	+	0.832725i	−0.998004	−	0.0631445i	$-0.979887\pi$
$769$	−1109.15	+	640.365i	−1.44232	+	0.832725i	−0.444317	+	0.895869i	$0.646554\pi$
$770$		0			0
$771$	−795.823	−	956.921i	−1.03220	−	1.24114i
$772$	−1.90331	−	3.29663i	−0.00246543	−	0.00427025i
$773$	955.209	−	551.490i	1.23572	−	0.713441i	0.267501	−	0.963558i	$-0.413802\pi$
$773$	955.209	−	551.490i	1.23572	−	0.713441i	0.968216	+	0.250117i	$0.0804690\pi$
$774$	−66.3792	+	358.051i	−0.0857612	+	0.462599i
$775$	−65.9167	−	38.0570i	−0.0850538	−	0.0491059i
$776$	2583.85	+	1491.79i	3.32971	+	1.92241i
$777$		0			0
$778$	1090.04	+	1888.00i	1.40108	+	2.42674i
$779$	−1033.82			−1.32711
$780$	1394.59	−	1159.81i	1.78794	−	1.48694i
$781$	15.0540			0.0192753
$782$	39.8000	+	22.9786i	0.0508952	+	0.0293843i
$783$	−710.160	−	9.34898i	−0.906973	−	0.0119399i
$784$		0			0
$785$	−559.536	+	969.145i	−0.712785	+	1.23458i
$786$	−310.562	+	841.752i	−0.395117	+	1.07093i
$787$	−1131.22	−	653.112i	−1.43739	−	0.829876i	−0.439719	−	0.898135i	$-0.644922\pi$
$787$	−1131.22	−	653.112i	−1.43739	−	0.829876i	−0.997668	+	0.0682596i	$0.978255\pi$
$788$	−755.271	+	1308.17i	−0.958466	+	1.66011i
$789$	−831.350	+	691.392i	−1.05368	+	0.876289i
$790$	634.371	+	366.254i	0.803001	+	0.463613i
$791$		0			0
$792$	−82.7693	+	446.461i	−0.104507	+	0.563713i
$793$	−290.475	+	503.117i	−0.366299	+	0.634448i
$794$			1772.21i			2.23200i
$795$	−394.045	+	1068.02i	−0.495654	+	1.34343i
$796$			386.703i			0.485808i
$797$	933.144	−	538.751i	1.17082	−	0.675974i	0.216948	−	0.976183i	$-0.430390\pi$
$797$	933.144	−	538.751i	1.17082	−	0.675974i	0.953873	+	0.300209i	$0.0970566\pi$
$798$		0			0
$799$	−0.841562	+	1.45763i	−0.00105327	+	0.00182432i
$800$	155.034	−	268.527i	0.193792	−	0.335658i
$801$	−534.421	+	625.664i	−0.667192	+	0.781104i
$802$	−759.909	−	1316.20i	−0.947517	−	1.64115i
$803$	136.017	−	78.5297i	0.169387	−	0.0977954i
$804$	−1121.62	−	413.820i	−1.39505	−	0.514702i
$805$		0			0
$806$	−316.233	−	547.731i	−0.392348	−	0.679567i
$807$	309.586	−	839.106i	0.383626	−	1.03978i
$808$			3503.07i			4.33548i
$809$	171.307	+	296.712i	0.211751	+	0.366764i	0.952263	−	0.305280i	$-0.0987501\pi$
$809$	171.307	+	296.712i	0.211751	+	0.366764i	−0.740512	+	0.672044i	$0.765417\pi$
$810$	−1623.90	+	257.037i	−2.00482	+	0.317329i
$811$			467.249i			0.576140i	0.957609	+	0.288070i	$0.0930135\pi$
$811$			467.249i			0.576140i	−0.957609	+	0.288070i	$0.906986\pi$
$812$		0			0
$813$	675.952	−	116.133i	0.831429	−	0.142845i
$814$	−598.893			−0.735740
$815$	884.620	+	510.736i	1.08542	+	0.626670i
$816$	200.240	−	34.4024i	0.245392	−	0.0421598i
$817$	263.326	−	152.031i	0.322308	−	0.186085i
$818$			1213.40i			1.48338i
$819$		0			0
$820$	1977.35			2.41141
$821$	73.1862	+	126.762i	0.0891428	+	0.154400i	0.907149	−	0.420810i	$-0.138254\pi$
$821$	73.1862	+	126.762i	0.0891428	+	0.154400i	−0.818006	+	0.575209i	$0.804921\pi$
$822$	−1648.21	−	608.103i	−2.00512	−	0.739785i
$823$	452.985	−	784.593i	0.550407	−	0.953333i	−0.447838	−	0.894115i	$-0.647806\pi$
$823$	452.985	−	784.593i	0.550407	−	0.953333i	0.998245	−	0.0592181i	$-0.0188607\pi$
$824$		−	100.683i		−	0.122188i
$825$	−27.8940	+	23.1980i	−0.0338109	+	0.0281188i
$826$		0			0
$827$	1352.67			1.63564			0.817820	−	0.575474i	$-0.195182\pi$
$827$	1352.67			1.63564			0.817820	+	0.575474i	$0.195182\pi$
$828$	−479.219	−	409.333i	−0.578767	−	0.494363i
$829$	736.928	−	425.465i	0.888936	−	0.513227i	0.0153414	−	0.999882i	$-0.495116\pi$
$829$	736.928	−	425.465i	0.888936	−	0.513227i	0.873594	+	0.486655i	$0.161783\pi$
$830$	416.186			0.501428
$831$	208.689	−	173.556i	0.251129	−	0.208852i
$832$	681.855	−	393.669i	0.819538	−	0.473160i
$833$		0			0
$834$	572.325	−	98.3289i	0.686241	−	0.117900i
$835$	−816.783	−	1414.71i	−0.978184	−	1.69426i
$836$	558.567	−	322.489i	0.668143	−	0.385752i
$837$	−5.34384	+	405.924i	−0.00638451	+	0.484975i
$838$	−1125.54	−	649.831i	−1.34313	−	0.775455i
$839$	1011.65	+	584.078i	1.20578	+	0.696160i	0.961835	−	0.273629i	$-0.0882239\pi$
$839$	1011.65	+	584.078i	1.20578	+	0.696160i	0.243948	+	0.969788i	$0.421557\pi$
$840$		0			0
$841$	74.5367	+	129.101i	0.0886287	+	0.153509i
$842$	2391.89			2.84073
$843$	15.2582	+	88.8109i	0.0180999	+	0.105351i
$844$	1296.94			1.53665
$845$	−189.409	−	109.355i	−0.224152	−	0.129414i
$846$	21.1702	−	24.7847i	0.0250239	−	0.0292963i
$847$		0			0
$848$	−1362.19	+	2359.38i	−1.60636	+	2.78229i
$849$	−984.448	+	169.134i	−1.15954	+	0.199216i
$850$	27.9225	+	16.1210i	0.0328499	+	0.0189659i
$851$	244.321	−	423.176i	0.287098	−	0.497269i
$852$	31.0661	+	180.821i	0.0364625	+	0.212231i
$853$	196.344	+	113.359i	0.230181	+	0.132895i	0.610655	−	0.791896i	$-0.290906\pi$
$853$	196.344	+	113.359i	0.230181	+	0.132895i	−0.380475	+	0.924791i	$0.624239\pi$
$854$		0			0
$855$	1043.85	+	891.624i	1.22088	+	1.04283i
$856$	−170.354	+	295.062i	−0.199012	+	0.344698i
$857$			859.852i			1.00333i	0.865063	+	0.501664i	$0.167279\pi$
$857$			859.852i			1.00333i	−0.865063	+	0.501664i	$0.832721\pi$
$858$	−297.112	+	51.0456i	−0.346284	+	0.0594937i
$859$		−	1216.11i		−	1.41572i	−0.706351	−	0.707862i	$-0.749660\pi$
$859$		−	1216.11i		−	1.41572i	0.706351	−	0.707862i	$-0.250340\pi$
$860$	−503.656	+	290.786i	−0.585646	+	0.338123i
$861$		0			0
$862$	1400.48	−	2425.69i	1.62468	−	2.81403i
$863$	460.235	−	797.151i	0.533297	−	0.923698i	−0.465947	−	0.884813i	$-0.654286\pi$
$863$	460.235	−	797.151i	0.533297	−	0.923698i	0.999244	−	0.0388848i	$-0.0123805\pi$
$864$	−1653.62	−	21.7693i	−1.91392	−	0.0251960i
$865$	611.054	+	1058.38i	0.706421	+	1.22356i
$866$	−459.549	+	265.321i	−0.530657	+	0.306375i
$867$	−145.301	−	845.729i	−0.167591	−	0.975466i
$868$		0			0
$869$	−43.1054	−	74.6608i	−0.0496035	−	0.0859158i
$870$	−1024.20	−	1231.53i	−1.17724	−	1.41555i
$871$		−	466.585i		−	0.535689i
$872$	1121.65	+	1942.75i	1.28629	+	2.22792i
$873$	825.787	−	966.776i	0.945919	−	1.10742i
$874$			743.142i			0.850276i
$875$		0			0
$876$	1223.95	+	1471.71i	1.39720	+	1.68003i
$877$	1659.80			1.89259			0.946294	−	0.323307i	$-0.104794\pi$
$877$	1659.80			1.89259			0.946294	+	0.323307i	$0.104794\pi$
$878$	774.059	+	446.903i	0.881616	+	0.509001i
$879$	261.939	−	709.963i	0.297997	−	0.807694i
$880$	−446.525	+	257.801i	−0.507414	+	0.292956i
$881$			41.9293i			0.0475929i	0.999717	+	0.0237964i	$0.00757536\pi$
$881$			41.9293i			0.0475929i	−0.999717	+	0.0237964i	$0.992425\pi$
$882$		0			0
$883$	−1376.86			−1.55930			−0.779650	−	0.626215i	$-0.784603\pi$
$883$	−1376.86			−1.55930			−0.779650	+	0.626215i	$0.784603\pi$
$884$	94.8592	+	164.301i	0.107307	+	0.185861i
$885$	128.947	+	750.538i	0.145703	+	0.848065i
$886$	914.598	−	1584.13i	1.03228	−	1.78796i
$887$			180.165i			0.203118i	0.994830	+	0.101559i	$0.0323830\pi$
$887$			180.165i			0.203118i	−0.994830	+	0.101559i	$0.967617\pi$
$888$	−726.504	−	4228.63i	−0.818136	−	4.76197i
$889$		0			0
$890$	−1855.75			−2.08511
$891$	180.642	+	69.3623i	0.202740	+	0.0778476i
$892$	−266.808	+	154.042i	−0.299112	+	0.172692i
$893$	−27.2167			−0.0304778
$894$	−976.221	−	360.174i	−1.09197	−	0.402880i
$895$	−787.202	+	454.491i	−0.879555	+	0.507811i
$896$		0			0
$897$	85.1393	−	230.763i	0.0949156	−	0.257260i
$898$	−592.333	−	1025.95i	−0.659613	−	1.14248i
$899$	−342.515	+	197.751i	−0.380995	+	0.219968i
$900$	−336.205	−	287.175i	−0.373561	−	0.319083i
$901$	−103.117	−	59.5349i	−0.114448	−	0.0660764i
$902$	−284.610	−	164.320i	−0.315532	−	0.182172i
$903$		0			0
$904$	−780.181	−	1351.31i	−0.863032	−	1.49481i
$905$	1201.62			1.32776
$906$	−2835.22	−	1046.05i	−3.12938	−	1.15458i
$907$	325.652			0.359043			0.179522	−	0.983754i	$-0.442545\pi$
$907$	325.652			0.359043			0.179522	+	0.983754i	$0.442545\pi$
$908$	2116.35	+	1221.87i	2.33078	+	1.34568i
$909$	1467.82	+	272.119i	1.61476	+	0.299361i
$910$		0			0
$911$	506.920	−	878.011i	0.556443	−	0.963788i	−0.441346	−	0.897337i	$-0.645499\pi$
$911$	506.920	−	878.011i	0.556443	−	0.963788i	0.997790	−	0.0664512i	$-0.0211677\pi$
$912$	2100.74	+	2525.99i	2.30344	+	2.76973i
$913$	−42.4197	−	24.4910i	−0.0464619	−	0.0268248i
$914$	272.582	−	472.126i	0.298230	−	0.516550i
$915$	789.000	+	291.100i	0.862296	+	0.318142i
$916$	−1293.17	−	746.611i	−1.41175	−	0.815077i
$917$		0			0
$918$	2.26366	−	171.950i	0.00246586	−	0.187310i
$919$	88.3910	−	153.098i	0.0961818	−	0.166592i	−0.813919	−	0.580978i	$-0.802670\pi$
$919$	88.3910	−	153.098i	0.0961818	−	0.166592i	0.910101	+	0.414386i	$0.136004\pi$
$920$		−	835.541i		−	0.908197i
$921$	−298.326	−	358.715i	−0.323915	−	0.389485i
$922$			2601.17i			2.82122i
$923$	−62.0106	+	35.8019i	−0.0671838	+	0.0387886i
$924$		0			0
$925$	171.408	−	296.887i	0.185306	−	0.320959i
$926$	768.742	−	1331.50i	0.830175	−	1.43790i
$927$	−42.1869	−	7.82104i	−0.0455091	−	0.00843693i
$928$	−805.583	−	1395.31i	−0.868086	−	1.50357i
$929$	−215.592	+	124.472i	−0.232069	+	0.133985i	−0.611526	−	0.791224i	$-0.709444\pi$
$929$	−215.592	+	124.472i	−0.232069	+	0.133985i	0.379457	+	0.925209i	$0.376111\pi$
$930$	−703.937	+	585.429i	−0.756922	+	0.629494i
$931$		0			0
$932$	−287.134	−	497.330i	−0.308083	−	0.533616i
$933$	−366.306	+	62.9336i	−0.392611	+	0.0674529i
$934$		−	2459.27i		−	2.63305i
$935$	−11.2673	−	19.5155i	−0.0120505	−	0.0208722i
$936$	−720.840	−	2035.91i	−0.770129	−	2.17512i
$937$		−	573.923i		−	0.612511i	−0.951949	−	0.306256i	$-0.900924\pi$
$937$		−	573.923i		−	0.612511i	0.951949	−	0.306256i	$-0.0990762\pi$
$938$		0			0
$939$	258.013	−	699.321i	0.274774	−	0.744751i
$940$	52.0566			0.0553794
$941$	1137.10	+	656.507i	1.20840	+	0.697669i	0.962409	−	0.271603i	$-0.0875538\pi$
$941$	1137.10	+	656.507i	1.20840	+	0.697669i	0.245990	+	0.969272i	$0.420887\pi$
$942$	1449.41	+	1742.82i	1.53865	+	1.85012i
$943$	232.215	−	134.070i	0.246252	−	0.142174i
$944$			1822.48i			1.93060i
$945$		0			0
$946$	96.6581			0.102176
$947$	−555.456	−	962.077i	−0.586542	−	1.01592i	−0.994681	−	0.103001i	$-0.967155\pi$
$947$	−555.456	−	962.077i	−0.586542	−	1.01592i	0.408139	−	0.912920i	$-0.366178\pi$
$948$	807.831	−	671.832i	0.852142	−	0.708683i
$949$	−373.523	+	646.961i	−0.393596	+	0.681729i
$950$			521.365i			0.548805i
$951$	462.749	+	170.730i	0.486592	+	0.179527i
$952$		0			0
$953$	667.783			0.700717			0.350358	−	0.936616i	$-0.386060\pi$
$953$	667.783			0.700717			0.350358	+	0.936616i	$0.386060\pi$
$954$	1753.35	+	1497.65i	1.83789	+	1.56986i
$955$	1216.19	−	702.168i	1.27350	−	0.735254i
$956$	−698.878			−0.731044
$957$	31.9206	+	185.794i	0.0333548	+	0.194142i
$958$	256.614	−	148.156i	0.267864	−	0.154651i
$959$		0			0
$960$	−728.785	−	876.312i	−0.759151	−	0.912825i
$961$	−367.466	−	636.470i	−0.382379	−	0.662300i
$962$	2466.96	−	1424.30i	2.56441	−	1.48056i
$963$	110.400	+	94.3003i	0.114642	+	0.0979235i
$964$	−10.4314	−	6.02260i	−0.0108210	−	0.00624751i
$965$	−1.86248	−	1.07531i	−0.00193004	−	0.00111431i
$966$		0			0
$967$	244.801	+	424.008i	0.253155	+	0.438478i	0.964393	−	0.264474i	$-0.0851983\pi$
$967$	244.801	+	424.008i	0.253155	+	0.438478i	−0.711238	+	0.702952i	$0.751865\pi$
$968$	−2434.92			−2.51541
$969$	−110.399	+	91.8134i	−0.113931	+	0.0947506i
$970$	2867.50			2.95619
$971$	503.855	+	290.901i	0.518903	+	0.299589i	0.736486	−	0.676453i	$-0.236484\pi$
$971$	503.855	+	290.901i	0.518903	+	0.299589i	−0.217583	+	0.976042i	$0.569817\pi$
$972$	−460.362	+	2312.91i	−0.473623	+	2.37953i
$973$		0			0
$974$	277.577	−	480.778i	0.284987	−	0.493612i
$975$	59.7311	−	161.896i	0.0612626	−	0.166047i
$976$	1742.99	+	1006.31i	1.78585	+	1.03106i
$977$	563.162	−	975.426i	0.576420	−	0.998389i	−0.419466	−	0.907771i	$-0.637783\pi$
$977$	563.162	−	975.426i	0.576420	−	0.998389i	0.995886	−	0.0906177i	$-0.0288841\pi$
$978$	1590.81	−	1323.00i	1.62660	−	1.35276i
$979$	189.147	+	109.204i	0.193204	+	0.111547i
$980$		0			0
$981$	901.160	−	319.068i	0.918614	−	0.325247i
$982$	−633.813	+	1097.80i	−0.645430	+	1.11792i
$983$		−	29.9046i		−	0.0304217i	−0.999884	−	0.0152109i	$-0.995158\pi$
$983$		−	29.9046i		−	0.0304217i	0.999884	−	0.0152109i	$-0.00484196\pi$
$984$	814.965	−	2208.89i	0.828216	−	2.24481i
$985$			853.405i			0.866401i
$986$	145.090	−	83.7678i	0.147150	−	0.0849572i
$987$		0			0
$988$	−1533.90	+	2656.80i	−1.55253	+	2.68907i
$989$	−39.4321	+	68.2984i	−0.0398707	+	0.0690580i
$990$	145.654	+	411.379i	0.147125	+	0.415534i
$991$	383.881	+	664.901i	0.387367	+	0.670940i	0.992095	−	0.125493i	$-0.0400512\pi$
$991$	383.881	+	664.901i	0.387367	+	0.670940i	−0.604727	+	0.796433i	$0.706718\pi$
$992$	−797.554	+	460.468i	−0.803986	+	0.464181i
$993$	1347.59	+	497.190i	1.35709	+	0.500695i
$994$		0			0
$995$	109.237	+	189.204i	0.109786	+	0.190155i
$996$	206.634	−	560.062i	0.207463	−	0.562312i
$997$			14.9244i			0.0149693i	0.999972	+	0.00748464i	$0.00238246\pi$
$997$			14.9244i			0.0149693i	−0.999972	+	0.00748464i	$0.997618\pi$
$998$	−946.094	−	1638.68i	−0.947990	−	1.64197i
$999$	−1828.27	−	24.0685i	−1.83010	−	0.0240926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.3.k.a.313.1		28
7.2	even	3		63.3.l.a.34.1	yes	28
7.3	odd	6		441.3.t.b.178.13		28
7.4	even	3		441.3.t.b.178.14		28
7.5	odd	6		63.3.l.a.34.2	yes	28
7.6	odd	2	inner	441.3.k.a.313.2		28
9.4	even	3		441.3.t.b.166.13		28
21.2	odd	6		189.3.l.a.181.13		28
21.5	even	6		189.3.l.a.181.14		28
63.2	odd	6		567.3.d.g.244.1		14
63.4	even	3	inner	441.3.k.a.31.2		28
63.5	even	6		189.3.l.a.118.13		28
63.13	odd	6		441.3.t.b.166.14		28
63.16	even	3		567.3.d.h.244.14		14
63.23	odd	6		189.3.l.a.118.14		28
63.31	odd	6	inner	441.3.k.a.31.1		28
63.40	odd	6		63.3.l.a.13.1	✓	28
63.47	even	6		567.3.d.g.244.2		14
63.58	even	3		63.3.l.a.13.2	yes	28
63.61	odd	6		567.3.d.h.244.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.l.a.13.1	✓	28	63.40	odd	6
63.3.l.a.13.2	yes	28	63.58	even	3
63.3.l.a.34.1	yes	28	7.2	even	3
63.3.l.a.34.2	yes	28	7.5	odd	6
189.3.l.a.118.13		28	63.5	even	6
189.3.l.a.118.14		28	63.23	odd	6
189.3.l.a.181.13		28	21.2	odd	6
189.3.l.a.181.14		28	21.5	even	6
441.3.k.a.31.1		28	63.31	odd	6	inner
441.3.k.a.31.2		28	63.4	even	3	inner
441.3.k.a.313.1		28	1.1	even	1	trivial
441.3.k.a.313.2		28	7.6	odd	2	inner
441.3.t.b.166.13		28	9.4	even	3
441.3.t.b.166.14		28	63.13	odd	6
441.3.t.b.178.13		28	7.3	odd	6
441.3.t.b.178.14		28	7.4	even	3
567.3.d.g.244.1		14	63.2	odd	6
567.3.d.g.244.2		14	63.47	even	6
567.3.d.h.244.13		14	63.61	odd	6
567.3.d.h.244.14		14	63.16	even	3

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	441.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.85100 - 3.20603i) q^{2} +(-2.30657 + 1.91826i) q^{3} +(-4.85242 + 8.40464i) q^{4} +5.48291i q^{5} +(10.4195 + 3.84424i) q^{6} +21.1194 q^{8} +(1.64056 - 8.84921i) q^{9} +O(q^{10})\)	\(q+(-1.85100 - 3.20603i) q^{2} +(-2.30657 + 1.91826i) q^{3} +(-4.85242 + 8.40464i) q^{4} +5.48291i q^{5} +(10.4195 + 3.84424i) q^{6} +21.1194 q^{8} +(1.64056 - 8.84921i) q^{9} +(17.5784 - 10.1489i) q^{10} -2.38890 q^{11} +(-4.92983 - 28.6941i) q^{12} +(9.84037 - 5.68134i) q^{13} +(-10.5176 - 12.6467i) q^{15} +(-19.6823 - 34.0908i) q^{16} +(1.48995 - 0.860221i) q^{17} +(-31.4075 + 11.1202i) q^{18} +(24.0929 + 13.9100i) q^{19} +(-46.0819 - 26.6054i) q^{20} +(4.42186 + 7.65888i) q^{22} -7.21566 q^{23} +(-48.7134 + 40.5124i) q^{24} -5.06228 q^{25} +(-36.4291 - 21.0324i) q^{26} +(13.1910 + 23.5584i) q^{27} +(-13.1522 + 22.7804i) q^{29} +(-21.0776 + 57.1290i) q^{30} +(13.0212 + 7.51777i) q^{31} +(-30.6253 + 53.0446i) q^{32} +(5.51017 - 4.58253i) q^{33} +(-5.51579 - 3.18454i) q^{34} +(66.4138 + 56.7284i) q^{36} +(-33.8598 + 58.6469i) q^{37} -102.990i q^{38} +(-11.7992 + 31.9808i) q^{39} +115.796i q^{40} +(-32.1822 + 18.5804i) q^{41} +(5.46479 - 9.46530i) q^{43} +(11.5919 - 20.0778i) q^{44} +(48.5194 + 8.99502i) q^{45} +(13.3562 + 23.1336i) q^{46} +(-0.847241 + 0.489155i) q^{47} +(110.794 + 40.8770i) q^{48} +(9.37029 + 16.2298i) q^{50} +(-1.78654 + 4.84226i) q^{51} +110.273i q^{52} +(-34.6044 - 59.9366i) q^{53} +(51.1122 - 85.8975i) q^{54} -13.0981i q^{55} +(-82.2551 + 14.1319i) q^{57} +97.3794 q^{58} +(-40.0948 - 23.1487i) q^{59} +(157.327 - 27.0298i) q^{60} +(-44.2780 + 25.5639i) q^{61} -55.6616i q^{62} +69.2916 q^{64} +(31.1503 + 53.9539i) q^{65} +(-24.8911 - 9.18349i) q^{66} +(20.5315 - 35.5615i) q^{67} +16.6966i q^{68} +(16.6434 - 13.8415i) q^{69} -6.30166 q^{71} +(34.6475 - 186.890i) q^{72} +(-56.9373 + 32.8728i) q^{73} +250.698 q^{74} +(11.6765 - 9.71077i) q^{75} +(-233.818 + 134.995i) q^{76} +(124.372 - 21.3679i) q^{78} +(18.0441 + 31.2532i) q^{79} +(186.917 - 107.916i) q^{80} +(-75.6172 - 29.0353i) q^{81} +(119.139 + 68.7847i) q^{82} +(17.7570 + 10.2520i) q^{83} +(4.71651 + 8.16923i) q^{85} -40.4614 q^{86} +(-13.3620 - 77.7740i) q^{87} -50.4520 q^{88} +(-79.1776 - 45.7132i) q^{89} +(-60.9713 - 172.205i) q^{90} +(35.0134 - 60.6450i) q^{92} +(-44.4553 + 7.63769i) q^{93} +(3.13649 + 1.81085i) q^{94} +(-76.2675 + 132.099i) q^{95} +(-31.1138 - 181.099i) q^{96} +(122.345 + 70.6360i) q^{97} +(-3.91912 + 21.1399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9	\( 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 12 q^{9} - 8 q^{11} - 54 q^{15} - 42 q^{16} - 138 q^{18} + 14 q^{22} - 8 q^{23} - 56 q^{25} - 38 q^{29} - 294 q^{30} - 168 q^{32} + 234 q^{36} - 18 q^{37} + 84 q^{39} - 66 q^{43} - 54 q^{44} + 20 q^{46} + 196 q^{50} + 318 q^{51} - 260 q^{53} - 198 q^{57} + 68 q^{58} + 366 q^{60} + 72 q^{64} - 102 q^{65} + 68 q^{67} - 332 q^{71} + 714 q^{72} + 1232 q^{74} - 168 q^{78} + 146 q^{79} - 516 q^{81} + 78 q^{85} + 680 q^{86} + 148 q^{88} + 606 q^{92} - 1146 q^{93} - 360 q^{95} + 900 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 12 * q^9 - 8 * q^11 - 54 * q^15 - 42 * q^16 - 138 * q^18 + 14 * q^22 - 8 * q^23 - 56 * q^25 - 38 * q^29 - 294 * q^30 - 168 * q^32 + 234 * q^36 - 18 * q^37 + 84 * q^39 - 66 * q^43 - 54 * q^44 + 20 * q^46 + 196 * q^50 + 318 * q^51 - 260 * q^53 - 198 * q^57 + 68 * q^58 + 366 * q^60 + 72 * q^64 - 102 * q^65 + 68 * q^67 - 332 * q^71 + 714 * q^72 + 1232 * q^74 - 168 * q^78 + 146 * q^79 - 516 * q^81 + 78 * q^85 + 680 * q^86 + 148 * q^88 + 606 * q^92 - 1146 * q^93 - 360 * q^95 + 900 * q^99

Introduction

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