LMFDB - Embedded newform 189.3.l.a.118.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(118,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("189.118");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.l (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:	$5.14987699641$
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			118.13
Character	$\chi$	$=$	189.118
Dual form			189.3.l.a.181.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85100 + 3.20603i) q^{2} +(-4.85242 + 8.40464i) q^{4} +(-4.74834 - 2.74145i) q^{5} +(-3.62621 + 5.98754i) q^{7} -21.1194 q^{8} +O(q^{10})$	\(q+(1.85100 + 3.20603i) q^{2} +(-4.85242 + 8.40464i) q^{4} +(-4.74834 - 2.74145i) q^{5} +(-3.62621 + 5.98754i) q^{7} -21.1194 q^{8} -20.2978i q^{10} +(-1.19445 - 2.06885i) q^{11} +(9.84037 + 5.68134i) q^{13} +(-25.9084 - 0.542783i) q^{14} +(-19.6823 - 34.0908i) q^{16} +1.72044i q^{17} +27.8201i q^{19} +(46.0819 - 26.6054i) q^{20} +(4.42186 - 7.65888i) q^{22} +(-3.60783 + 6.24894i) q^{23} +(2.53114 + 4.38406i) q^{25} +42.0647i q^{26} +(-32.7272 - 59.5310i) q^{28} +(13.1522 + 22.7804i) q^{29} +(-13.0212 - 7.51777i) q^{31} +(30.6253 - 53.0446i) q^{32} +(-5.51579 + 3.18454i) q^{34} +(33.6330 - 18.4898i) q^{35} +67.7196 q^{37} +(-89.1921 + 51.4951i) q^{38} +(100.282 + 57.8978i) q^{40} +(32.1822 + 18.5804i) q^{41} +(5.46479 + 9.46530i) q^{43} +23.1839 q^{44} -26.7124 q^{46} +(-0.847241 + 0.489155i) q^{47} +(-22.7012 - 43.4241i) q^{49} +(-9.37029 + 16.2298i) q^{50} +(-95.4993 + 55.1365i) q^{52} -69.2088 q^{53} +13.0981i q^{55} +(76.5832 - 126.453i) q^{56} +(-48.6897 + 84.3330i) q^{58} +(-40.0948 - 23.1487i) q^{59} +(44.2780 - 25.5639i) q^{61} -55.6616i q^{62} +69.2916 q^{64} +(-31.1503 - 53.9539i) q^{65} +(20.5315 - 35.5615i) q^{67} +(-14.4597 - 8.34831i) q^{68} +(121.534 + 73.6039i) q^{70} +6.30166 q^{71} +65.7456i q^{73} +(125.349 + 217.111i) q^{74} +(-233.818 - 134.995i) q^{76} +(16.7186 + 0.350257i) q^{77} +(18.0441 + 31.2532i) q^{79} +215.833i q^{80} +137.569i q^{82} +(-17.7570 + 10.2520i) q^{83} +(4.71651 - 8.16923i) q^{85} +(-20.2307 + 35.0406i) q^{86} +(25.2260 + 43.6927i) q^{88} +91.4264i q^{89} +(-69.7005 + 38.3179i) q^{91} +(-35.0134 - 60.6450i) q^{92} +(-3.13649 - 1.81085i) q^{94} +(76.2675 - 132.099i) q^{95} +(122.345 - 70.6360i) q^{97} +(97.1990 - 153.159i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 26 q^{4} - 8 q^{8}+O(q^{10}) $ 28 * q + 2 * q^2 - 26 * q^4 - 8 * q^8	$ 28 q + 2 q^{2} - 26 q^{4} - 8 q^{8} - 4 q^{11} - 34 q^{14} - 42 q^{16} + 14 q^{22} - 4 q^{23} + 28 q^{25} + 20 q^{28} + 38 q^{29} + 168 q^{32} + 264 q^{35} + 36 q^{37} - 66 q^{43} - 108 q^{44} - 40 q^{46} - 38 q^{49} - 196 q^{50} - 520 q^{53} - 332 q^{56} - 34 q^{58} + 72 q^{64} + 102 q^{65} + 68 q^{67} + 102 q^{70} + 332 q^{71} + 616 q^{74} - 334 q^{77} + 146 q^{79} + 78 q^{85} + 340 q^{86} - 74 q^{88} - 384 q^{91} - 606 q^{92} + 360 q^{95} + 1076 q^{98}+O(q^{100}) $ 28 * q + 2 * q^2 - 26 * q^4 - 8 * q^8 - 4 * q^11 - 34 * q^14 - 42 * q^16 + 14 * q^22 - 4 * q^23 + 28 * q^25 + 20 * q^28 + 38 * q^29 + 168 * q^32 + 264 * q^35 + 36 * q^37 - 66 * q^43 - 108 * q^44 - 40 * q^46 - 38 * q^49 - 196 * q^50 - 520 * q^53 - 332 * q^56 - 34 * q^58 + 72 * q^64 + 102 * q^65 + 68 * q^67 + 102 * q^70 + 332 * q^71 + 616 * q^74 - 334 * q^77 + 146 * q^79 + 78 * q^85 + 340 * q^86 - 74 * q^88 - 384 * q^91 - 606 * q^92 + 360 * q^95 + 1076 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.85100	+	3.20603i	0.925501	+	1.60302i	0.790753	+	0.612136i	$0.209689\pi$
$2$	1.85100	+	3.20603i	0.925501	+	1.60302i	0.134749	+	0.990880i	$0.456977\pi$
$3$		0			0
$3$		0			0
$4$	−4.85242	+	8.40464i	−1.21311	+	2.10116i
$5$	−4.74834	−	2.74145i	−0.949668	−	0.548291i	−0.0566899	−	0.998392i	$-0.518055\pi$
$5$	−4.74834	−	2.74145i	−0.949668	−	0.548291i	−0.892978	+	0.450101i	$0.851388\pi$
$6$		0			0
$7$	−3.62621	+	5.98754i	−0.518030	+	0.855363i
$7$	−3.62621	+	5.98754i	−0.518030	+	0.855363i
$8$	−21.1194			−2.63992
$9$		0			0
$10$		−	20.2978i		−	2.02978i
$11$	−1.19445	−	2.06885i	−0.108586	−	0.188077i	0.806611	−	0.591082i	$-0.201299\pi$
$11$	−1.19445	−	2.06885i	−0.108586	−	0.188077i	−0.915198	+	0.403005i	$0.867966\pi$
$12$		0			0
$13$	9.84037	+	5.68134i	0.756952	+	0.437026i	0.828200	−	0.560432i	$-0.189365\pi$
$13$	9.84037	+	5.68134i	0.756952	+	0.437026i	−0.0712485	+	0.997459i	$0.522698\pi$
$14$	−25.9084	−	0.542783i	−1.85060	−	0.0387702i
$15$		0			0
$16$	−19.6823	−	34.0908i	−1.23014	−	2.13067i
$17$			1.72044i			0.101202i	0.998719	+	0.0506012i	$0.0161137\pi$
$17$			1.72044i			0.101202i	−0.998719	+	0.0506012i	$0.983886\pi$
$18$		0			0
$19$			27.8201i			1.46422i	0.681189	+	0.732108i	$0.261463\pi$
$19$			27.8201i			1.46422i	−0.681189	+	0.732108i	$0.738537\pi$
$20$	46.0819	−	26.6054i	2.30409	−	1.33027i
$21$		0			0
$22$	4.42186	−	7.65888i	0.200993	−	0.348131i
$23$	−3.60783	+	6.24894i	−0.156862	+	0.271693i	−0.933736	−	0.357964i	$-0.883471\pi$
$23$	−3.60783	+	6.24894i	−0.156862	+	0.271693i	0.776873	+	0.629657i	$0.216804\pi$
$24$		0			0
$25$	2.53114	+	4.38406i	0.101246	+	0.175362i
$26$			42.0647i			1.61787i
$27$		0			0
$28$	−32.7272	−	59.5310i	−1.16883	−	2.12611i
$29$	13.1522	+	22.7804i	0.453526	+	0.785530i	0.998602	−	0.0528567i	$-0.0168327\pi$
$29$	13.1522	+	22.7804i	0.453526	+	0.785530i	−0.545076	+	0.838386i	$0.683499\pi$
$30$		0			0
$31$	−13.0212	−	7.51777i	−0.420037	−	0.242509i	0.275056	−	0.961428i	$-0.411304\pi$
$31$	−13.0212	−	7.51777i	−0.420037	−	0.242509i	−0.695093	+	0.718920i	$0.744637\pi$
$32$	30.6253	−	53.0446i	0.957041	−	1.65764i
$33$		0			0
$34$	−5.51579	+	3.18454i	−0.162229	+	0.0936630i
$35$	33.6330	−	18.4898i	0.960943	−	0.528279i
$36$		0			0
$37$	67.7196			1.83026			0.915130	−	0.403159i	$-0.132088\pi$
$37$	67.7196			1.83026			0.915130	+	0.403159i	$0.132088\pi$
$38$	−89.1921	+	51.4951i	−2.34716	+	1.35513i
$39$		0			0
$40$	100.282	+	57.8978i	2.50705	+	1.44744i
$41$	32.1822	+	18.5804i	0.784931	+	0.453180i	0.838175	−	0.545401i	$-0.183623\pi$
$41$	32.1822	+	18.5804i	0.784931	+	0.453180i	−0.0532441	+	0.998582i	$0.516956\pi$
$42$		0			0
$43$	5.46479	+	9.46530i	0.127088	+	0.220123i	0.922547	−	0.385884i	$-0.126104\pi$
$43$	5.46479	+	9.46530i	0.127088	+	0.220123i	−0.795459	+	0.606007i	$0.792770\pi$
$44$	23.1839			0.526906
$45$		0			0
$46$	−26.7124			−0.580704
$47$	−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	$0.336646\pi$
$48$		0			0
$49$	−22.7012	−	43.4241i	−0.463291	−	0.886206i
$50$	−9.37029	+	16.2298i	−0.187406	+	0.324596i
$51$		0			0
$52$	−95.4993	+	55.1365i	−1.83652	+	1.06032i
$53$	−69.2088			−1.30583			−0.652913	−	0.757433i	$-0.726453\pi$
$53$	−69.2088			−1.30583			−0.652913	+	0.757433i	$0.726453\pi$
$54$		0			0
$55$			13.0981i			0.238147i
$56$	76.5832	−	126.453i	1.36756	−	2.25809i
$57$		0			0
$58$	−48.6897	+	84.3330i	−0.839478	+	1.45402i
$59$	−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	$0.795005\pi$
$60$		0			0
$61$	44.2780	−	25.5639i	0.725869	−	0.419081i	−0.0910399	−	0.995847i	$-0.529019\pi$
$61$	44.2780	−	25.5639i	0.725869	−	0.419081i	0.816909	+	0.576766i	$0.195686\pi$
$62$		−	55.6616i		−	0.897768i
$63$		0			0
$64$	69.2916			1.08268
$65$	−31.1503	−	53.9539i	−0.479235	−	0.830059i
$66$		0			0
$67$	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	$0.0675289\pi$
$68$	−14.4597	−	8.34831i	−0.212643	−	0.122769i
$69$		0			0
$70$	121.534	+	73.6039i	1.73619	+	1.05148i
$71$	6.30166			0.0887557			0.0443779	−	0.999015i	$-0.485869\pi$
$71$	6.30166			0.0887557			0.0443779	+	0.999015i	$0.485869\pi$
$72$		0			0
$73$			65.7456i			0.900624i	0.892871	+	0.450312i	$0.148687\pi$
$73$			65.7456i			0.900624i	−0.892871	+	0.450312i	$0.851313\pi$
$74$	125.349	+	217.111i	1.69391	+	2.93393i
$75$		0			0
$76$	−233.818	−	134.995i	−3.07655	−	1.77625i
$77$	16.7186	+	0.350257i	0.217125	+	0.00454879i
$78$		0			0
$79$	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	$0.759982\pi$
$80$			215.833i			2.69791i
$81$		0			0
$82$			137.569i			1.67767i
$83$	−17.7570	+	10.2520i	−0.213940	+	0.123518i	−0.603141	−	0.797635i	$-0.706084\pi$
$83$	−17.7570	+	10.2520i	−0.213940	+	0.123518i	0.389201	+	0.921153i	$0.372751\pi$
$84$		0			0
$85$	4.71651	−	8.16923i	0.0554884	−	0.0961086i
$86$	−20.2307	+	35.0406i	−0.235241	+	0.407449i
$87$		0			0
$88$	25.2260	+	43.6927i	0.286659	+	0.496508i
$89$			91.4264i			1.02726i	0.858011	+	0.513631i	$0.171700\pi$
$89$			91.4264i			1.02726i	−0.858011	+	0.513631i	$0.828300\pi$
$90$		0			0
$91$	−69.7005	+	38.3179i	−0.765939	+	0.421076i
$92$	−35.0134	−	60.6450i	−0.380581	−	0.659185i
$93$		0			0
$94$	−3.13649	−	1.81085i	−0.0333669	−	0.0192644i
$95$	76.2675	−	132.099i	0.802816	−	1.39052i
$96$		0			0
$97$	122.345	−	70.6360i	1.26129	−	0.728206i	0.287966	−	0.957641i	$-0.407021\pi$
$97$	122.345	−	70.6360i	1.26129	−	0.728206i	0.973324	+	0.229434i	$0.0736876\pi$
$98$	97.1990	−	153.159i	0.991827	−	1.56285i
$99$		0			0
$100$	−49.1286			−0.491286
$101$	143.648	−	82.9350i	1.42225	−	0.821138i	0.425762	−	0.904835i	$-0.360006\pi$
$101$	143.648	−	82.9350i	1.42225	−	0.821138i	0.996491	+	0.0836968i	$0.0266727\pi$
$102$		0			0
$103$	−4.12861	−	2.38366i	−0.0400836	−	0.0231423i	0.479824	−	0.877365i	$-0.340700\pi$
$103$	−4.12861	−	2.38366i	−0.0400836	−	0.0231423i	−0.519908	+	0.854222i	$0.674034\pi$
$104$	−207.822	−	119.986i	−1.99829	−	1.15371i
$105$		0			0
$106$	−128.106	−	221.886i	−1.20854	−	2.09326i
$107$	−16.1325			−0.150771			−0.0753854	−	0.997154i	$-0.524019\pi$
$107$	−16.1325			−0.150771			−0.0753854	+	0.997154i	$0.524019\pi$
$108$		0			0
$109$	−106.220			−0.974493			−0.487247	−	0.873264i	$-0.661999\pi$
$109$	−106.220			−0.974493			−0.487247	+	0.873264i	$0.661999\pi$
$110$	−41.9929	+	24.2446i	−0.381754	+	0.220406i
$111$		0			0
$112$	275.492	+	5.77159i	2.45975	+	0.0515321i
$113$	36.9415	−	63.9845i	0.326916	−	0.566235i	−0.654982	−	0.755644i	$-0.727324\pi$
$113$	36.9415	−	63.9845i	0.326916	−	0.566235i	0.981898	+	0.189409i	$0.0606573\pi$
$114$		0			0
$115$	34.2624	−	19.7814i	0.297934	−	0.172012i
$116$	−255.281			−2.20070
$117$		0			0
$118$		−	171.393i		−	1.45249i
$119$	−10.3012	−	6.23868i	−0.0865648	−	0.0524259i
$120$		0			0
$121$	57.6466	−	99.8468i	0.476418	−	0.825180i
$122$	163.917	+	94.6378i	1.34359	+	0.775720i
$123$		0			0
$124$	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
$129$		0			0
$130$	115.318	−	199.737i	0.887065	−	1.53644i
$131$	−69.9631	−	40.3932i	−0.534069	−	0.308345i	0.208603	−	0.978000i	$-0.433108\pi$
$131$	−69.9631	−	40.3932i	−0.534069	−	0.308345i	−0.742672	+	0.669655i	$0.766442\pi$
$132$		0			0
$133$	−166.574	−	100.881i	−1.25244	−	0.758507i
$134$	152.015			1.13444
$135$		0			0
$136$		−	36.3346i		−	0.267166i
$137$	−79.0928	−	136.993i	−0.577319	−	0.999947i	−0.995785	−	0.0917141i	$-0.970765\pi$
$137$	−79.0928	−	136.993i	−0.577319	−	0.999947i	0.418466	−	0.908232i	$-0.362568\pi$
$138$		0			0
$139$	45.2826	+	26.1439i	0.325774	+	0.188086i	0.653963	−	0.756526i	$-0.273105\pi$
$139$	45.2826	+	26.1439i	0.325774	+	0.188086i	−0.328189	+	0.944612i	$0.606438\pi$
$140$	−7.80170	+	372.394i	−0.0557264	+	2.65995i
$141$		0			0
$142$	11.6644	+	20.2033i	0.0821435	+	0.142277i
$143$		−	27.1443i		−	0.189820i
$144$		0			0
$145$		−	144.225i		−	0.994656i
$146$	−210.782	+	121.695i	−1.44371	+	0.833529i
$147$		0			0
$148$	−328.604	+	569.159i	−2.22030	+	3.84567i
$149$	−46.8460	+	81.1397i	−0.314403	+	0.544561i	−0.979310	−	0.202364i	$-0.935138\pi$
$149$	−46.8460	+	81.1397i	−0.314403	+	0.544561i	0.664908	+	0.746926i	$0.268471\pi$
$150$		0			0
$151$	136.054	+	235.652i	0.901020	+	1.56061i	0.826173	+	0.563417i	$0.190513\pi$
$151$	136.054	+	235.652i	0.901020	+	1.56061i	0.0748465	+	0.997195i	$0.476153\pi$
$152$		−	587.543i		−	3.86541i
$153$		0			0
$154$	29.8233	+	54.2487i	0.193658	+	0.352264i
$155$	41.2192	+	71.3938i	0.265930	+	0.460605i
$156$		0			0
$157$	−176.758	−	102.051i	−1.12584	−	0.650007i	−0.182958	−	0.983121i	$-0.558567\pi$
$157$	−176.758	−	102.051i	−1.12584	−	0.650007i	−0.942886	+	0.333114i	$0.891901\pi$
$158$	−66.7993	+	115.700i	−0.422780	+	0.732277i
$159$		0			0
$160$	−290.839	+	167.916i	−1.81774	+	1.04947i
$161$	−24.3330	−	44.2620i	−0.151137	−	0.274919i
$162$		0			0
$163$	−186.301			−1.14295			−0.571476	−	0.820619i	$-0.693629\pi$
$163$	−186.301			−1.14295			−0.571476	+	0.820619i	$0.693629\pi$
$164$	−312.323	+	180.320i	−1.90441	+	1.09951i
$165$		0			0
$166$	−65.7365	−	37.9530i	−0.396003	−	0.228633i
$167$	258.022	+	148.969i	1.54504	+	0.892030i	0.998509	+	0.0545920i	$0.0173858\pi$
$167$	258.022	+	148.969i	1.54504	+	0.892030i	0.546532	+	0.837438i	$0.315948\pi$
$168$		0			0
$169$	−19.9447	−	34.5453i	−0.118016	−	0.204410i
$170$	34.9211			0.205418
$171$		0			0
$172$	−106.070			−0.616686
$173$	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	$0.110523\pi$
$174$		0			0
$175$	−35.4282	−	0.742225i	−0.202447	−	0.00424129i
$176$	−47.0190	+	81.4394i	−0.267154	+	0.462724i
$177$		0			0
$178$	−293.116	+	169.231i	−1.64672	+	0.950733i
$179$	165.785			0.926171			0.463086	−	0.886314i	$-0.346742\pi$
$179$	165.785			0.926171			0.463086	+	0.886314i	$0.346742\pi$
$180$		0			0
$181$			219.158i			1.21082i	0.795915	+	0.605408i	$0.206990\pi$
$181$			219.158i			1.21082i	−0.795915	+	0.605408i	$0.793010\pi$
$182$	−251.864	−	152.535i	−1.38387	−	0.838107i
$183$		0			0
$184$	76.1951	−	131.974i	0.414104	−	0.717248i
$185$	−321.556	−	185.650i	−1.73814	−	1.00351i
$186$		0			0
$187$	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	$0.0672523\pi$
$191$	128.065	+	221.815i	0.670497	+	1.16133i	−0.307267	+	0.951623i	$0.599414\pi$
$192$		0			0
$193$	−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	$0.166990\pi$
$194$	452.922	+	261.495i	2.33465	+	1.34791i
$195$		0			0
$196$	475.120	+	19.9164i	2.42408	+	0.101614i
$197$	−155.648			−0.790092			−0.395046	−	0.918661i	$-0.629271\pi$
$197$	−155.648			−0.790092			−0.395046	+	0.918661i	$0.629271\pi$
$198$		0			0
$199$		−	39.8464i		−	0.200233i	−0.994976	−	0.100117i	$-0.968078\pi$
$199$		−	39.8464i		−	0.200233i	0.994976	−	0.100117i	$-0.0319216\pi$
$200$	−53.4561	−	92.5886i	−0.267280	−	0.462943i
$201$		0			0
$202$	531.784	+	307.026i	2.63259	+	1.51993i
$203$	−184.091	−	3.85673i	−0.906853	−	0.0189987i
$204$		0			0
$205$	−101.875	−	176.452i	−0.496949	−	0.860741i
$206$		−	17.6486i		−	0.0856729i
$207$		0			0
$208$		−	447.288i		−	2.15042i
$209$	57.5555	−	33.2297i	0.275385	−	0.158994i
$210$		0			0
$211$	−66.8190	+	115.734i	−0.316678	+	0.548502i	−0.979793	−	0.200016i	$-0.935901\pi$
$211$	−66.8190	+	115.734i	−0.316678	+	0.548502i	0.663115	+	0.748518i	$0.269234\pi$
$212$	335.830	−	581.675i	1.58411	−	2.74375i
$213$		0			0
$214$	−29.8613	−	51.7212i	−0.139539	−	0.241688i
$215$		−	59.9259i		−	0.278725i
$216$		0			0
$217$	92.2303	−	50.7037i	0.425025	−	0.233658i
$218$	−196.613	−	340.544i	−0.901895	−	1.56213i
$219$		0			0
$220$	−110.085	−	63.5575i	−0.500386	−	0.288898i
$221$	−9.77441	+	16.9298i	−0.0442281	+	0.0766053i
$222$		0			0
$223$	27.4922	−	15.8727i	0.123284	−	0.0711778i	−0.437090	−	0.899418i	$-0.643991\pi$
$223$	27.4922	−	15.8727i	0.123284	−	0.0711778i	0.560374	+	0.828240i	$0.310658\pi$
$224$	206.553	+	375.721i	0.922111	+	1.67733i
$225$		0			0
$226$	273.515			1.21024
$227$	−218.071	+	125.904i	−0.960667	+	0.554641i	−0.896378	−	0.443290i	$-0.853811\pi$
$227$	−218.071	+	125.904i	−0.960667	+	0.554641i	−0.0642884	+	0.997931i	$0.520478\pi$
$228$		0			0
$229$	133.250	+	76.9317i	0.581876	+	0.335946i	0.761879	−	0.647720i	$-0.224277\pi$
$229$	133.250	+	76.9317i	0.581876	+	0.335946i	−0.180002	+	0.983666i	$0.557611\pi$
$230$	126.840	+	73.2308i	0.551476	+	0.318395i
$231$		0			0
$232$	−277.767	−	481.107i	−1.19727	−	2.07374i
$233$	−59.1732			−0.253962			−0.126981	−	0.991905i	$-0.540529\pi$
$233$	−59.1732			−0.253962			−0.126981	+	0.991905i	$0.540529\pi$
$234$		0			0
$235$	5.36398			0.0228255
$236$	389.113	−	224.655i	1.64879	−	0.951927i
$237$		0			0
$238$	0.933827	−	44.5738i	0.00392364	−	0.187285i
$239$	−36.0066	+	62.3653i	−0.150655	+	0.260943i	−0.931469	−	0.363822i	$-0.881472\pi$
$239$	−36.0066	+	62.3653i	−0.150655	+	0.260943i	0.780813	+	0.624765i	$0.214805\pi$
$240$		0			0
$241$	−1.07487	+	0.620576i	−0.00446004	+	0.00257500i	−0.502228	−	0.864735i	$-0.667486\pi$
$241$	−1.07487	+	0.620576i	−0.00446004	+	0.00257500i	0.497768	+	0.867310i	$0.334153\pi$
$242$	426.816			1.76370
$243$		0			0
$244$			496.188i			2.03356i
$245$	−11.2521	+	268.427i	−0.0459269	+	1.09562i
$246$		0			0
$247$	−158.055	+	273.760i	−0.639901	+	1.10834i
$248$	274.999	+	158.770i	1.10887	+	0.640204i
$249$		0			0
$250$	−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
$255$		0			0
$256$	117.268	−	203.114i	0.458079	−	0.793415i
$257$	−359.285	−	207.433i	−1.39800	−	0.807134i	−0.403815	−	0.914841i	$-0.632316\pi$
$257$	−359.285	−	207.433i	−1.39800	−	0.807134i	−0.994183	+	0.107707i	$0.965649\pi$
$258$		0			0
$259$	−245.565	+	405.474i	−0.948129	+	1.56554i
$260$	604.617			2.32545
$261$		0			0
$262$		−	299.072i		−	1.14150i
$263$	180.213	+	312.139i	0.685222	+	1.18684i	0.973367	+	0.229252i	$0.0736281\pi$
$263$	180.213	+	312.139i	0.685222	+	1.18684i	−0.288145	+	0.957587i	$0.593039\pi$
$264$		0			0
$265$	328.627	+	189.733i	1.24010	+	0.715973i
$266$	15.1003	−	720.773i	0.0567680	−	2.70967i
$267$		0			0
$268$	199.255	+	345.119i	0.743488	+	1.28776i
$269$		−	298.132i		−	1.10830i	−0.832418	−	0.554148i	$-0.813044\pi$
$269$		−	298.132i		−	1.10830i	0.832418	−	0.554148i	$-0.186956\pi$
$270$		0			0
$271$		−	228.618i		−	0.843611i	−0.906686	−	0.421805i	$-0.861397\pi$
$271$		−	228.618i		−	0.843611i	0.906686	−	0.421805i	$-0.138603\pi$
$272$	58.6512	−	33.8623i	0.215629	−	0.124494i
$273$		0			0
$274$	292.802	−	507.148i	1.06862	−	1.85090i
$275$	6.04663	−	10.4731i	0.0219878	−	0.0380839i
$276$		0			0
$277$	45.2378	+	78.3542i	0.163313	+	0.282867i	0.936055	−	0.351854i	$-0.114449\pi$
$277$	45.2378	+	78.3542i	0.163313	+	0.282867i	−0.772742	+	0.634721i	$0.781115\pi$
$278$			193.570i			0.696295i
$279$		0			0
$280$	−710.308	+	390.492i	−2.53681	+	1.39462i
$281$	−15.0187	−	26.0131i	−0.0534473	−	0.0925734i	0.838064	−	0.545572i	$-0.183688\pi$
$281$	−15.0187	−	26.0131i	−0.0534473	−	0.0925734i	−0.891511	+	0.452999i	$0.850354\pi$
$282$		0			0
$283$	−288.349	−	166.479i	−1.01890	−	0.588264i	−0.105117	−	0.994460i	$-0.533522\pi$
$283$	−288.349	−	166.479i	−1.01890	−	0.588264i	−0.913786	+	0.406196i	$0.866855\pi$
$284$	−30.5783	+	52.9632i	−0.107670	+	0.186490i
$285$		0			0
$286$	87.0254	−	50.2442i	0.304285	−	0.175679i
$287$	−227.950	+	125.316i	−0.794251	+	0.436640i
$288$		0			0
$289$	286.040			0.989758
$290$	462.390	−	266.961i	1.59445	−	0.920556i
$291$		0			0
$292$	−552.568	−	319.025i	−1.89236	−	1.09255i
$293$	218.453	+	126.124i	0.745573	+	0.430457i	0.824092	−	0.566456i	$-0.191686\pi$
$293$	218.453	+	126.124i	0.745573	+	0.430457i	−0.0785193	+	0.996913i	$0.525019\pi$
$294$		0			0
$295$	126.922	+	219.836i	0.430245	+	0.745206i
$296$	−1430.20			−4.83174
$297$		0			0
$298$	−346.848			−1.16392
$299$	−71.0048	+	40.9946i	−0.237474	+	0.137106i
$300$		0			0
$301$	−76.4903	−	1.60248i	−0.254121	−	0.00532386i
$302$	−503.672	+	872.386i	−1.66779	+	2.88870i
$303$		0			0
$304$	948.409	−	547.564i	3.11976	−	1.80120i
$305$	−280.329			−0.919113
$306$		0			0
$307$		−	155.519i		−	0.506576i	−0.967391	−	0.253288i	$-0.918488\pi$
$307$		−	155.519i		−	0.506576i	0.967391	−	0.253288i	$-0.0815120\pi$
$308$	−84.0696	+	138.814i	−0.272953	+	0.450696i
$309$		0			0
$310$	−152.594	+	264.300i	−0.492238	+	0.852581i
$311$	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	$0.602838\pi$
$312$		0			0
$313$	215.178	−	124.233i	0.687471	−	0.396911i	−0.115193	−	0.993343i	$-0.536749\pi$
$313$	215.178	−	124.233i	0.687471	−	0.396911i	0.802664	+	0.596432i	$0.203415\pi$
$314$		−	755.587i		−	2.40633i
$315$		0			0
$316$	−350.230			−1.10832
$317$	82.2066	+	142.386i	0.259327	+	0.449167i	0.966062	−	0.258311i	$-0.0831660\pi$
$317$	82.2066	+	142.386i	0.259327	+	0.449167i	−0.706735	+	0.707478i	$0.749833\pi$
$318$		0			0
$319$	31.4194	−	54.4200i	0.0984933	−	0.170595i
$320$	−329.020	−	189.960i	−1.02819	−	0.593624i
$321$		0			0
$322$	96.8647	−	159.942i	0.300822	−	0.496713i
$323$	−47.8628			−0.148182
$324$		0			0
$325$			57.5211i			0.176988i
$326$	−344.844	−	597.287i	−1.05780	−	1.83217i
$327$		0			0
$328$	−679.667	−	392.406i	−2.07216	−	1.19636i
$329$	0.143439	−	6.84667i	0.000435984	−	0.0208105i
$330$		0			0
$331$	−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	$-0.424021\pi$
$332$		−	198.988i		−	0.599363i
$333$		0			0
$334$			1102.97i			3.30230i
$335$	−194.981	+	112.572i	−0.582032	+	0.336036i
$336$		0			0
$337$	−10.8833	+	18.8505i	−0.0322947	+	0.0559361i	−0.881721	−	0.471771i	$-0.843615\pi$
$337$	−10.8833	+	18.8505i	−0.0322947	+	0.0559361i	0.849426	+	0.527707i	$0.176948\pi$
$338$	73.8355	−	127.887i	0.218448	−	0.378363i
$339$		0			0
$340$	45.7730	+	79.2812i	0.134626	+	0.233180i
$341$			35.9184i			0.105332i
$342$		0			0
$343$	342.323	+	21.5403i	0.998026	+	0.0627998i
$344$	−115.413	−	199.901i	−0.335503	−	0.581108i
$345$		0			0
$346$	714.606	+	412.578i	2.06533	+	1.19242i
$347$	−317.158	+	549.333i	−0.913999	+	1.58309i	−0.105639	+	0.994405i	$0.533689\pi$
$347$	−317.158	+	549.333i	−0.913999	+	1.58309i	−0.808360	+	0.588688i	$0.799645\pi$
$348$		0			0
$349$	12.9494	−	7.47635i	0.0371044	−	0.0214222i	−0.481333	−	0.876538i	$-0.659847\pi$
$349$	12.9494	−	7.47635i	0.0371044	−	0.0214222i	0.518437	+	0.855116i	$0.326514\pi$
$350$	−63.1981	−	114.958i	−0.180566	−	0.328451i
$351$		0			0
$352$	−146.321			−0.415686
$353$	144.273	−	83.2961i	0.408705	−	0.235966i	−0.281528	−	0.959553i	$-0.590841\pi$
$353$	144.273	−	83.2961i	0.408705	−	0.235966i	0.690233	+	0.723587i	$0.257508\pi$
$354$		0			0
$355$	−29.9224	−	17.2757i	−0.0842884	−	0.0486639i
$356$	−768.406	−	443.640i	−2.15844	−	1.24618i
$357$		0			0
$358$	306.868	+	531.511i	0.857173	+	1.48467i
$359$	543.026			1.51261			0.756303	−	0.654221i	$-0.227003\pi$
$359$	543.026			1.51261			0.756303	+	0.654221i	$0.227003\pi$
$360$		0			0
$361$	−412.958			−1.14393
$362$	−702.626	+	405.661i	−1.94096	+	1.12061i
$363$		0			0
$364$	16.1681	−	771.742i	0.0444179	−	2.12017i
$365$	180.238	−	312.182i	0.493804	−	0.855293i
$366$		0			0
$367$	−305.169	+	176.189i	−0.831523	+	0.480080i	−0.854374	−	0.519659i	$-0.826059\pi$
$367$	−305.169	+	176.189i	−0.831523	+	0.480080i	0.0228511	+	0.999739i	$0.492726\pi$
$368$	284.042			0.771853
$369$		0			0
$370$		−	1374.56i		−	3.71502i
$371$	250.966	−	414.390i	0.676457	−	1.11696i
$372$		0			0
$373$	−102.902	+	178.231i	−0.275876	+	0.477832i	−0.970356	−	0.241680i	$-0.922301\pi$
$373$	−102.902	+	178.231i	−0.275876	+	0.477832i	0.694479	+	0.719513i	$0.255635\pi$
$374$	13.1767	+	7.60754i	0.0352317	+	0.0203410i
$375$		0			0
$376$	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
$381$		0			0
$382$	−474.097	+	821.160i	−1.24109	+	2.14963i
$383$	103.312	+	59.6474i	0.269745	+	0.155737i	0.628772	−	0.777590i	$-0.283558\pi$
$383$	103.312	+	59.6474i	0.269745	+	0.155737i	−0.359027	+	0.933327i	$0.616891\pi$
$384$		0			0
$385$	−78.4254	−	47.4965i	−0.203702	−	0.123367i
$386$	−1.45207			−0.00376184
$387$		0			0
$388$			1371.02i			3.53356i
$389$	−294.445	−	509.994i	−0.756929	−	1.31104i	−0.944410	−	0.328771i	$-0.893366\pi$
$389$	−294.445	−	509.994i	−0.756929	−	1.31104i	0.187481	−	0.982268i	$-0.439968\pi$
$390$		0			0
$391$	−10.7509	−	6.20706i	−0.0274960	−	0.0158748i
$392$	479.436	+	917.090i	1.22305	+	2.33951i
$393$		0			0
$394$	−288.105	−	499.013i	−0.731232	−	1.26653i
$395$		−	197.868i		−	0.500932i
$396$		0			0
$397$		−	478.715i		−	1.20583i	−0.797805	−	0.602916i	$-0.794006\pi$
$397$		−	478.715i		−	1.20583i	0.797805	−	0.602916i	$-0.205994\pi$
$398$	127.749	−	73.7557i	0.320977	−	0.185316i
$399$		0			0
$400$	99.6374	−	172.577i	0.249093	−	0.431443i
$401$	205.269	−	355.537i	0.511894	−	0.886626i	−0.488011	−	0.872837i	$-0.662277\pi$
$401$	205.269	−	355.537i	0.511894	−	0.886626i	0.999905	−	0.0137888i	$-0.00438926\pi$
$402$		0			0
$403$	−85.4220	−	147.955i	−0.211965	−	0.367135i
$404$			1609.74i			3.98451i
$405$		0			0
$406$	−328.388	−	597.341i	−0.808838	−	1.47128i
$407$	−80.8876	−	140.101i	−0.198741	−	0.344230i
$408$		0			0
$409$	283.857	+	163.885i	0.694026	+	0.400696i	0.805119	−	0.593114i	$-0.202102\pi$
$409$	283.857	+	163.885i	0.694026	+	0.400696i	−0.111092	+	0.993810i	$0.535435\pi$
$410$	377.140	−	653.226i	0.919854	−	1.59323i
$411$		0			0
$412$	40.0675	−	23.1330i	0.0972513	−	0.0561481i
$413$	283.996	−	156.127i	0.687641	−	0.378031i
$414$		0			0
$415$	112.422			0.270896
$416$	602.729	−	347.986i	1.44887	−	0.836504i
$417$		0			0
$418$	213.071	+	123.016i	0.509739	+	0.294298i
$419$	−304.035	−	175.535i	−0.725622	−	0.418938i	0.0911967	−	0.995833i	$-0.470931\pi$
$419$	−304.035	−	175.535i	−0.725622	−	0.418938i	−0.816818	+	0.576895i	$0.804264\pi$
$420$		0			0
$421$	−323.054	−	559.546i	−0.767349	−	1.32909i	−0.938996	−	0.343928i	$-0.888242\pi$
$421$	−323.054	−	559.546i	−0.767349	−	1.32909i	0.171647	−	0.985158i	$-0.445091\pi$
$422$	−494.729			−1.17234
$423$		0			0
$424$	1461.65			3.44728
$425$	−7.54252	+	4.35468i	−0.0177471	+	0.0102463i
$426$		0			0
$427$	−7.49630	+	357.816i	−0.0175557	+	0.837978i
$428$	78.2816	−	135.588i	0.182901	−	0.316794i
$429$		0			0
$430$	192.124	−	110.923i	0.446801	−	0.257961i
$431$	756.604			1.75546			0.877730	−	0.479155i	$-0.159057\pi$
$431$	756.604			1.75546			0.877730	+	0.479155i	$0.159057\pi$
$432$		0			0
$433$			143.339i			0.331037i	0.986207	+	0.165518i	$0.0529297\pi$
$433$			143.339i			0.331037i	−0.986207	+	0.165518i	$0.947070\pi$
$434$	333.276	+	201.841i	0.767917	+	0.465071i
$435$		0			0
$436$	515.423	−	892.739i	1.18216	−	2.04757i
$437$	−173.846	−	100.370i	−0.397817	−	0.229680i
$438$		0			0
$439$	209.092	−	120.719i	0.476291	−	0.274987i	−0.242578	−	0.970132i	$-0.577993\pi$
$439$	209.092	−	120.719i	0.476291	−	0.274987i	0.718870	+	0.695145i	$0.244660\pi$
$440$		−	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	$-0.978356\pi$
$443$	−247.055	−	427.912i	−0.557686	−	0.965940i	0.440003	−	0.897996i	$-0.354977\pi$
$444$		0			0
$445$	250.641	−	434.123i	0.563239	−	0.975558i
$446$	101.776	+	58.7607i	0.228198	+	0.131750i
$447$		0			0
$448$	−251.266	+	414.886i	−0.560861	+	0.926085i
$449$	−320.006			−0.712709			−0.356355	−	0.934351i	$-0.615980\pi$
$449$	−320.006			−0.712709			−0.356355	+	0.934351i	$0.615980\pi$
$450$		0			0
$451$		−	88.7733i		−	0.196837i
$452$	358.511	+	620.960i	0.793167	+	1.37380i
$453$		0			0
$454$	−807.301	−	466.096i	−1.77820	−	1.02664i
$455$	436.008	+	9.13443i	0.958260	+	0.0200757i
$456$		0			0
$457$	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	$0.781823\pi$
$458$			569.603i			1.24368i
$459$		0			0
$460$			383.951i			0.834675i
$461$	608.502	−	351.319i	1.31996	−	0.762080i	0.336239	−	0.941777i	$-0.390845\pi$
$461$	608.502	−	351.319i	1.31996	−	0.762080i	0.983722	+	0.179697i	$0.0575117\pi$
$462$		0			0
$463$	207.655	−	359.670i	0.448500	−	0.776825i	−0.549789	−	0.835304i	$-0.685292\pi$
$463$	207.655	−	359.670i	0.448500	−	0.776825i	0.998289	+	0.0584791i	$0.0186251\pi$
$464$	517.733	−	896.741i	1.11580	−	1.93263i
$465$		0			0
$466$	−109.530	−	189.711i	−0.235043	−	0.407106i
$467$		−	664.307i		−	1.42250i	−0.702939	−	0.711250i	$-0.748130\pi$
$467$		−	664.307i		−	1.42250i	0.702939	−	0.711250i	$-0.251870\pi$
$468$		0			0
$469$	138.475	+	251.886i	0.295255	+	0.537071i
$470$	9.92875	+	17.1971i	0.0211250	+	0.0365896i
$471$		0			0
$472$	846.776	+	488.886i	1.79402	+	1.03578i
$473$	13.0548	−	22.6116i	0.0276001	−	0.0478047i
$474$		0			0
$475$	−121.965	+	70.4165i	−0.256768	+	0.148245i
$476$	102.420	−	56.3053i	0.215167	−	0.118288i
$477$		0			0
$478$	−266.594			−0.557727
$479$	69.3175	−	40.0205i	0.144713	−	0.0835501i	−0.425895	−	0.904772i	$-0.640041\pi$
$479$	69.3175	−	40.0205i	0.144713	−	0.0835501i	0.570608	+	0.821222i	$0.306707\pi$
$480$		0			0
$481$	666.386	+	384.738i	1.38542	+	0.799871i
$482$	−3.97917	−	2.29738i	−0.00825554	−	0.00476634i
$483$		0			0
$484$	559.451	+	968.998i	1.15589	+	2.00206i
$485$	−774.581			−1.59708
$486$		0			0
$487$	−149.960			−0.307927			−0.153963	−	0.988077i	$-0.549204\pi$
$487$	−149.960			−0.307927			−0.153963	+	0.988077i	$0.549204\pi$
$488$	−935.124	+	539.894i	−1.91624	+	1.10634i
$489$		0			0
$490$	−881.412	+	460.784i	−1.79880	+	0.940376i
$491$	171.208	−	296.541i	0.348692	−	0.603953i	−0.637325	−	0.770595i	$-0.719959\pi$
$491$	171.208	−	296.541i	0.348692	−	0.603953i	0.986017	+	0.166642i	$0.0532925\pi$
$492$		0			0
$493$	−39.1923	+	22.6277i	−0.0794975	+	0.0458979i
$494$	−1170.24			−2.36892
$495$		0			0
$496$			591.868i			1.19328i
$497$	−22.8511	+	37.7314i	−0.0459781	+	0.0759183i
$498$		0			0
$499$	−255.562	+	442.647i	−0.512149	+	0.887069i	0.487751	+	0.872983i	$0.337817\pi$
$499$	−255.562	+	442.647i	−0.512149	+	0.887069i	−0.999901	+	0.0140861i	$0.995516\pi$
$500$	−918.768	−	530.451i	−1.83754	−	1.06090i
$501$		0			0
$502$	−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
$507$		0			0
$508$	−199.616	+	345.745i	−0.392944	+	0.680600i
$509$	263.720	+	152.259i	0.518114	+	0.299133i	0.736163	−	0.676804i	$-0.236636\pi$
$509$	263.720	+	152.259i	0.518114	+	0.299133i	−0.218048	+	0.975938i	$0.569969\pi$
$510$		0			0
$511$	−393.654	−	238.407i	−0.770360	−	0.466550i
$512$	914.316			1.78577
$513$		0			0
$514$		−	1535.84i		−	2.98802i
$515$	13.0694	+	22.6368i	0.0253774	+	0.0439550i
$516$		0			0
$517$	2.02397	+	1.16854i	0.00391484	+	0.00226023i
$518$	−1754.50	−	36.7571i	−3.38707	−	0.0709596i
$519$		0			0
$520$	657.874	+	1139.47i	1.26514	+	2.19129i
$521$			622.374i			1.19458i	0.802027	+	0.597288i	$0.203755\pi$
$521$			622.374i			1.19458i	−0.802027	+	0.597288i	$0.796245\pi$
$522$		0			0
$523$		−	23.9568i		−	0.0458065i	−0.999738	−	0.0229032i	$-0.992709\pi$
$523$		−	23.9568i		−	0.0458065i	0.999738	−	0.0229032i	$-0.00729096\pi$
$524$	678.981	−	392.010i	1.29577	−	0.748110i
$525$		0			0
$526$	−667.151	+	1155.54i	−1.26835	+	2.19684i
$527$	12.9339	−	22.4021i	0.0245425	−	0.0425088i
$528$		0			0
$529$	238.467	+	413.037i	0.450789	+	0.780789i
$530$			1404.78i			2.65054i
$531$		0			0
$532$	1656.16	−	910.475i	3.11308	−	1.71142i
$533$	211.123	+	365.676i	0.396103	+	0.686071i
$534$		0			0
$535$	76.6025	+	44.2265i	0.143182	+	0.0826663i
$536$	−433.611	+	751.037i	−0.808977	+	1.40119i
$537$		0			0
$538$	955.819	−	551.843i	1.77662	−	1.02573i
$539$	−62.7224	+	98.8333i	−0.116368	+	0.183364i
$540$		0			0
$541$	767.691			1.41902			0.709511	−	0.704695i	$-0.248916\pi$
$541$	767.691			1.41902			0.709511	+	0.704695i	$0.248916\pi$
$542$	732.958	−	423.173i	1.35232	−	0.780763i
$543$		0			0
$544$	91.2601	+	52.6890i	0.167758	+	0.0968549i
$545$	504.367	+	291.197i	0.925445	+	0.534306i
$546$		0			0
$547$	175.373	+	303.756i	0.320610	+	0.555312i	0.980614	−	0.195950i	$-0.0627789\pi$
$547$	175.373	+	303.756i	0.320610	+	0.555312i	−0.660004	+	0.751262i	$0.729446\pi$
$548$	1535.17			2.80140
$549$		0			0
$550$	44.7693			0.0813988
$551$	−633.752	+	365.897i	−1.15018	+	0.664060i
$552$		0			0
$553$	−252.562	−	5.29120i	−0.456712	−	0.00956817i
$554$	−167.471	+	290.068i	−0.302293	+	0.523588i
$555$		0			0
$556$	−439.461	+	253.723i	−0.790397	+	0.456336i
$557$	−155.290			−0.278797			−0.139398	−	0.990236i	$-0.544517\pi$
$557$	−155.290			−0.278797			−0.139398	+	0.990236i	$0.544517\pi$
$558$		0			0
$559$			124.189i			0.222164i
$560$	−1292.31	−	782.654i	−2.30769	−	1.39760i
$561$		0			0
$562$	55.5992	−	96.3007i	0.0989310	−	0.171354i
$563$	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	$0.456423\pi$
$564$		0			0
$565$	−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	0.642859	−	0.765984i	$-0.277748\pi$
$569$	−194.560	−	336.987i	−0.341932	−	0.592244i	−0.984792	+	0.173740i	$0.944415\pi$
$570$		0			0
$571$	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	$-0.0828788\pi$
$572$	228.138	+	131.716i	0.398843	+	0.230272i
$573$		0			0
$574$	−823.702	−	498.855i	−1.43502	−	0.869085i
$575$	−36.5277			−0.0635264
$576$		0			0
$577$		−	772.770i		−	1.33929i	−0.742682	−	0.669645i	$-0.766446\pi$
$577$		−	772.770i		−	1.33929i	0.742682	−	0.669645i	$-0.233554\pi$
$578$	529.461	+	917.053i	0.916022	+	1.58660i
$579$		0			0
$580$	1212.16	+	699.841i	2.08993	+	1.20662i
$581$	3.00627	−	143.497i	0.00517431	−	0.246982i
$582$		0			0
$583$	82.6664	+	143.182i	0.141795	+	0.245596i
$584$		−	1388.50i		−	2.37758i
$585$		0			0
$586$			933.822i			1.59355i
$587$	−212.938	+	122.940i	−0.362757	+	0.209438i	−0.670289	−	0.742100i	$-0.733830\pi$
$587$	−212.938	+	122.940i	−0.362757	+	0.209438i	0.307533	+	0.951538i	$0.400497\pi$
$588$		0			0
$589$	209.145	−	362.250i	0.355085	−	0.615025i
$590$	−469.867	+	813.834i	−0.796385	+	1.37938i
$591$		0			0
$592$	−1332.88	−	2308.61i	−2.25148	−	3.89969i
$593$		−	1002.47i		−	1.69051i	−0.534363	−	0.845255i	$-0.679448\pi$
$593$		−	1002.47i		−	1.69051i	0.534363	−	0.845255i	$-0.320552\pi$
$594$		0			0
$595$	31.8106	+	57.8636i	0.0534631	+	0.0972498i
$596$	−454.633	−	787.448i	−0.762807	−	1.32122i
$597$		0			0
$598$	−262.860	−	151.762i	−0.439565	−	0.253783i
$599$	181.436	−	314.257i	0.302899	−	0.524636i	−0.673893	−	0.738829i	$-0.735379\pi$
$599$	181.436	−	314.257i	0.302899	−	0.524636i	0.976791	+	0.214193i	$0.0687123\pi$
$600$		0			0
$601$	−491.710	+	283.889i	−0.818154	+	0.472361i	−0.849779	−	0.527139i	$-0.823265\pi$
$601$	−491.710	+	283.889i	−0.818154	+	0.472361i	0.0316257	+	0.999500i	$0.489932\pi$
$602$	−136.446	−	248.197i	−0.226655	−	0.412287i
$603$		0			0
$604$	−2640.76			−4.37213
$605$	−547.451	+	316.071i	−0.904877	+	0.522431i
$606$		0			0
$607$	−202.120	−	116.694i	−0.332982	−	0.192247i	0.324182	−	0.945995i	$-0.394911\pi$
$607$	−202.120	−	116.694i	−0.332982	−	0.192247i	−0.657164	+	0.753747i	$0.728244\pi$
$608$	1475.71	+	851.999i	2.42715	+	1.40131i
$609$		0			0
$610$	−518.890	−	898.744i	−0.850640	−	1.47335i
$611$	−11.1162			−0.0181935
$612$		0			0
$613$	277.664			0.452959			0.226479	−	0.974016i	$-0.427278\pi$
$613$	277.664			0.452959			0.226479	+	0.974016i	$0.427278\pi$
$614$	498.598	−	287.866i	0.812049	−	0.468837i
$615$		0			0
$616$	−353.087	−	7.39721i	−0.573193	−	0.0120085i
$617$	−148.590	+	257.365i	−0.240826	+	0.417123i	−0.960950	−	0.276723i	$-0.910752\pi$
$617$	−148.590	+	257.365i	−0.240826	+	0.417123i	0.720124	+	0.693846i	$0.244085\pi$
$618$		0			0
$619$	769.088	−	444.033i	1.24247	−	0.717339i	0.272872	−	0.962050i	$-0.412026\pi$
$619$	769.088	−	444.033i	1.24247	−	0.717339i	0.969596	+	0.244711i	$0.0786930\pi$
$620$	−800.052			−1.29041
$621$		0			0
$622$			458.645i			0.737371i
$623$	−547.419	−	331.531i	−0.878682	−	0.532153i
$624$		0			0
$625$	362.965	−	628.674i	0.580744	−	1.00588i
$626$	796.592	+	459.912i	1.27251	+	0.734684i
$627$		0			0
$628$	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
$633$		0			0
$634$	−304.329	+	527.114i	−0.480015	+	0.831410i
$635$	−195.334	−	112.776i	−0.307613	−	0.177600i
$636$		0			0
$637$	23.3186	−	556.283i	0.0366070	−	0.873286i
$638$	232.629			0.364623
$639$		0			0
$640$		−	63.1381i		−	0.0986532i
$641$	323.888	+	560.991i	0.505286	+	0.875181i	0.999981	+	0.00611473i	$0.00194639\pi$
$641$	323.888	+	560.991i	0.505286	+	0.875181i	−0.494695	+	0.869067i	$0.664720\pi$
$642$		0			0
$643$	−209.826	−	121.143i	−0.326324	−	0.188403i	0.327884	−	0.944718i	$-0.393664\pi$
$643$	−209.826	−	121.143i	−0.326324	−	0.188403i	−0.654208	+	0.756315i	$0.726998\pi$
$644$	490.080	+	10.2672i	0.760994	+	0.0159429i
$645$		0			0
$646$	−88.5942	−	153.450i	−0.137143	−	0.237538i
$647$		−	846.128i		−	1.30777i	−0.756594	−	0.653885i	$-0.773138\pi$
$647$		−	846.128i		−	1.30777i	0.756594	−	0.653885i	$-0.226862\pi$
$648$		0			0
$649$			110.600i			0.170416i
$650$	−184.414	+	106.472i	−0.283714	+	0.163803i
$651$		0			0
$652$	904.011	−	1565.79i	1.38652	−	2.40152i
$653$	−219.326	+	379.884i	−0.335875	+	0.581752i	−0.983652	−	0.180077i	$-0.942365\pi$
$653$	−219.326	+	379.884i	−0.335875	+	0.581752i	0.647778	+	0.761829i	$0.275699\pi$
$654$		0			0
$655$	221.472	+	383.601i	0.338126	+	0.585651i
$656$		−	1462.82i		−	2.22991i
$657$		0			0
$658$	22.2161	−	12.2133i	0.0337631	−	0.0185613i
$659$	317.963	+	550.728i	0.482493	+	0.835703i	0.999798	−	0.0200985i	$-0.00639797\pi$
$659$	317.963	+	550.728i	0.482493	+	0.835703i	−0.517305	+	0.855801i	$0.673065\pi$
$660$		0			0
$661$	−487.140	−	281.250i	−0.736975	−	0.425492i	0.0839937	−	0.996466i	$-0.473232\pi$
$661$	−487.140	−	281.250i	−0.736975	−	0.425492i	−0.820968	+	0.570974i	$0.806566\pi$
$662$	886.250	−	1535.03i	1.33875	−	2.31878i
$663$		0			0
$664$	375.017	−	216.516i	0.564784	−	0.326078i
$665$	514.387	+	935.674i	0.773515	+	1.40703i
$666$		0			0
$667$	−189.804			−0.284564
$668$	−2504.06	+	1445.72i	−3.74860	+	2.16425i
$669$		0			0
$670$	−721.819	−	416.743i	−1.07734	−	0.622004i
$671$	−105.776	−	61.0696i	−0.157639	−	0.0910128i
$672$		0			0
$673$	507.452	+	878.932i	0.754014	+	1.30599i	0.945863	+	0.324566i	$0.105218\pi$
$673$	507.452	+	878.932i	0.754014	+	1.30599i	−0.191849	+	0.981424i	$0.561448\pi$
$674$	−80.5802			−0.119555
$675$		0			0
$676$	387.121			0.572664
$677$	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	$0.295582\pi$
$678$		0			0
$679$	−20.7131	+	988.687i	−0.0305053	+	1.45609i
$680$	−99.6097	+	172.529i	−0.146485	+	0.253719i
$681$		0			0
$682$	−115.155	+	66.4850i	−0.168849	+	0.0974853i
$683$	−283.210			−0.414656			−0.207328	−	0.978272i	$-0.566477\pi$
$683$	−283.210			−0.414656			−0.207328	+	0.978272i	$0.566477\pi$
$684$		0			0
$685$			867.317i			1.26616i
$686$	564.582	+	1137.37i	0.823005	+	1.65797i
$687$		0			0
$688$	215.120	−	372.598i	0.312674	−	0.541567i
$689$	−681.041	−	393.199i	−0.988448	−	0.570681i
$690$		0			0
$691$	1101.97	−	636.224i	1.59475	−	0.920729i	0.602274	−	0.798290i	$-0.294262\pi$
$691$	1101.97	−	636.224i	1.59475	−	0.920729i	0.992476	−	0.122440i	$-0.0390718\pi$
$692$			2163.15i			3.12595i
$693$		0			0
$694$	−2348.24			−3.38363
$695$	−143.345	−	248.280i	−0.206252	−	0.357238i
$696$		0			0
$697$	−31.9665	+	55.3675i	−0.0458629	+	0.0794369i
$698$	47.9388	+	27.6775i	0.0686803	+	0.0396526i
$699$		0			0
$700$	178.151	−	294.160i	0.254501	−	0.420228i
$701$	941.137			1.34256			0.671282	−	0.741202i	$-0.265744\pi$
$701$	941.137			1.34256			0.671282	+	0.741202i	$0.265744\pi$
$702$		0			0
$703$			1883.97i			2.67989i
$704$	−82.7653	−	143.354i	−0.117564	−	0.203627i
$705$		0			0
$706$	534.100	+	308.363i	0.756515	+	0.436774i
$707$	−24.3196	+	1160.83i	−0.0343984	+	1.64192i
$708$		0			0
$709$	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	$0.607113\pi$
$710$		−	127.909i		−	0.180154i
$711$		0			0
$712$		−	1930.87i		−	2.71189i
$713$	93.9562	−	54.2456i	0.131776	−	0.0760808i
$714$		0			0
$715$	−74.4148	+	128.890i	−0.104077	+	0.180266i
$716$	−804.457	+	1393.36i	−1.12354	+	1.94603i
$717$		0			0
$718$	1005.14	+	1740.96i	1.39992	+	2.42473i
$719$		−	69.3677i		−	0.0964781i	−0.998836	−	0.0482390i	$-0.984639\pi$
$719$		−	69.3677i		−	0.0964781i	0.998836	−	0.0482390i	$-0.0153609\pi$
$720$		0			0
$721$	29.2434	−	16.0766i	0.0405595	−	0.0222976i
$722$	−764.386	−	1323.95i	−1.05871	−	1.83373i
$723$		0			0
$724$	−1841.94	−	1063.45i	−2.54412	−	1.46885i
$725$	−66.5804	+	115.321i	−0.0918350	+	0.159063i
$726$		0			0
$727$	−953.931	+	550.752i	−1.31215	+	0.757568i	−0.982451	−	0.186519i	$-0.940279\pi$
$727$	−953.931	+	550.752i	−1.31215	+	0.757568i	−0.329695	+	0.944087i	$0.606946\pi$
$728$	1472.03	−	809.249i	2.02202	−	1.11161i
$729$		0			0
$730$	1334.49			1.82806
$731$	−16.2845	+	9.40185i	−0.0222770	+	0.0128616i
$732$		0			0
$733$	−1049.65	−	606.014i	−1.43199	−	0.826759i	−0.434716	−	0.900568i	$-0.643151\pi$
$733$	−1049.65	−	606.014i	−1.43199	−	0.826759i	−0.997272	+	0.0738089i	$0.976485\pi$
$734$	−1129.74	−	652.254i	−1.53915	−	0.888629i
$735$		0			0
$736$	220.982	+	382.752i	0.300247	+	0.520043i
$737$	−98.0951			−0.133101
$738$		0			0
$739$	−767.480			−1.03854			−0.519269	−	0.854611i	$-0.673796\pi$
$739$	−767.480			−1.03854			−0.519269	+	0.854611i	$0.673796\pi$
$740$	3120.65	−	1801.71i	4.21709	−	2.43474i
$741$		0			0
$742$	1793.09	+	37.5654i	2.41656	+	0.0506272i
$743$	39.2644	−	68.0079i	0.0528458	−	0.0915315i	−0.838392	−	0.545067i	$-0.816504\pi$
$743$	39.2644	−	68.0079i	0.0528458	−	0.0915315i	0.891238	+	0.453536i	$0.149838\pi$
$744$		0			0
$745$	444.881	−	256.852i	0.597156	−	0.344768i
$746$	−761.887			−1.02130
$747$		0			0
$748$			39.8865i			0.0533242i
$749$	58.4997	−	96.5939i	0.0781038	−	0.128964i
$750$		0			0
$751$	−174.564	+	302.353i	−0.232442	+	0.402601i	−0.958526	−	0.285005i	$-0.908005\pi$
$751$	−174.564	+	302.353i	−0.232442	+	0.402601i	0.726084	+	0.687606i	$0.241338\pi$
$752$	33.3513	+	19.2554i	0.0443502	+	0.0256056i
$753$		0			0
$754$	−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
$759$		0			0
$760$	−1610.72	+	2789.85i	−2.11937	+	3.67086i
$761$	−367.230	−	212.020i	−0.482563	−	0.278608i	0.238921	−	0.971039i	$-0.423206\pi$
$761$	−367.230	−	212.020i	−0.482563	−	0.278608i	−0.721484	+	0.692431i	$0.756540\pi$
$762$		0			0
$763$	385.175	−	635.995i	0.504816	−	0.833545i
$764$	−2485.70			−3.25353
$765$		0			0
$766$			441.630i			0.576540i
$767$	−263.032	−	455.584i	−0.342936	−	0.593982i
$768$		0			0
$769$	−1109.15	−	640.365i	−1.44232	−	0.832725i	−0.444317	−	0.895869i	$-0.646554\pi$
$769$	−1109.15	−	640.365i	−1.44232	−	0.832725i	−0.998004	+	0.0631445i	$0.979887\pi$
$770$	7.10944	−	339.350i	0.00923303	−	0.440715i
$771$		0			0
$772$	−1.90331	−	3.29663i	−0.00246543	−	0.00427025i
$773$			1102.98i			1.42688i	0.700715	+	0.713441i	$0.252864\pi$
$773$			1102.98i			1.42688i	−0.700715	+	0.713441i	$0.747136\pi$
$774$		0			0
$775$		−	76.1141i		−	0.0982117i
$776$	−2583.85	+	1491.79i	−3.32971	+	1.92241i
$777$		0			0
$778$	1090.04	−	1888.00i	1.40108	−	2.42674i
$779$	−516.908	+	895.311i	−0.663553	+	1.14931i
$780$		0			0
$781$	−7.52701	−	13.0372i	−0.00963765	−	0.0166929i
$782$		−	45.9571i		−	0.0587687i
$783$		0			0
$784$	−1033.55	+	1628.59i	−1.31830	+	2.07728i
$785$	559.536	+	969.145i	0.712785	+	1.23458i
$786$		0			0
$787$	1131.22	+	653.112i	1.43739	+	0.829876i	0.997668	−	0.0682596i	$-0.0217446\pi$
$787$	1131.22	+	653.112i	1.43739	+	0.829876i	0.439719	+	0.898135i	$0.355078\pi$
$788$	755.271	−	1308.17i	0.958466	−	1.66011i
$789$		0			0
$790$	634.371	−	366.254i	0.803001	−	0.463613i
$791$	249.152	+	453.210i	0.314984	+	0.572958i
$792$		0			0
$793$	580.950			0.732597
$794$	1534.78	−	886.103i	1.93297	−	1.11600i
$795$		0			0
$796$	334.895	+	193.351i	0.420722	+	0.242904i
$797$	−933.144	−	538.751i	−1.17082	−	0.675974i	−0.216948	−	0.976183i	$-0.569610\pi$
$797$	−933.144	−	538.751i	−1.17082	−	0.675974i	−0.953873	+	0.300209i	$0.902943\pi$
$798$		0			0
$799$	−0.841562	−	1.45763i	−0.00105327	−	0.00182432i
$800$	310.068			0.387585
$801$		0			0
$802$	1519.82			1.89503
$803$	136.017	−	78.5297i	0.169387	−	0.0977954i
$804$		0			0
$805$	−5.80065	+	276.879i	−0.00720577	+	0.343949i
$806$	316.233	−	547.731i	0.392348	−	0.679567i
$807$		0			0
$808$	−3033.75	+	1751.53i	−3.75464	+	2.16774i
$809$	342.613			0.423502			0.211751	−	0.977324i	$-0.432083\pi$
$809$	342.613			0.423502			0.211751	+	0.977324i	$0.432083\pi$
$810$		0			0
$811$		−	467.249i		−	0.576140i	−0.957609	−	0.288070i	$-0.906986\pi$
$811$		−	467.249i		−	0.576140i	0.957609	−	0.288070i	$-0.0930135\pi$
$812$	925.702	−	1528.51i	1.14003	−	1.88240i
$813$		0			0
$814$	299.446	−	518.656i	0.367870	−	0.637170i
$815$	884.620	+	510.736i	1.08542	+	0.626670i
$816$		0			0
$817$	−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	0.818006	−	0.575209i	$-0.195079\pi$
$821$	−73.1862	−	126.762i	−0.0891428	−	0.154400i	−0.907149	+	0.420810i	$0.861746\pi$
$822$		0			0
$823$	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	$-0.0188607\pi$
$824$	87.1937	+	50.3413i	0.105818	+	0.0610938i
$825$		0			0
$826$	1026.22	+	621.508i	1.24240	+	0.752431i
$827$	−1352.67			−1.63564			−0.817820	−	0.575474i	$-0.804818\pi$
$827$	−1352.67			−1.63564			−0.817820	+	0.575474i	$0.804818\pi$
$828$		0			0
$829$		−	850.931i		−	1.02645i	−0.858253	−	0.513227i	$-0.828450\pi$
$829$		−	850.931i		−	1.02645i	0.858253	−	0.513227i	$-0.171550\pi$
$830$	208.093	+	360.427i	0.250714	+	0.434250i
$831$		0			0
$832$	681.855	+	393.669i	0.819538	+	0.473160i
$833$	74.7086	−	39.0561i	0.0896862	−	0.0468861i
$834$		0			0
$835$	−816.783	−	1414.71i	−0.978184	−	1.69426i
$836$			644.978i			0.771505i
$837$		0			0
$838$		−	1299.66i		−	1.55091i
$839$	−1011.65	+	584.078i	−1.20578	+	0.696160i	−0.961835	−	0.273629i	$-0.911776\pi$
$839$	−1011.65	+	584.078i	−1.20578	+	0.696160i	−0.243948	+	0.969788i	$0.578443\pi$
$840$		0			0
$841$	74.5367	−	129.101i	0.0886287	−	0.153509i
$842$	1195.95	−	2071.44i	1.42036	−	2.46014i
$843$		0			0
$844$	−648.468	−	1123.18i	−0.768327	−	1.33078i
$845$			218.710i			0.258829i
$846$		0			0
$847$	388.798	+	707.226i	0.459030	+	0.834978i
$848$	1362.19	+	2359.38i	1.60636	+	2.78229i
$849$		0			0
$850$	−27.9225	−	16.1210i	−0.0328499	−	0.0189659i
$851$	−244.321	+	423.176i	−0.287098	+	0.497269i
$852$		0			0
$853$	196.344	−	113.359i	0.230181	−	0.132895i	−0.380475	−	0.924791i	$-0.624239\pi$
$853$	196.344	−	113.359i	0.230181	−	0.132895i	0.610655	+	0.791896i	$0.290906\pi$
$854$	−1161.05	+	638.286i	−1.35954	+	0.747407i
$855$		0			0
$856$	340.708			0.398023
$857$	744.654	−	429.926i	0.868908	−	0.501664i	0.00192259	−	0.999998i	$-0.499388\pi$
$857$	744.654	−	429.926i	0.868908	−	0.501664i	0.866985	+	0.498334i	$0.166055\pi$
$858$		0			0
$859$	−1053.18	−	608.054i	−1.22605	−	0.707862i	−0.259851	−	0.965649i	$-0.583674\pi$
$859$	−1053.18	−	608.054i	−1.22605	−	0.707862i	−0.966202	+	0.257786i	$0.917007\pi$
$860$	503.656	+	290.786i	0.585646	+	0.338123i
$861$		0			0
$862$	1400.48	+	2425.69i	1.62468	+	2.81403i
$863$	920.471			1.06659			0.533297	−	0.845928i	$-0.320953\pi$
$863$	920.471			1.06659			0.533297	+	0.845928i	$0.320953\pi$
$864$		0			0
$865$	−1222.11			−1.41284
$866$	−459.549	+	265.321i	−0.530657	+	0.306375i
$867$		0			0
$868$	−21.3942	+	1021.20i	−0.0246477	+	1.17650i
$869$	43.1054	−	74.6608i	0.0496035	−	0.0859158i
$870$		0			0
$871$	404.074	−	233.292i	0.463920	−	0.267844i
$872$	2243.29			2.57259
$873$		0			0
$874$		−	743.142i		−	0.850276i
$875$	−654.538	−	396.405i	−0.748043	−	0.453034i
$876$		0			0
$877$	−829.900	+	1437.43i	−0.946294	+	1.63903i	−0.193155	+	0.981168i	$0.561872\pi$
$877$	−829.900	+	1437.43i	−0.946294	+	1.63903i	−0.753139	+	0.657862i	$0.771461\pi$
$878$	774.059	+	446.903i	0.881616	+	0.509001i
$879$		0			0
$880$	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
$885$		0			0
$886$	914.598	−	1584.13i	1.03228	−	1.78796i
$887$	−156.028	−	90.0826i	−0.175905	−	0.101559i	0.409462	−	0.912327i	$-0.365716\pi$
$887$	−156.028	−	90.0826i	−0.175905	−	0.101559i	−0.585367	+	0.810768i	$0.699050\pi$
$888$		0			0
$889$	−149.173	+	246.311i	−0.167798	+	0.277066i
$890$	1855.75			2.08511
$891$		0			0
$892$			308.083i			0.345385i
$893$	−13.6083	−	23.5703i	−0.0152389	−	0.0263946i
$894$		0			0
$895$	−787.202	−	454.491i	−0.879555	−	0.507811i
$896$	−80.5904	−	1.68838i	−0.0899446	−	0.00188435i
$897$		0			0
$898$	−592.333	−	1025.95i	−0.659613	−	1.14248i
$899$		−	395.502i		−	0.439936i
$900$		0			0
$901$		−	119.070i		−	0.132153i
$902$	284.610	−	164.320i	0.315532	−	0.182172i
$903$		0			0
$904$	−780.181	+	1351.31i	−0.863032	+	1.49481i
$905$	600.811	−	1040.63i	0.663879	−	1.14987i
$906$		0			0
$907$	−162.826	−	282.023i	−0.179522	−	0.310940i	0.762195	−	0.647347i	$-0.224122\pi$
$907$	−162.826	−	282.023i	−0.179522	−	0.310940i	−0.941717	+	0.336407i	$0.890788\pi$
$908$		−	2443.75i		−	2.69135i
$909$		0			0
$910$	777.767	+	1414.76i	0.854689	+	1.55468i
$911$	−506.920	−	878.011i	−0.556443	−	0.963788i	−0.997790	−	0.0664512i	$-0.978832\pi$
$911$	−506.920	−	878.011i	−0.556443	−	0.963788i	0.441346	−	0.897337i	$-0.354501\pi$
$912$		0			0
$913$	42.4197	+	24.4910i	0.0464619	+	0.0268248i
$914$	−272.582	+	472.126i	−0.298230	+	0.516550i
$915$		0			0
$916$	−1293.17	+	746.611i	−1.41175	+	0.815077i
$917$	495.557	−	272.433i	0.540411	−	0.297091i
$918$		0			0
$919$	−176.782			−0.192364			−0.0961818	−	0.995364i	$-0.530663\pi$
$919$	−176.782			−0.192364			−0.0961818	+	0.995364i	$0.530663\pi$
$920$	−723.600	+	417.771i	−0.786521	+	0.454098i
$921$		0			0
$922$	2252.68	+	1300.58i	2.44325	+	1.41061i
$923$	62.0106	+	35.8019i	0.0671838	+	0.0387886i
$924$		0			0
$925$	171.408	+	296.887i	0.185306	+	0.320959i
$926$	1537.48			1.66035
$927$		0			0
$928$	1611.17			1.73617
$929$	−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	$0.376111\pi$
$930$		0			0
$931$	1208.06	−	631.550i	1.29760	−	0.678357i
$932$	287.134	−	497.330i	0.308083	−	0.533616i
$933$		0			0
$934$	2129.79	−	1229.63i	2.28029	−	1.31653i
$935$	−22.5345			−0.0241011
$936$		0			0
$937$			573.923i			0.612511i	0.951949	+	0.306256i	$0.0990762\pi$
$937$			573.923i			0.612511i	−0.951949	+	0.306256i	$0.900924\pi$
$938$	−551.239	+	910.197i	−0.587674	+	0.970359i
$939$		0			0
$940$	−26.0283	+	45.0824i	−0.0276897	+	0.0479600i
$941$	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	$0.420887\pi$
$942$		0			0
$943$	−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	$0.0328446\pi$
$947$	555.456	+	962.077i	0.586542	+	1.01592i	−0.408139	+	0.912920i	$0.633822\pi$
$948$		0			0
$949$	−373.523	+	646.961i	−0.393596	+	0.681729i
$950$	−451.515	−	260.682i	−0.475279	−	0.274403i
$951$		0			0
$952$	217.555	+	131.757i	0.228524	+	0.138400i
$953$	−667.783			−0.700717			−0.350358	−	0.936616i	$-0.613940\pi$
$953$	−667.783			−0.700717			−0.350358	+	0.936616i	$0.613940\pi$
$954$		0			0
$955$		−	1404.34i		−	1.47051i
$956$	−349.439	−	605.246i	−0.365522	−	0.633102i
$957$		0			0
$958$	256.614	+	148.156i	0.267864	+	0.154651i
$959$	1107.06	+	23.1930i	1.15439	+	0.0241845i
$960$		0			0
$961$	−367.466	−	636.470i	−0.382379	−	0.662300i
$962$			2848.61i			2.96113i
$963$		0			0
$964$		−	12.0452i		−	0.0124950i
$965$	1.86248	−	1.07531i	0.00193004	−	0.00111431i
$966$		0			0
$967$	244.801	−	424.008i	0.253155	−	0.438478i	−0.711238	−	0.702952i	$-0.751865\pi$
$967$	244.801	−	424.008i	0.253155	−	0.438478i	0.964393	+	0.264474i	$0.0851983\pi$
$968$	−1217.46	+	2108.70i	−1.25771	+	2.17841i
$969$		0			0
$970$	−1433.75	−	2483.33i	−1.47810	−	2.56014i
$971$		−	581.802i		−	0.599178i	−0.954068	−	0.299589i	$-0.903150\pi$
$971$		−	581.802i		−	0.599178i	0.954068	−	0.299589i	$-0.0968495\pi$
$972$		0			0
$973$	−320.742	+	176.328i	−0.329642	+	0.181221i
$974$	−277.577	−	480.778i	−0.284987	−	0.493612i
$975$		0			0
$976$	−1742.99	−	1006.31i	−1.78585	−	1.03106i
$977$	−563.162	+	975.426i	−0.576420	+	0.998389i	0.419466	+	0.907771i	$0.362217\pi$
$977$	−563.162	+	975.426i	−0.576420	+	0.998389i	−0.995886	+	0.0906177i	$0.971116\pi$
$978$		0			0
$979$	189.147	−	109.204i	0.193204	−	0.111547i
$980$	−2201.43	−	1397.09i	−2.24636	−	1.42560i
$981$		0			0
$982$	1267.63			1.29086
$983$	−25.8981	+	14.9523i	−0.0263460	+	0.0152109i	−0.513115	−	0.858320i	$-0.671509\pi$
$983$	−25.8981	+	14.9523i	−0.0263460	+	0.0152109i	0.486769	+	0.873531i	$0.338175\pi$
$984$		0			0
$985$	739.070	+	426.702i	0.750325	+	0.433200i
$986$	−145.090	−	83.7678i	−0.147150	−	0.0849572i
$987$		0			0
$988$	−1533.90	−	2656.80i	−1.55253	−	2.68907i
$989$	−78.8642			−0.0797413
$990$		0			0
$991$	−767.762			−0.774735			−0.387367	−	0.921925i	$-0.626615\pi$
$991$	−767.762			−0.774735			−0.387367	+	0.921925i	$0.626615\pi$
$992$	−797.554	+	460.468i	−0.803986	+	0.464181i
$993$		0			0
$994$	−163.266	−	3.42043i	−0.164251	−	0.00344108i
$995$	−109.237	+	189.204i	−0.109786	+	0.190155i
$996$		0			0
$997$	−12.9249	+	7.46219i	−0.0129638	+	0.00748464i	−0.506468	−	0.862259i	$-0.669049\pi$
$997$	−12.9249	+	7.46219i	−0.0129638	+	0.00748464i	0.493504	+	0.869743i	$0.335716\pi$
$998$	−1892.19			−1.89598
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.l.a.118.13		28
3.2	odd	2		63.3.l.a.13.1	✓	28
7.6	odd	2	inner	189.3.l.a.118.14		28
9.2	odd	6		63.3.l.a.34.2	yes	28
9.4	even	3		567.3.d.g.244.2		14
9.5	odd	6		567.3.d.h.244.13		14
9.7	even	3	inner	189.3.l.a.181.14		28
21.2	odd	6		441.3.k.a.31.1		28
21.5	even	6		441.3.k.a.31.2		28
21.11	odd	6		441.3.t.b.166.14		28
21.17	even	6		441.3.t.b.166.13		28
21.20	even	2		63.3.l.a.13.2	yes	28
63.2	odd	6		441.3.t.b.178.13		28
63.11	odd	6		441.3.k.a.313.2		28
63.13	odd	6		567.3.d.g.244.1		14
63.20	even	6		63.3.l.a.34.1	yes	28
63.34	odd	6	inner	189.3.l.a.181.13		28
63.38	even	6		441.3.k.a.313.1		28
63.41	even	6		567.3.d.h.244.14		14
63.47	even	6		441.3.t.b.178.14		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.l.a.13.1	✓	28	3.2	odd	2
63.3.l.a.13.2	yes	28	21.20	even	2
63.3.l.a.34.1	yes	28	63.20	even	6
63.3.l.a.34.2	yes	28	9.2	odd	6
189.3.l.a.118.13		28	1.1	even	1	trivial
189.3.l.a.118.14		28	7.6	odd	2	inner
189.3.l.a.181.13		28	63.34	odd	6	inner
189.3.l.a.181.14		28	9.7	even	3	inner
441.3.k.a.31.1		28	21.2	odd	6
441.3.k.a.31.2		28	21.5	even	6
441.3.k.a.313.1		28	63.38	even	6
441.3.k.a.313.2		28	63.11	odd	6
441.3.t.b.166.13		28	21.17	even	6
441.3.t.b.166.14		28	21.11	odd	6
441.3.t.b.178.13		28	63.2	odd	6
441.3.t.b.178.14		28	63.47	even	6
567.3.d.g.244.1		14	63.13	odd	6
567.3.d.g.244.2		14	9.4	even	3
567.3.d.h.244.13		14	9.5	odd	6
567.3.d.h.244.14		14	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.85100 + 3.20603i) q^{2} +(-4.85242 + 8.40464i) q^{4} +(-4.74834 - 2.74145i) q^{5} +(-3.62621 + 5.98754i) q^{7} -21.1194 q^{8} +O(q^{10})\)	\(q+(1.85100 + 3.20603i) q^{2} +(-4.85242 + 8.40464i) q^{4} +(-4.74834 - 2.74145i) q^{5} +(-3.62621 + 5.98754i) q^{7} -21.1194 q^{8} -20.2978i q^{10} +(-1.19445 - 2.06885i) q^{11} +(9.84037 + 5.68134i) q^{13} +(-25.9084 - 0.542783i) q^{14} +(-19.6823 - 34.0908i) q^{16} +1.72044i q^{17} +27.8201i q^{19} +(46.0819 - 26.6054i) q^{20} +(4.42186 - 7.65888i) q^{22} +(-3.60783 + 6.24894i) q^{23} +(2.53114 + 4.38406i) q^{25} +42.0647i q^{26} +(-32.7272 - 59.5310i) q^{28} +(13.1522 + 22.7804i) q^{29} +(-13.0212 - 7.51777i) q^{31} +(30.6253 - 53.0446i) q^{32} +(-5.51579 + 3.18454i) q^{34} +(33.6330 - 18.4898i) q^{35} +67.7196 q^{37} +(-89.1921 + 51.4951i) q^{38} +(100.282 + 57.8978i) q^{40} +(32.1822 + 18.5804i) q^{41} +(5.46479 + 9.46530i) q^{43} +23.1839 q^{44} -26.7124 q^{46} +(-0.847241 + 0.489155i) q^{47} +(-22.7012 - 43.4241i) q^{49} +(-9.37029 + 16.2298i) q^{50} +(-95.4993 + 55.1365i) q^{52} -69.2088 q^{53} +13.0981i q^{55} +(76.5832 - 126.453i) q^{56} +(-48.6897 + 84.3330i) q^{58} +(-40.0948 - 23.1487i) q^{59} +(44.2780 - 25.5639i) q^{61} -55.6616i q^{62} +69.2916 q^{64} +(-31.1503 - 53.9539i) q^{65} +(20.5315 - 35.5615i) q^{67} +(-14.4597 - 8.34831i) q^{68} +(121.534 + 73.6039i) q^{70} +6.30166 q^{71} +65.7456i q^{73} +(125.349 + 217.111i) q^{74} +(-233.818 - 134.995i) q^{76} +(16.7186 + 0.350257i) q^{77} +(18.0441 + 31.2532i) q^{79} +215.833i q^{80} +137.569i q^{82} +(-17.7570 + 10.2520i) q^{83} +(4.71651 - 8.16923i) q^{85} +(-20.2307 + 35.0406i) q^{86} +(25.2260 + 43.6927i) q^{88} +91.4264i q^{89} +(-69.7005 + 38.3179i) q^{91} +(-35.0134 - 60.6450i) q^{92} +(-3.13649 - 1.81085i) q^{94} +(76.2675 - 132.099i) q^{95} +(122.345 - 70.6360i) q^{97} +(97.1990 - 153.159i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 26 q^{4} - 8 q^{8}+O(q^{10}) \) 28 * q + 2 * q^2 - 26 * q^4 - 8 * q^8	\( 28 q + 2 q^{2} - 26 q^{4} - 8 q^{8} - 4 q^{11} - 34 q^{14} - 42 q^{16} + 14 q^{22} - 4 q^{23} + 28 q^{25} + 20 q^{28} + 38 q^{29} + 168 q^{32} + 264 q^{35} + 36 q^{37} - 66 q^{43} - 108 q^{44} - 40 q^{46} - 38 q^{49} - 196 q^{50} - 520 q^{53} - 332 q^{56} - 34 q^{58} + 72 q^{64} + 102 q^{65} + 68 q^{67} + 102 q^{70} + 332 q^{71} + 616 q^{74} - 334 q^{77} + 146 q^{79} + 78 q^{85} + 340 q^{86} - 74 q^{88} - 384 q^{91} - 606 q^{92} + 360 q^{95} + 1076 q^{98}+O(q^{100}) \) 28 * q + 2 * q^2 - 26 * q^4 - 8 * q^8 - 4 * q^11 - 34 * q^14 - 42 * q^16 + 14 * q^22 - 4 * q^23 + 28 * q^25 + 20 * q^28 + 38 * q^29 + 168 * q^32 + 264 * q^35 + 36 * q^37 - 66 * q^43 - 108 * q^44 - 40 * q^46 - 38 * q^49 - 196 * q^50 - 520 * q^53 - 332 * q^56 - 34 * q^58 + 72 * q^64 + 102 * q^65 + 68 * q^67 + 102 * q^70 + 332 * q^71 + 616 * q^74 - 334 * q^77 + 146 * q^79 + 78 * q^85 + 340 * q^86 - 74 * q^88 - 384 * q^91 - 606 * q^92 + 360 * q^95 + 1076 * q^98

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