LMFDB - Embedded newform 476.3.s.a.341.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,3,Mod(341,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("476.341");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	476.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.9700605836$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.15
Character	$\chi$	$=$	476.341
Dual form			476.3.s.a.409.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.91865 - 1.10773i) q^{3} +(-0.540464 - 0.312037i) q^{5} +(-1.03671 - 6.92281i) q^{7} +(-2.04587 + 3.54354i) q^{9} +O(q^{10})$	\(q+(1.91865 - 1.10773i) q^{3} +(-0.540464 - 0.312037i) q^{5} +(-1.03671 - 6.92281i) q^{7} +(-2.04587 + 3.54354i) q^{9} +(-0.619075 - 1.07227i) q^{11} -17.2278i q^{13} -1.38261 q^{15} +(-3.57071 + 2.06155i) q^{17} +(-7.00707 - 4.04554i) q^{19} +(-9.65767 - 12.1340i) q^{21} +(15.1335 - 26.2120i) q^{23} +(-12.3053 - 21.3133i) q^{25} +29.0042i q^{27} -33.2115 q^{29} +(-3.47074 + 2.00383i) q^{31} +(-2.37557 - 1.37154i) q^{33} +(-1.59987 + 4.06502i) q^{35} +(26.5242 - 45.9412i) q^{37} +(-19.0837 - 33.0540i) q^{39} +18.9564i q^{41} +17.6339 q^{43} +(2.21143 - 1.27677i) q^{45} +(-15.6354 - 9.02712i) q^{47} +(-46.8505 + 14.3538i) q^{49} +(-4.56729 + 7.91078i) q^{51} +(12.8144 + 22.1952i) q^{53} +0.772698i q^{55} -17.9255 q^{57} +(37.9347 - 21.9016i) q^{59} +(-21.0502 - 12.1533i) q^{61} +(26.6522 + 10.4895i) q^{63} +(-5.37570 + 9.31099i) q^{65} +(-35.3435 - 61.2167i) q^{67} -67.0554i q^{69} +44.1041 q^{71} +(80.5240 - 46.4905i) q^{73} +(-47.2189 - 27.2618i) q^{75} +(-6.78132 + 5.39736i) q^{77} +(-50.1676 + 86.8928i) q^{79} +(13.7161 + 23.7569i) q^{81} +58.0322i q^{83} +2.57312 q^{85} +(-63.7212 + 36.7894i) q^{87} +(-47.6584 - 27.5156i) q^{89} +(-119.264 + 17.8601i) q^{91} +(-4.43942 + 7.68930i) q^{93} +(2.52471 + 4.37293i) q^{95} +67.7953i q^{97} +5.06618 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9}+O(q^{10}) $ 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9	$ 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + 8 q^{11} + 16 q^{15} - 54 q^{19} - 16 q^{21} - 52 q^{23} + 150 q^{25} + 8 q^{29} + 78 q^{31} - 6 q^{33} + 10 q^{35} - 34 q^{37} - 60 q^{39} - 76 q^{43} - 72 q^{45} - 6 q^{47} - 56 q^{49} - 172 q^{53} - 64 q^{57} + 30 q^{59} + 444 q^{61} + 206 q^{63} - 54 q^{65} - 56 q^{67} + 204 q^{71} - 48 q^{73} + 132 q^{75} - 494 q^{77} - 16 q^{79} - 342 q^{81} + 594 q^{87} - 252 q^{89} + 284 q^{91} - 146 q^{93} + 148 q^{95} - 180 q^{99}+O(q^{100}) $ 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9 + 8 * q^11 + 16 * q^15 - 54 * q^19 - 16 * q^21 - 52 * q^23 + 150 * q^25 + 8 * q^29 + 78 * q^31 - 6 * q^33 + 10 * q^35 - 34 * q^37 - 60 * q^39 - 76 * q^43 - 72 * q^45 - 6 * q^47 - 56 * q^49 - 172 * q^53 - 64 * q^57 + 30 * q^59 + 444 * q^61 + 206 * q^63 - 54 * q^65 - 56 * q^67 + 204 * q^71 - 48 * q^73 + 132 * q^75 - 494 * q^77 - 16 * q^79 - 342 * q^81 + 594 * q^87 - 252 * q^89 + 284 * q^91 - 146 * q^93 + 148 * q^95 - 180 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.91865	−	1.10773i	0.639549	−	0.369244i	−0.144892	−	0.989447i	$-0.546283\pi$
$3$	1.91865	−	1.10773i	0.639549	−	0.369244i	0.784441	+	0.620204i	$0.212950\pi$
$4$		0			0
$5$	−0.540464	−	0.312037i	−0.108093	−	0.0624074i	0.444979	−	0.895541i	$-0.353211\pi$
$5$	−0.540464	−	0.312037i	−0.108093	−	0.0624074i	−0.553072	+	0.833134i	$0.686544\pi$
$6$		0			0
$7$	−1.03671	−	6.92281i	−0.148101	−	0.988972i
$7$	−1.03671	−	6.92281i	−0.148101	−	0.988972i
$8$		0			0
$9$	−2.04587	+	3.54354i	−0.227318	+	0.393727i
$10$		0			0
$11$	−0.619075	−	1.07227i	−0.0562796	−	0.0974790i	0.836513	−	0.547947i	$-0.184590\pi$
$11$	−0.619075	−	1.07227i	−0.0562796	−	0.0974790i	−0.892793	+	0.450468i	$0.851257\pi$
$12$		0			0
$13$		−	17.2278i		−	1.32521i	−0.748968	−	0.662606i	$-0.769450\pi$
$13$		−	17.2278i		−	1.32521i	0.748968	−	0.662606i	$-0.230550\pi$
$14$		0			0
$15$	−1.38261			−0.0921742
$16$		0			0
$17$	−3.57071	+	2.06155i	−0.210042	+	0.121268i
$17$	−3.57071	+	2.06155i	−0.210042	+	0.121268i
$18$		0			0
$19$	−7.00707	−	4.04554i	−0.368793	−	0.212923i	0.304138	−	0.952628i	$-0.401632\pi$
$19$	−7.00707	−	4.04554i	−0.368793	−	0.212923i	−0.672931	+	0.739705i	$0.734965\pi$
$20$		0			0
$21$	−9.65767	−	12.1340i	−0.459889	−	0.577811i
$22$		0			0
$23$	15.1335	−	26.2120i	0.657979	−	1.13965i	−0.323160	−	0.946345i	$-0.604745\pi$
$23$	15.1335	−	26.2120i	0.657979	−	1.13965i	0.981138	−	0.193308i	$-0.0619216\pi$
$24$		0			0
$25$	−12.3053	−	21.3133i	−0.492211	−	0.852534i
$26$		0			0
$27$			29.0042i			1.07423i
$28$		0			0
$29$	−33.2115			−1.14523			−0.572613	−	0.819826i	$-0.694070\pi$
$29$	−33.2115			−1.14523			−0.572613	+	0.819826i	$0.694070\pi$
$30$		0			0
$31$	−3.47074	+	2.00383i	−0.111959	+	0.0646398i	−0.554934	−	0.831894i	$-0.687257\pi$
$31$	−3.47074	+	2.00383i	−0.111959	+	0.0646398i	0.442975	+	0.896534i	$0.353923\pi$
$32$		0			0
$33$	−2.37557	−	1.37154i	−0.0719870	−	0.0415617i
$34$		0			0
$35$	−1.59987	+	4.06502i	−0.0457106	+	0.116143i
$36$		0			0
$37$	26.5242	−	45.9412i	0.716870	−	1.24166i	−0.245364	−	0.969431i	$-0.578907\pi$
$37$	26.5242	−	45.9412i	0.716870	−	1.24166i	0.962234	−	0.272224i	$-0.0877592\pi$
$38$		0			0
$39$	−19.0837	−	33.0540i	−0.489326	−	0.847537i
$40$		0			0
$41$			18.9564i			0.462351i	0.972912	+	0.231176i	$0.0742572\pi$
$41$			18.9564i			0.462351i	−0.972912	+	0.231176i	$0.925743\pi$
$42$		0			0
$43$	17.6339			0.410091			0.205045	−	0.978752i	$-0.434266\pi$
$43$	17.6339			0.410091			0.205045	+	0.978752i	$0.434266\pi$
$44$		0			0
$45$	2.21143	−	1.27677i	0.0491430	−	0.0283727i
$46$		0			0
$47$	−15.6354	−	9.02712i	−0.332669	−	0.192066i	0.324357	−	0.945935i	$-0.394852\pi$
$47$	−15.6354	−	9.02712i	−0.332669	−	0.192066i	−0.657025	+	0.753868i	$0.728186\pi$
$48$		0			0
$49$	−46.8505	+	14.3538i	−0.956132	+	0.292935i
$50$		0			0
$51$	−4.56729	+	7.91078i	−0.0895547	+	0.155113i
$52$		0			0
$53$	12.8144	+	22.1952i	0.241781	+	0.418777i	0.961222	−	0.275777i	$-0.0889351\pi$
$53$	12.8144	+	22.1952i	0.241781	+	0.418777i	−0.719441	+	0.694554i	$0.755602\pi$
$54$		0			0
$55$			0.772698i			0.0140490i
$56$		0			0
$57$	−17.9255			−0.314482
$58$		0			0
$59$	37.9347	−	21.9016i	0.642961	−	0.371213i	−0.142794	−	0.989753i	$-0.545608\pi$
$59$	37.9347	−	21.9016i	0.642961	−	0.371213i	0.785754	+	0.618539i	$0.212275\pi$
$60$		0			0
$61$	−21.0502	−	12.1533i	−0.345086	−	0.199235i	0.317433	−	0.948281i	$-0.397179\pi$
$61$	−21.0502	−	12.1533i	−0.345086	−	0.199235i	−0.662519	+	0.749045i	$0.730512\pi$
$62$		0			0
$63$	26.6522	+	10.4895i	0.423051	+	0.166500i
$64$		0			0
$65$	−5.37570	+	9.31099i	−0.0827031	+	0.143246i
$66$		0			0
$67$	−35.3435	−	61.2167i	−0.527515	−	0.913683i	−0.999486	−	0.0320683i	$-0.989791\pi$
$67$	−35.3435	−	61.2167i	−0.527515	−	0.913683i	0.471971	−	0.881614i	$-0.343543\pi$
$68$		0			0
$69$		−	67.0554i		−	0.971817i
$70$		0			0
$71$	44.1041			0.621184			0.310592	−	0.950543i	$-0.399473\pi$
$71$	44.1041			0.621184			0.310592	+	0.950543i	$0.399473\pi$
$72$		0			0
$73$	80.5240	−	46.4905i	1.10307	−	0.636857i	0.166043	−	0.986118i	$-0.446901\pi$
$73$	80.5240	−	46.4905i	1.10307	−	0.636857i	0.937025	+	0.349262i	$0.113568\pi$
$74$		0			0
$75$	−47.2189	−	27.2618i	−0.629585	−	0.363491i
$76$		0			0
$77$	−6.78132	+	5.39736i	−0.0880690	+	0.0700956i
$78$		0			0
$79$	−50.1676	+	86.8928i	−0.635033	+	1.09991i	0.351475	+	0.936197i	$0.385680\pi$
$79$	−50.1676	+	86.8928i	−0.635033	+	1.09991i	−0.986508	+	0.163712i	$0.947653\pi$
$80$		0			0
$81$	13.7161	+	23.7569i	0.169334	+	0.293295i
$82$		0			0
$83$			58.0322i			0.699184i	0.936902	+	0.349592i	$0.113680\pi$
$83$			58.0322i			0.699184i	−0.936902	+	0.349592i	$0.886320\pi$
$84$		0			0
$85$	2.57312			0.0302721
$86$		0			0
$87$	−63.7212	+	36.7894i	−0.732427	+	0.422867i
$88$		0			0
$89$	−47.6584	−	27.5156i	−0.535487	−	0.309164i	0.207761	−	0.978180i	$-0.433382\pi$
$89$	−47.6584	−	27.5156i	−0.535487	−	0.309164i	−0.743248	+	0.669016i	$0.766716\pi$
$90$		0			0
$91$	−119.264	+	17.8601i	−1.31060	+	0.196265i
$92$		0			0
$93$	−4.43942	+	7.68930i	−0.0477357	+	0.0826806i
$94$		0			0
$95$	2.52471	+	4.37293i	0.0265759	+	0.0460309i
$96$		0			0
$97$			67.7953i			0.698920i	0.936951	+	0.349460i	$0.113635\pi$
$97$			67.7953i			0.698920i	−0.936951	+	0.349460i	$0.886365\pi$
$98$		0			0
$99$	5.06618			0.0511735
$100$		0			0
$101$	131.940	−	76.1754i	1.30633	−	0.754212i	0.324852	−	0.945765i	$-0.394686\pi$
$101$	131.940	−	76.1754i	1.30633	−	0.754212i	0.981482	+	0.191553i	$0.0613523\pi$
$102$		0			0
$103$	12.3381	+	7.12342i	0.119788	+	0.0691594i	0.558697	−	0.829372i	$-0.311302\pi$
$103$	12.3381	+	7.12342i	0.119788	+	0.0691594i	−0.438909	+	0.898532i	$0.644635\pi$
$104$		0			0
$105$	1.43336	+	9.57156i	0.0136511	+	0.0911577i
$106$		0			0
$107$	8.51498	−	14.7484i	0.0795793	−	0.137835i	−0.823489	−	0.567332i	$-0.807976\pi$
$107$	8.51498	−	14.7484i	0.0795793	−	0.137835i	0.903068	+	0.429497i	$0.141309\pi$
$108$		0			0
$109$	−18.5786	−	32.1791i	−0.170446	−	0.295221i	0.768130	−	0.640294i	$-0.221187\pi$
$109$	−18.5786	−	32.1791i	−0.170446	−	0.295221i	−0.938576	+	0.345073i	$0.887854\pi$
$110$		0			0
$111$		−	117.527i		−	1.05880i
$112$		0			0
$113$	98.6467			0.872980			0.436490	−	0.899709i	$-0.356221\pi$
$113$	98.6467			0.872980			0.436490	+	0.899709i	$0.356221\pi$
$114$		0			0
$115$	−16.3582	+	9.44443i	−0.142246	+	0.0821255i
$116$		0			0
$117$	61.0473	+	35.2457i	0.521772	+	0.301245i
$118$		0			0
$119$	17.9735	+	22.5821i	0.151038	+	0.189766i
$120$		0			0
$121$	59.7335	−	103.461i	0.493665	−	0.855053i
$122$		0			0
$123$	20.9986	+	36.3706i	0.170720	+	0.295696i
$124$		0			0
$125$			30.9607i			0.247685i
$126$		0			0
$127$	233.679			1.83999			0.919996	−	0.391927i	$-0.128191\pi$
$127$	233.679			1.83999			0.919996	+	0.391927i	$0.128191\pi$
$128$		0			0
$129$	33.8332	−	19.5336i	0.262273	−	0.151423i
$130$		0			0
$131$	−116.738	−	67.3988i	−0.891131	−	0.514495i	−0.0168190	−	0.999859i	$-0.505354\pi$
$131$	−116.738	−	67.3988i	−0.891131	−	0.514495i	−0.874312	+	0.485364i	$0.838687\pi$
$132$		0			0
$133$	−20.7422	+	52.7026i	−0.155956	+	0.396260i
$134$		0			0
$135$	9.05040	−	15.6757i	0.0670400	−	0.116117i
$136$		0			0
$137$	67.3030	+	116.572i	0.491262	+	0.850891i	0.999949	−	0.0100601i	$-0.00320228\pi$
$137$	67.3030	+	116.572i	0.491262	+	0.850891i	−0.508687	+	0.860952i	$0.669869\pi$
$138$		0			0
$139$			268.307i			1.93027i	0.261754	+	0.965135i	$0.415699\pi$
$139$			268.307i			1.93027i	−0.261754	+	0.965135i	$0.584301\pi$
$140$		0			0
$141$	−39.9985			−0.283677
$142$		0			0
$143$	−18.4728	+	10.6653i	−0.129180	+	0.0745823i
$144$		0			0
$145$	17.9496	+	10.3632i	0.123791	+	0.0714706i
$146$		0			0
$147$	−73.9893	+	79.4376i	−0.503329	+	0.540392i
$148$		0			0
$149$	95.9954	−	166.269i	0.644265	−	1.11590i	−0.340206	−	0.940351i	$-0.610497\pi$
$149$	95.9954	−	166.269i	0.644265	−	1.11590i	0.984471	−	0.175548i	$-0.0561698\pi$
$150$		0			0
$151$	95.9987	+	166.275i	0.635753	+	1.10116i	0.986355	+	0.164632i	$0.0526437\pi$
$151$	95.9987	+	166.275i	0.635753	+	1.10116i	−0.350602	+	0.936525i	$0.614023\pi$
$152$		0			0
$153$		−	16.8706i		−	0.110266i
$154$		0			0
$155$	2.50108			0.0161360
$156$		0			0
$157$	−107.202	+	61.8931i	−0.682816	+	0.394224i	−0.800915	−	0.598778i	$-0.795653\pi$
$157$	−107.202	+	61.8931i	−0.682816	+	0.394224i	0.118099	+	0.993002i	$0.462320\pi$
$158$		0			0
$159$	49.1726	+	28.3898i	0.309262	+	0.178552i
$160$		0			0
$161$	−197.150	−	77.5922i	−1.22453	−	0.481939i
$162$		0			0
$163$	−39.5269	+	68.4627i	−0.242497	+	0.420016i	−0.961425	−	0.275068i	$-0.911300\pi$
$163$	−39.5269	+	68.4627i	−0.242497	+	0.420016i	0.718928	+	0.695084i	$0.244633\pi$
$164$		0			0
$165$	0.855941	+	1.48253i	0.00518752	+	0.00898505i
$166$		0			0
$167$			195.275i			1.16931i	0.811281	+	0.584656i	$0.198771\pi$
$167$			195.275i			1.16931i	−0.811281	+	0.584656i	$0.801229\pi$
$168$		0			0
$169$	−127.796			−0.756187
$170$		0			0
$171$	28.6711	−	16.5532i	0.167667	−	0.0968026i
$172$		0			0
$173$	190.672	+	110.084i	1.10215	+	0.636326i	0.936785	−	0.349906i	$-0.113786\pi$
$173$	190.672	+	110.084i	1.10215	+	0.636326i	0.165365	+	0.986232i	$0.447120\pi$
$174$		0			0
$175$	−134.791	+	107.283i	−0.770236	+	0.613044i
$176$		0			0
$177$	48.5221	−	84.0428i	0.274136	−	0.474818i
$178$		0			0
$179$	149.229	+	258.471i	0.833679	+	1.44397i	0.895101	+	0.445863i	$0.147103\pi$
$179$	149.229	+	258.471i	0.833679	+	1.44397i	−0.0614225	+	0.998112i	$0.519564\pi$
$180$		0			0
$181$			143.271i			0.791551i	0.918347	+	0.395776i	$0.129524\pi$
$181$			143.271i			0.791551i	−0.918347	+	0.395776i	$0.870476\pi$
$182$		0			0
$183$	−53.8505			−0.294265
$184$		0			0
$185$	−28.6707	+	16.5531i	−0.154977	+	0.0894760i
$186$		0			0
$187$	4.42108	+	2.55251i	0.0236421	+	0.0136498i
$188$		0			0
$189$	200.791	−	30.0688i	1.06238	−	0.159094i
$190$		0			0
$191$	−49.5826	+	85.8796i	−0.259595	+	0.449632i	−0.966133	−	0.258043i	$-0.916922\pi$
$191$	−49.5826	+	85.8796i	−0.259595	+	0.449632i	0.706539	+	0.707675i	$0.250256\pi$
$192$		0			0
$193$	−107.084	−	185.475i	−0.554839	−	0.961010i	−0.997916	−	0.0645260i	$-0.979446\pi$
$193$	−107.084	−	185.475i	−0.554839	−	0.961010i	0.443077	−	0.896484i	$-0.353887\pi$
$194$		0			0
$195$			23.8193i			0.122150i
$196$		0			0
$197$	259.342			1.31646			0.658229	−	0.752818i	$-0.271306\pi$
$197$	259.342			1.31646			0.658229	+	0.752818i	$0.271306\pi$
$198$		0			0
$199$	−37.5295	+	21.6677i	−0.188591	+	0.108883i	−0.591323	−	0.806435i	$-0.701394\pi$
$199$	−37.5295	+	21.6677i	−0.188591	+	0.108883i	0.402732	+	0.915318i	$0.368061\pi$
$200$		0			0
$201$	−135.623	−	78.3021i	−0.674743	−	0.389563i
$202$		0			0
$203$	34.4306	+	229.917i	0.169609	+	1.13260i
$204$		0			0
$205$	5.91510	−	10.2453i	0.0288541	−	0.0499769i
$206$		0			0
$207$	61.9223	+	107.253i	0.299141	+	0.518128i
$208$		0			0
$209$			10.0180i			0.0479328i
$210$		0			0
$211$	−178.016			−0.843678			−0.421839	−	0.906671i	$-0.638615\pi$
$211$	−178.016			−0.843678			−0.421839	+	0.906671i	$0.638615\pi$
$212$		0			0
$213$	84.6201	−	48.8554i	0.397277	−	0.229368i
$214$		0			0
$215$	−9.53049	−	5.50243i	−0.0443279	−	0.0255927i
$216$		0			0
$217$	17.4703	+	21.9499i	0.0805083	+	0.101152i
$218$		0			0
$219$	102.998	−	178.398i	0.470310	−	0.814602i
$220$		0			0
$221$	35.5159	+	61.5154i	0.160706	+	0.278350i
$222$		0			0
$223$		−	222.495i		−	0.997734i	−0.866679	−	0.498867i	$-0.833750\pi$
$223$		−	222.495i		−	0.997734i	0.866679	−	0.498867i	$-0.166250\pi$
$224$		0			0
$225$	100.700			0.447554
$226$		0			0
$227$	36.7370	−	21.2101i	0.161837	−	0.0934366i	−0.416894	−	0.908955i	$-0.636881\pi$
$227$	36.7370	−	21.2101i	0.161837	−	0.0934366i	0.578731	+	0.815518i	$0.303548\pi$
$228$		0			0
$229$	−43.7736	−	25.2727i	−0.191151	−	0.110361i	0.401370	−	0.915916i	$-0.368534\pi$
$229$	−43.7736	−	25.2727i	−0.191151	−	0.110361i	−0.592521	+	0.805555i	$0.701867\pi$
$230$		0			0
$231$	−7.03212	+	17.8675i	−0.0304421	+	0.0773485i
$232$		0			0
$233$	198.221	−	343.329i	0.850734	−	1.47351i	−0.0298138	−	0.999555i	$-0.509491\pi$
$233$	198.221	−	343.329i	0.850734	−	1.47351i	0.880547	−	0.473958i	$-0.157175\pi$
$234$		0			0
$235$	5.63359	+	9.75767i	0.0239727	+	0.0415220i
$236$		0			0
$237$			222.289i			0.937927i
$238$		0			0
$239$	−25.0145			−0.104663			−0.0523316	−	0.998630i	$-0.516665\pi$
$239$	−25.0145			−0.104663			−0.0523316	+	0.998630i	$0.516665\pi$
$240$		0			0
$241$	125.380	−	72.3884i	0.520251	−	0.300367i	−0.216787	−	0.976219i	$-0.569558\pi$
$241$	125.380	−	72.3884i	0.520251	−	0.300367i	0.737037	+	0.675852i	$0.236224\pi$
$242$		0			0
$243$	−173.433	−	100.132i	−0.713716	−	0.412064i
$244$		0			0
$245$	29.7999	+	6.86137i	0.121632	+	0.0280056i
$246$		0			0
$247$	−69.6955	+	120.716i	−0.282168	+	0.488729i
$248$		0			0
$249$	64.2841	+	111.343i	0.258169	+	0.447162i
$250$		0			0
$251$		−	153.407i		−	0.611185i	−0.952162	−	0.305593i	$-0.901145\pi$
$251$		−	153.407i		−	0.611185i	0.952162	−	0.305593i	$-0.0988545\pi$
$252$		0			0
$253$	−37.4751			−0.148123
$254$		0			0
$255$	4.93691	−	2.85033i	0.0193604	−	0.0111778i
$256$		0			0
$257$	−329.387	−	190.172i	−1.28166	−	0.739968i	−0.304510	−	0.952509i	$-0.598493\pi$
$257$	−329.387	−	190.172i	−1.28166	−	0.739968i	−0.977152	+	0.212541i	$0.931826\pi$
$258$		0			0
$259$	−345.540	−	135.994i	−1.33413	−	0.525074i
$260$		0			0
$261$	67.9464	−	117.687i	0.260331	−	0.450906i
$262$		0			0
$263$	61.6549	+	106.789i	0.234429	+	0.406043i	0.959107	−	0.283045i	$-0.0913446\pi$
$263$	61.6549	+	106.789i	0.234429	+	0.406043i	−0.724677	+	0.689088i	$0.758011\pi$
$264$		0			0
$265$		−	15.9943i		−	0.0603558i
$266$		0			0
$267$	−121.919			−0.456627
$268$		0			0
$269$	101.529	−	58.6177i	0.377431	−	0.217910i	−0.299269	−	0.954169i	$-0.596743\pi$
$269$	101.529	−	58.6177i	0.377431	−	0.217910i	0.676700	+	0.736259i	$0.263409\pi$
$270$		0			0
$271$	−344.945	−	199.154i	−1.27286	−	0.734885i	−0.297334	−	0.954774i	$-0.596097\pi$
$271$	−344.945	−	199.154i	−1.27286	−	0.734885i	−0.975525	+	0.219888i	$0.929431\pi$
$272$		0			0
$273$	−209.042	+	166.380i	−0.765721	+	0.609451i
$274$		0			0
$275$	−15.2358	+	26.3891i	−0.0554028	+	0.0959604i
$276$		0			0
$277$	−9.66248	−	16.7359i	−0.0348826	−	0.0604184i	0.848057	−	0.529905i	$-0.177772\pi$
$277$	−9.66248	−	16.7359i	−0.0348826	−	0.0604184i	−0.882940	+	0.469487i	$0.844439\pi$
$278$		0			0
$279$		−	16.3983i		−	0.0587753i
$280$		0			0
$281$	374.496			1.33273			0.666363	−	0.745627i	$-0.267850\pi$
$281$	374.496			1.33273			0.666363	+	0.745627i	$0.267850\pi$
$282$		0			0
$283$	167.904	−	96.9397i	0.593302	−	0.342543i	−0.173100	−	0.984904i	$-0.555378\pi$
$283$	167.904	−	96.9397i	0.593302	−	0.342543i	0.766402	+	0.642361i	$0.222045\pi$
$284$		0			0
$285$	9.68807	+	5.59341i	0.0339932	+	0.0196260i
$286$		0			0
$287$	131.231	−	19.6522i	0.457252	−	0.0684746i
$288$		0			0
$289$	8.50000	−	14.7224i	0.0294118	−	0.0509427i
$290$		0			0
$291$	75.0989	+	130.075i	0.258072	+	0.446993i
$292$		0			0
$293$		−	489.542i		−	1.67079i	−0.549650	−	0.835395i	$-0.685239\pi$
$293$		−	489.542i		−	1.67079i	0.549650	−	0.835395i	$-0.314761\pi$
$294$		0			0
$295$	−27.3364			−0.0926659
$296$		0			0
$297$	31.1003	−	17.9558i	0.104715	−	0.0604572i
$298$		0			0
$299$	−451.574	−	260.716i	−1.51028	−	0.871961i
$300$		0			0
$301$	−18.2812	−	122.076i	−0.0607347	−	0.405568i
$302$		0			0
$303$	168.764	−	292.307i	0.556976	−	0.964711i
$304$		0			0
$305$	7.58459	+	13.1369i	0.0248675	+	0.0430718i
$306$		0			0
$307$		−	162.954i		−	0.530793i	−0.964139	−	0.265397i	$-0.914497\pi$
$307$		−	162.954i		−	0.530793i	0.964139	−	0.265397i	$-0.0855029\pi$
$308$		0			0
$309$	31.5633			0.102147
$310$		0			0
$311$	−347.632	+	200.706i	−1.11779	+	0.645356i	−0.940836	−	0.338863i	$-0.889958\pi$
$311$	−347.632	+	200.706i	−1.11779	+	0.645356i	−0.176953	+	0.984219i	$0.556624\pi$
$312$		0			0
$313$	−285.918	−	165.075i	−0.913476	−	0.527395i	−0.0319279	−	0.999490i	$-0.510165\pi$
$313$	−285.918	−	165.075i	−0.913476	−	0.527395i	−0.881548	+	0.472095i	$0.843498\pi$
$314$		0			0
$315$	−11.1315	−	13.9857i	−0.0353380	−	0.0443990i
$316$		0			0
$317$	146.229	−	253.276i	0.461290	−	0.798977i	−0.537736	−	0.843113i	$-0.680720\pi$
$317$	146.229	−	253.276i	0.461290	−	0.798977i	0.999026	+	0.0441362i	$0.0140536\pi$
$318$		0			0
$319$	20.5604	+	35.6117i	0.0644528	+	0.111635i
$320$		0			0
$321$		−	37.7292i		−	0.117537i
$322$		0			0
$323$	33.3603			0.103283
$324$		0			0
$325$	−367.181	+	211.992i	−1.12979	+	0.652283i
$326$		0			0
$327$	−71.2915	−	41.1601i	−0.218017	−	0.125872i
$328$		0			0
$329$	−46.2837	+	117.600i	−0.140680	+	0.357445i
$330$		0			0
$331$	53.3923	−	92.4782i	0.161306	−	0.279390i	−0.774031	−	0.633147i	$-0.781763\pi$
$331$	53.3923	−	92.4782i	0.161306	−	0.279390i	0.935337	+	0.353757i	$0.115096\pi$
$332$		0			0
$333$	108.530	+	187.979i	0.325916	+	0.564502i
$334$		0			0
$335$			44.1139i			0.131683i
$336$		0			0
$337$	−419.326			−1.24429			−0.622145	−	0.782902i	$-0.713739\pi$
$337$	−419.326			−1.24429			−0.622145	+	0.782902i	$0.713739\pi$
$338$		0			0
$339$	189.268	−	109.274i	0.558313	−	0.322342i
$340$		0			0
$341$	4.29730	+	2.48105i	0.0126021	+	0.00727580i
$342$		0			0
$343$	147.939	+	309.456i	0.431309	+	0.902204i
$344$		0			0
$345$	−20.9238	+	36.2410i	−0.0606486	+	0.105047i
$346$		0			0
$347$	−262.837	−	455.248i	−0.757457	−	1.31195i	−0.944144	−	0.329534i	$-0.893108\pi$
$347$	−262.837	−	455.248i	−0.757457	−	1.31195i	0.186687	−	0.982419i	$-0.440225\pi$
$348$		0			0
$349$			10.8177i			0.0309962i	0.999880	+	0.0154981i	$0.00493339\pi$
$349$			10.8177i			0.0309962i	−0.999880	+	0.0154981i	$0.995067\pi$
$350$		0			0
$351$	499.678			1.42358
$352$		0			0
$353$	−139.815	+	80.7222i	−0.396077	+	0.228675i	−0.684790	−	0.728741i	$-0.740106\pi$
$353$	−139.815	+	80.7222i	−0.396077	+	0.228675i	0.288713	+	0.957416i	$0.406773\pi$
$354$		0			0
$355$	−23.8367	−	13.7621i	−0.0671456	−	0.0387665i
$356$		0			0
$357$	59.4997	+	23.4173i	0.166666	+	0.0655947i
$358$		0			0
$359$	70.5178	−	122.140i	0.196428	−	0.340224i	−0.750940	−	0.660371i	$-0.770399\pi$
$359$	70.5178	−	122.140i	0.196428	−	0.340224i	0.947368	+	0.320147i	$0.103732\pi$
$360$		0			0
$361$	−147.767	−	255.940i	−0.409328	−	0.708976i
$362$		0			0
$363$		−	264.674i		−	0.729131i
$364$		0			0
$365$	−58.0271			−0.158978
$366$		0			0
$367$	−177.180	+	102.295i	−0.482779	+	0.278732i	−0.721574	−	0.692338i	$-0.756581\pi$
$367$	−177.180	+	102.295i	−0.482779	+	0.278732i	0.238795	+	0.971070i	$0.423248\pi$
$368$		0			0
$369$	−67.1728	−	38.7823i	−0.182040	−	0.105101i
$370$		0			0
$371$	140.368	−	111.721i	0.378351	−	0.301136i
$372$		0			0
$373$	308.870	−	534.978i	0.828068	−	1.43426i	−0.0714830	−	0.997442i	$-0.522773\pi$
$373$	308.870	−	534.978i	0.828068	−	1.43426i	0.899551	−	0.436815i	$-0.143893\pi$
$374$		0			0
$375$	34.2961	+	59.4025i	0.0914562	+	0.158407i
$376$		0			0
$377$			572.160i			1.51767i
$378$		0			0
$379$	66.7160			0.176032			0.0880159	−	0.996119i	$-0.471947\pi$
$379$	66.7160			0.176032			0.0880159	+	0.996119i	$0.471947\pi$
$380$		0			0
$381$	448.347	−	258.853i	1.17676	−	0.679405i
$382$		0			0
$383$	87.6871	+	50.6261i	0.228948	+	0.132183i	0.610087	−	0.792335i	$-0.291135\pi$
$383$	87.6871	+	50.6261i	0.228948	+	0.132183i	−0.381139	+	0.924518i	$0.624468\pi$
$384$		0			0
$385$	5.34924	−	0.801060i	0.0138941	−	0.00208067i
$386$		0			0
$387$	−36.0766	+	62.4865i	−0.0932212	+	0.161464i
$388$		0			0
$389$	241.955	+	419.078i	0.621992	+	1.07732i	0.989114	+	0.147149i	$0.0470096\pi$
$389$	241.955	+	419.078i	0.621992	+	1.07732i	−0.367123	+	0.930173i	$0.619657\pi$
$390$		0			0
$391$			124.794i			0.319167i
$392$		0			0
$393$	−298.639			−0.759896
$394$		0			0
$395$	54.2276	−	31.3083i	0.137285	−	0.0792615i
$396$		0			0
$397$	−627.021	−	362.011i	−1.57940	−	0.911866i	−0.994943	−	0.100441i	$-0.967975\pi$
$397$	−627.021	−	362.011i	−1.57940	−	0.911866i	−0.584456	−	0.811426i	$-0.698692\pi$
$398$		0			0
$399$	18.5834	+	124.094i	0.0465750	+	0.311014i
$400$		0			0
$401$	51.8733	−	89.8472i	0.129360	−	0.224058i	−0.794069	−	0.607828i	$-0.792041\pi$
$401$	51.8733	−	89.8472i	0.129360	−	0.224058i	0.923429	+	0.383770i	$0.125374\pi$
$402$		0			0
$403$	34.5216	+	59.7931i	0.0856615	+	0.148370i
$404$		0			0
$405$		−	17.1197i		−	0.0422708i
$406$		0			0
$407$	−65.6819			−0.161380
$408$		0			0
$409$	−524.145	+	302.615i	−1.28153	+	0.739890i	−0.977127	−	0.212654i	$-0.931789\pi$
$409$	−524.145	+	302.615i	−1.28153	+	0.739890i	−0.304400	+	0.952544i	$0.598456\pi$
$410$		0			0
$411$	258.261	+	149.107i	0.628372	+	0.362791i
$412$		0			0
$413$	−190.948	−	239.909i	−0.462343	−	0.580893i
$414$		0			0
$415$	18.1082	−	31.3643i	0.0436343	−	0.0755767i
$416$		0			0
$417$	297.212	+	514.787i	0.712739	+	1.23450i
$418$		0			0
$419$		−	624.531i		−	1.49053i	−0.666770	−	0.745263i	$-0.732324\pi$
$419$		−	624.531i		−	1.49053i	0.666770	−	0.745263i	$-0.267676\pi$
$420$		0			0
$421$	158.939			0.377526			0.188763	−	0.982023i	$-0.439552\pi$
$421$	158.939			0.377526			0.188763	+	0.982023i	$0.439552\pi$
$422$		0			0
$423$	63.9760	−	36.9366i	0.151243	−	0.0873205i
$424$		0			0
$425$	87.8772	+	50.7359i	0.206770	+	0.119379i
$426$		0			0
$427$	−62.3124	+	158.326i	−0.145931	+	0.370787i
$428$		0			0
$429$	−23.6285	+	40.9258i	−0.0550781	+	0.0953981i
$430$		0			0
$431$	250.643	+	434.126i	0.581538	+	1.00725i	0.995297	+	0.0968670i	$0.0308822\pi$
$431$	250.643	+	434.126i	0.581538	+	1.00725i	−0.413759	+	0.910386i	$0.635785\pi$
$432$		0			0
$433$			236.178i			0.545445i	0.962093	+	0.272723i	$0.0879241\pi$
$433$			236.178i			0.545445i	−0.962093	+	0.272723i	$0.912076\pi$
$434$		0			0
$435$	45.9187			0.105560
$436$		0			0
$437$	−212.083	+	122.446i	−0.485316	+	0.280197i
$438$		0			0
$439$	−318.947	−	184.144i	−0.726531	−	0.419463i	0.0906208	−	0.995885i	$-0.471115\pi$
$439$	−318.947	−	184.144i	−0.726531	−	0.419463i	−0.817152	+	0.576423i	$0.804448\pi$
$440$		0			0
$441$	44.9864	−	195.383i	0.102010	−	0.443045i
$442$		0			0
$443$	−147.432	+	255.359i	−0.332803	+	0.576431i	−0.983060	−	0.183283i	$-0.941328\pi$
$443$	−147.432	+	255.359i	−0.332803	+	0.576431i	0.650257	+	0.759714i	$0.274661\pi$
$444$		0			0
$445$	17.1718	+	29.7424i	0.0385882	+	0.0668368i
$446$		0			0
$447$		−	425.348i		−	0.951562i
$448$		0			0
$449$	−408.554			−0.909920			−0.454960	−	0.890512i	$-0.650346\pi$
$449$	−408.554			−0.909920			−0.454960	+	0.890512i	$0.650346\pi$
$450$		0			0
$451$	20.3264	−	11.7354i	0.0450696	−	0.0260209i
$452$		0			0
$453$	368.375	+	212.681i	0.813190	+	0.469496i
$454$		0			0
$455$	70.0312	+	27.5622i	0.153915	+	0.0605762i
$456$		0			0
$457$	−78.7398	+	136.381i	−0.172297	+	0.298427i	−0.939223	−	0.343309i	$-0.888452\pi$
$457$	−78.7398	+	136.381i	−0.172297	+	0.298427i	0.766925	+	0.641736i	$0.221786\pi$
$458$		0			0
$459$	−59.7937	−	103.566i	−0.130270	−	0.225634i
$460$		0			0
$461$			643.351i			1.39555i	0.716315	+	0.697777i	$0.245827\pi$
$461$			643.351i			1.39555i	−0.716315	+	0.697777i	$0.754173\pi$
$462$		0			0
$463$	231.866			0.500791			0.250396	−	0.968144i	$-0.419439\pi$
$463$	231.866			0.500791			0.250396	+	0.968144i	$0.419439\pi$
$464$		0			0
$465$	4.79869	−	2.77053i	0.0103198	−	0.00595812i
$466$		0			0
$467$	263.521	+	152.144i	0.564285	+	0.325790i	0.754863	−	0.655882i	$-0.227703\pi$
$467$	263.521	+	152.144i	0.564285	+	0.325790i	−0.190579	+	0.981672i	$0.561036\pi$
$468$		0			0
$469$	−387.151	+	308.140i	−0.825481	+	0.657015i
$470$		0			0
$471$	−137.122	+	237.502i	−0.291129	+	0.504251i
$472$		0			0
$473$	−10.9167	−	18.9083i	−0.0230797	−	0.0399752i
$474$		0			0
$475$			199.126i			0.419212i
$476$		0			0
$477$	−104.866			−0.219845
$478$		0			0
$479$	339.621	−	196.080i	0.709020	−	0.409353i	−0.101678	−	0.994817i	$-0.532421\pi$
$479$	339.621	−	196.080i	0.709020	−	0.409353i	0.810698	+	0.585464i	$0.199088\pi$
$480$		0			0
$481$	−791.464	−	456.952i	−1.64546	−	0.950005i
$482$		0			0
$483$	−464.212	+	69.5167i	−0.961100	+	0.143927i
$484$		0			0
$485$	21.1546	−	36.6409i	0.0436178	−	0.0755483i
$486$		0			0
$487$	235.345	+	407.630i	0.483255	+	0.837022i	0.999815	−	0.0192289i	$-0.00612112\pi$
$487$	235.345	+	407.630i	0.483255	+	0.837022i	−0.516560	+	0.856251i	$0.672788\pi$
$488$		0			0
$489$			175.141i			0.358161i
$490$		0			0
$491$	739.366			1.50584			0.752918	−	0.658114i	$-0.228645\pi$
$491$	739.366			1.50584			0.752918	+	0.658114i	$0.228645\pi$
$492$		0			0
$493$	118.589	−	68.4673i	0.240545	−	0.138879i
$494$		0			0
$495$	−2.73809	−	1.58084i	−0.00553149	−	0.00319361i
$496$		0			0
$497$	−45.7229	−	305.324i	−0.0919978	−	0.614334i
$498$		0			0
$499$	263.499	−	456.394i	0.528054	−	0.914616i	−0.471411	−	0.881914i	$-0.656255\pi$
$499$	263.499	−	456.394i	0.528054	−	0.914616i	0.999465	−	0.0327028i	$-0.0104115\pi$
$500$		0			0
$501$	216.312	+	374.664i	0.431761	+	0.747832i
$502$		0			0
$503$		−	521.864i		−	1.03750i	−0.854925	−	0.518751i	$-0.826397\pi$
$503$		−	521.864i		−	1.03750i	0.854925	−	0.518751i	$-0.173603\pi$
$504$		0			0
$505$	−95.0783			−0.188274
$506$		0			0
$507$	−245.194	+	141.563i	−0.483618	+	0.279217i
$508$		0			0
$509$	660.937	+	381.592i	1.29850	+	0.749690i	0.980145	−	0.198282i	$-0.0635361\pi$
$509$	660.937	+	381.592i	1.29850	+	0.749690i	0.318355	+	0.947971i	$0.396869\pi$
$510$		0			0
$511$	−405.325	−	509.255i	−0.793199	−	0.996585i
$512$		0			0
$513$	117.338	−	203.235i	0.228728	−	0.396169i
$514$		0			0
$515$	−4.44554	−	7.69990i	−0.00863212	−	0.0149513i
$516$		0			0
$517$			22.3539i			0.0432376i
$518$		0			0
$519$	487.776			0.939838
$520$		0			0
$521$	−281.669	+	162.622i	−0.540632	+	0.312134i	−0.745335	−	0.666690i	$-0.767711\pi$
$521$	−281.669	+	162.622i	−0.540632	+	0.312134i	0.204703	+	0.978824i	$0.434377\pi$
$522$		0			0
$523$	122.432	+	70.6860i	0.234095	+	0.135155i	0.612460	−	0.790502i	$-0.290180\pi$
$523$	122.432	+	70.6860i	0.234095	+	0.135155i	−0.378365	+	0.925657i	$0.623513\pi$
$524$		0			0
$525$	−139.776	+	355.150i	−0.266241	+	0.676476i
$526$		0			0
$527$	8.26202	−	14.3102i	0.0156775	−	0.0271542i
$528$		0			0
$529$	−193.546	−	335.232i	−0.365872	−	0.633708i
$530$		0			0
$531$			179.231i			0.337535i
$532$		0			0
$533$	326.576			0.612713
$534$		0			0
$535$	−9.20409	+	5.31398i	−0.0172039	+	0.00993268i
$536$		0			0
$537$	572.633	+	330.610i	1.06636	+	0.615661i
$538$		0			0
$539$	44.3951	+	41.3503i	0.0823657	+	0.0767166i
$540$		0			0
$541$	200.235	−	346.817i	0.370120	−	0.641067i	−0.619464	−	0.785025i	$-0.712650\pi$
$541$	200.235	−	346.817i	0.370120	−	0.641067i	0.989584	+	0.143958i	$0.0459832\pi$
$542$		0			0
$543$	158.705	+	274.886i	0.292275	+	0.506236i
$544$		0			0
$545$			23.1888i			0.0425483i
$546$		0			0
$547$	476.057			0.870305			0.435153	−	0.900357i	$-0.356694\pi$
$547$	476.057			0.870305			0.435153	+	0.900357i	$0.356694\pi$
$548$		0			0
$549$	86.1318	−	49.7282i	0.156889	−	0.0905797i
$550$		0			0
$551$	232.716	+	134.358i	0.422352	+	0.243845i
$552$		0			0
$553$	653.551	+	257.218i	1.18183	+	0.465132i
$554$		0			0
$555$	−36.6727	+	63.5189i	−0.0660769	+	0.114449i
$556$		0			0
$557$	205.434	+	355.822i	0.368822	+	0.638819i	0.989382	−	0.145341i	$-0.0464278\pi$
$557$	205.434	+	355.822i	0.368822	+	0.638819i	−0.620559	+	0.784159i	$0.713094\pi$
$558$		0			0
$559$		−	303.793i		−	0.543457i
$560$		0			0
$561$	11.3100			0.0201604
$562$		0			0
$563$	468.066	−	270.238i	0.831379	−	0.479997i	−0.0229457	−	0.999737i	$-0.507304\pi$
$563$	468.066	−	270.238i	0.831379	−	0.479997i	0.854325	+	0.519740i	$0.173971\pi$
$564$		0			0
$565$	−53.3150	−	30.7814i	−0.0943629	−	0.0544804i
$566$		0			0
$567$	150.245	−	119.583i	0.264983	−	0.210904i
$568$		0			0
$569$	76.0101	−	131.653i	0.133585	−	0.231377i	−0.791471	−	0.611207i	$-0.790684\pi$
$569$	76.0101	−	131.653i	0.133585	−	0.231377i	0.925056	+	0.379830i	$0.124018\pi$
$570$		0			0
$571$	152.180	+	263.584i	0.266515	+	0.461618i	0.967959	−	0.251106i	$-0.0807944\pi$
$571$	152.180	+	263.584i	0.266515	+	0.461618i	−0.701444	+	0.712724i	$0.747461\pi$
$572$		0			0
$573$			219.697i			0.383415i
$574$		0			0
$575$	−744.887			−1.29546
$576$		0			0
$577$	−669.451	+	386.507i	−1.16023	+	0.669857i	−0.951358	−	0.308087i	$-0.900311\pi$
$577$	−669.451	+	386.507i	−1.16023	+	0.669857i	−0.208868	+	0.977944i	$0.566978\pi$
$578$		0			0
$579$	−410.912	−	237.240i	−0.709693	−	0.409742i
$580$		0			0
$581$	401.746	−	60.1623i	0.691473	−	0.103550i
$582$		0			0
$583$	15.8662	−	27.4810i	0.0272147	−	0.0471372i
$584$		0			0
$585$	−21.9959	−	38.0981i	−0.0375999	−	0.0651249i
$586$		0			0
$587$			972.880i			1.65738i	0.559710	+	0.828689i	$0.310913\pi$
$587$			972.880i			1.65738i	−0.559710	+	0.828689i	$0.689087\pi$
$588$		0			0
$589$	32.4263			0.0550532
$590$		0			0
$591$	497.586	−	287.281i	0.841938	−	0.486093i
$592$		0			0
$593$	−347.338	−	200.535i	−0.585730	−	0.338171i	0.177678	−	0.984089i	$-0.443142\pi$
$593$	−347.338	−	200.535i	−0.585730	−	0.338171i	−0.763407	+	0.645918i	$0.776475\pi$
$594$		0			0
$595$	−2.66757	−	17.8132i	−0.00448331	−	0.0299382i
$596$		0			0
$597$	−48.0039	+	83.1452i	−0.0804086	+	0.139272i
$598$		0			0
$599$	−336.995	−	583.692i	−0.562595	−	0.974444i	−0.997269	−	0.0738556i	$-0.976470\pi$
$599$	−336.995	−	583.692i	−0.562595	−	0.974444i	0.434674	−	0.900588i	$-0.356864\pi$
$600$		0			0
$601$			680.518i			1.13231i	0.824299	+	0.566154i	$0.191569\pi$
$601$			680.518i			1.13231i	−0.824299	+	0.566154i	$0.808431\pi$
$602$		0			0
$603$	289.232			0.479655
$604$		0			0
$605$	−64.5676	+	37.2781i	−0.106723	+	0.0616168i
$606$		0			0
$607$	−323.020	−	186.496i	−0.532159	−	0.307242i	0.209736	−	0.977758i	$-0.432739\pi$
$607$	−323.020	−	186.496i	−0.532159	−	0.307242i	−0.741895	+	0.670516i	$0.766073\pi$
$608$		0			0
$609$	320.746	+	402.990i	0.526677	+	0.661723i
$610$		0			0
$611$	−155.517	+	269.363i	−0.254529	+	0.440857i
$612$		0			0
$613$	−523.887	−	907.398i	−0.854627	−	1.48026i	−0.876990	−	0.480508i	$-0.840452\pi$
$613$	−523.887	−	907.398i	−0.854627	−	1.48026i	0.0223629	−	0.999750i	$-0.492881\pi$
$614$		0			0
$615$		−	26.2094i		−	0.0426168i
$616$		0			0
$617$	−471.508			−0.764195			−0.382097	−	0.924122i	$-0.624798\pi$
$617$	−471.508			−0.764195			−0.382097	+	0.924122i	$0.624798\pi$
$618$		0			0
$619$	−35.3993	+	20.4378i	−0.0571879	+	0.0330174i	−0.528321	−	0.849045i	$-0.677178\pi$
$619$	−35.3993	+	20.4378i	−0.0571879	+	0.0330174i	0.471133	+	0.882062i	$0.343845\pi$
$620$		0			0
$621$	760.259	+	438.936i	1.22425	+	0.706821i
$622$		0			0
$623$	−141.077	+	358.455i	−0.226448	+	0.575369i
$624$		0			0
$625$	−297.971	+	516.101i	−0.476753	+	0.825761i
$626$		0			0
$627$	11.0972	+	19.2209i	0.0176989	+	0.0306554i
$628$		0			0
$629$			218.724i			0.347733i
$630$		0			0
$631$	−549.020			−0.870079			−0.435040	−	0.900411i	$-0.643266\pi$
$631$	−549.020			−0.870079			−0.435040	+	0.900411i	$0.643266\pi$
$632$		0			0
$633$	−341.550	+	197.194i	−0.539573	+	0.311523i
$634$		0			0
$635$	−126.295	−	72.9166i	−0.198890	−	0.114829i
$636$		0			0
$637$	247.284	+	807.129i	0.388201	+	1.26708i
$638$		0			0
$639$	−90.2310	+	156.285i	−0.141207	+	0.244577i
$640$		0			0
$641$	−158.826	−	275.094i	−0.247778	−	0.429164i	0.715131	−	0.698990i	$-0.246367\pi$
$641$	−158.826	−	275.094i	−0.247778	−	0.429164i	−0.962909	+	0.269827i	$0.913034\pi$
$642$		0			0
$643$		−	22.5164i		−	0.0350177i	−0.999847	−	0.0175088i	$-0.994426\pi$
$643$		−	22.5164i		−	0.0350177i	0.999847	−	0.0175088i	$-0.00557352\pi$
$644$		0			0
$645$	−24.3808			−0.0377998
$646$		0			0
$647$	609.777	−	352.055i	0.942468	−	0.544134i	0.0517348	−	0.998661i	$-0.483525\pi$
$647$	609.777	−	352.055i	0.942468	−	0.544134i	0.890733	+	0.454527i	$0.150192\pi$
$648$		0			0
$649$	−46.9688	−	27.1175i	−0.0723711	−	0.0417835i
$650$		0			0
$651$	57.8339	+	22.7617i	0.0888385	+	0.0349642i
$652$		0			0
$653$	−389.203	+	674.120i	−0.596023	+	1.03234i	0.397378	+	0.917655i	$0.369920\pi$
$653$	−389.203	+	674.120i	−0.596023	+	1.03234i	−0.993402	+	0.114688i	$0.963413\pi$
$654$		0			0
$655$	42.0619	+	72.8533i	0.0642166	+	0.111226i
$656$		0			0
$657$			380.454i			0.579077i
$658$		0			0
$659$	902.245			1.36911			0.684556	−	0.728960i	$-0.259996\pi$
$659$	902.245			1.36911			0.684556	+	0.728960i	$0.259996\pi$
$660$		0			0
$661$	504.731	−	291.407i	0.763587	−	0.440857i	−0.0669952	−	0.997753i	$-0.521341\pi$
$661$	504.731	−	291.407i	0.763587	−	0.440857i	0.830582	+	0.556896i	$0.188008\pi$
$662$		0			0
$663$	136.285	+	78.6842i	0.205558	+	0.118679i
$664$		0			0
$665$	27.6556	−	22.0116i	0.0415874	−	0.0331001i
$666$		0			0
$667$	−502.607	+	870.541i	−0.753534	+	1.30516i
$668$		0			0
$669$	−246.464	−	426.888i	−0.368407	−	0.638099i
$670$		0			0
$671$			30.0953i			0.0448515i
$672$		0			0
$673$	−323.814			−0.481150			−0.240575	−	0.970631i	$-0.577336\pi$
$673$	−323.814			−0.481150			−0.240575	+	0.970631i	$0.577336\pi$
$674$		0			0
$675$	618.177	−	356.905i	0.915818	−	0.528748i
$676$		0			0
$677$	−401.310	−	231.696i	−0.592777	−	0.342240i	0.173418	−	0.984848i	$-0.444519\pi$
$677$	−401.310	−	231.696i	−0.592777	−	0.342240i	−0.766195	+	0.642608i	$0.777852\pi$
$678$		0			0
$679$	469.333	−	70.2837i	0.691213	−	0.103511i
$680$		0			0
$681$	46.9902	−	81.3894i	0.0690017	−	0.119515i
$682$		0			0
$683$	299.199	+	518.228i	0.438066	+	0.758752i	0.997540	−	0.0700952i	$-0.0223303\pi$
$683$	299.199	+	518.228i	0.438066	+	0.758752i	−0.559474	+	0.828848i	$0.688997\pi$
$684$		0			0
$685$		−	84.0041i		−	0.122634i
$686$		0			0
$687$	−111.981			−0.163000
$688$		0			0
$689$	382.373	−	220.763i	0.554969	−	0.320411i
$690$		0			0
$691$	579.735	+	334.710i	0.838980	+	0.484385i	0.856917	−	0.515454i	$-0.172377\pi$
$691$	579.735	+	334.710i	0.838980	+	0.484385i	−0.0179377	+	0.999839i	$0.505710\pi$
$692$		0			0
$693$	−5.25213	−	35.0722i	−0.00757884	−	0.0506092i
$694$		0			0
$695$	83.7219	−	145.011i	0.120463	−	0.208648i
$696$		0			0
$697$	−39.0796	−	67.6879i	−0.0560683	−	0.0971132i
$698$		0			0
$699$		−	878.301i		−	1.25651i
$700$		0			0
$701$	−861.795			−1.22938			−0.614690	−	0.788769i	$-0.710719\pi$
$701$	−861.795			−1.22938			−0.614690	+	0.788769i	$0.710719\pi$
$702$		0			0
$703$	−371.714	+	214.609i	−0.528754	+	0.305276i
$704$		0			0
$705$	21.6177	+	12.4810i	0.0306635	+	0.0177036i
$706$		0			0
$707$	−664.130	−	834.422i	−0.939364	−	1.18023i
$708$		0			0
$709$	102.683	−	177.853i	0.144828	−	0.250850i	−0.784481	−	0.620153i	$-0.787070\pi$
$709$	102.683	−	177.853i	0.144828	−	0.250850i	0.929309	+	0.369303i	$0.120404\pi$
$710$		0			0
$711$	−205.272	−	355.542i	−0.288709	−	0.500059i
$712$		0			0
$713$			121.300i			0.170127i
$714$		0			0
$715$	13.3118			0.0186180
$716$		0			0
$717$	−47.9939	+	27.7093i	−0.0669371	+	0.0386462i
$718$		0			0
$719$	−859.329	−	496.134i	−1.19517	−	0.690033i	−0.235697	−	0.971827i	$-0.575737\pi$
$719$	−859.329	−	496.134i	−1.19517	−	0.690033i	−0.959475	+	0.281794i	$0.909071\pi$
$720$		0			0
$721$	36.5230	−	92.7993i	0.0506561	−	0.128709i
$722$		0			0
$723$	160.374	−	277.775i	0.221817	−	0.384198i
$724$		0			0
$725$	408.677	+	707.849i	0.563692	+	0.976343i
$726$		0			0
$727$		−	159.131i		−	0.218887i	−0.993993	−	0.109444i	$-0.965093\pi$
$727$		−	159.131i		−	0.218887i	0.993993	−	0.109444i	$-0.0349069\pi$
$728$		0			0
$729$	−690.565			−0.947276
$730$		0			0
$731$	−62.9656	+	36.3532i	−0.0861363	+	0.0497308i
$732$		0			0
$733$	757.187	+	437.162i	1.03300	+	0.596401i	0.917842	−	0.396946i	$-0.129930\pi$
$733$	757.187	+	437.162i	1.03300	+	0.596401i	0.115155	+	0.993347i	$0.463263\pi$
$734$		0			0
$735$	64.7761	−	19.8458i	0.0881307	−	0.0270010i
$736$		0			0
$737$	−43.7606	+	75.7955i	−0.0593766	+	0.102843i
$738$		0			0
$739$	117.975	+	204.338i	0.159641	+	0.276506i	0.934739	−	0.355335i	$-0.115633\pi$
$739$	117.975	+	204.338i	0.159641	+	0.276506i	−0.775098	+	0.631841i	$0.782300\pi$
$740$		0			0
$741$			308.815i			0.416755i
$742$		0			0
$743$	1048.29			1.41088			0.705442	−	0.708767i	$-0.250748\pi$
$743$	1048.29			1.41088			0.705442	+	0.708767i	$0.250748\pi$
$744$		0			0
$745$	−103.764	+	59.9083i	−0.139281	+	0.0804138i
$746$		0			0
$747$	−205.640	−	118.726i	−0.275288	−	0.158937i
$748$		0			0
$749$	−110.928	−	43.6578i	−0.148101	−	0.0582882i
$750$		0			0
$751$	−471.374	+	816.443i	−0.627662	+	1.08714i	0.360358	+	0.932814i	$0.382654\pi$
$751$	−471.374	+	816.443i	−0.627662	+	1.08714i	−0.988020	+	0.154328i	$0.950679\pi$
$752$		0			0
$753$	−169.934	−	294.335i	−0.225676	−	0.390883i
$754$		0			0
$755$		−	119.821i		−	0.158703i
$756$		0			0
$757$	921.968			1.21792			0.608962	−	0.793200i	$-0.291586\pi$
$757$	921.968			1.21792			0.608962	+	0.793200i	$0.291586\pi$
$758$		0			0
$759$	−71.9015	+	41.5123i	−0.0947318	+	0.0546934i
$760$		0			0
$761$	1042.33	+	601.792i	1.36969	+	0.790791i	0.990888	−	0.134687i	$-0.0430029\pi$
$761$	1042.33	+	601.792i	1.36969	+	0.790791i	0.378802	+	0.925478i	$0.376336\pi$
$762$		0			0
$763$	−203.509	+	161.976i	−0.266722	+	0.212289i
$764$		0			0
$765$	−5.26427	+	9.11798i	−0.00688140	+	0.0119189i
$766$		0			0
$767$	−377.315	−	653.529i	−0.491937	−	0.852059i
$768$		0			0
$769$		−	524.255i		−	0.681736i	−0.940111	−	0.340868i	$-0.889279\pi$
$769$		−	524.255i		−	0.681736i	0.940111	−	0.340868i	$-0.110721\pi$
$770$		0			0
$771$	−842.636			−1.09291
$772$		0			0
$773$	1301.07	−	751.173i	1.68314	−	0.971764i	0.723595	−	0.690225i	$-0.242489\pi$
$773$	1301.07	−	751.173i	1.68314	−	0.971764i	0.959550	−	0.281539i	$-0.0908448\pi$
$774$		0			0
$775$	85.4169	+	49.3154i	0.110215	+	0.0636328i
$776$		0			0
$777$	−813.614	+	121.840i	−1.04712	+	0.156809i
$778$		0			0
$779$	76.6888	−	132.829i	0.0984452	−	0.170512i
$780$		0			0
$781$	−27.3037	−	47.2915i	−0.0349600	−	0.0605524i
$782$		0			0
$783$		−	963.275i		−	1.23024i
$784$		0			0
$785$	77.2519			0.0984100
$786$		0			0
$787$	−1297.64	+	749.191i	−1.64884	+	0.951958i	−0.671304	+	0.741182i	$0.734266\pi$
$787$	−1297.64	+	749.191i	−1.64884	+	0.951958i	−0.977534	+	0.210776i	$0.932401\pi$
$788$		0			0
$789$	236.588	+	136.594i	0.299858	+	0.173123i
$790$		0			0
$791$	−102.268	−	682.912i	−0.129289	−	0.863353i
$792$		0			0
$793$	−209.375	+	362.648i	−0.264029	+	0.457311i
$794$		0			0
$795$	−17.7173	−	30.6873i	−0.0222860	−	0.0386004i
$796$		0			0
$797$			389.701i			0.488960i	0.969654	+	0.244480i	$0.0786173\pi$
$797$			389.701i			0.488960i	−0.969654	+	0.244480i	$0.921383\pi$
$798$		0			0
$799$	74.4395			0.0931659
$800$		0			0
$801$	195.005	−	112.586i	0.243452	−	0.140557i
$802$		0			0
$803$	−99.7008	−	57.5623i	−0.124160	−	0.0716840i
$804$		0			0
$805$	82.3407	+	103.454i	0.102287	+	0.128514i
$806$		0			0
$807$	129.865	−	224.933i	0.160924	−	0.278728i
$808$		0			0
$809$	−655.891	−	1136.04i	−0.810743	−	1.40425i	−0.912345	−	0.409423i	$-0.865730\pi$
$809$	−655.891	−	1136.04i	−0.810743	−	1.40425i	0.101601	−	0.994825i	$-0.467603\pi$
$810$		0			0
$811$		−	58.7187i		−	0.0724029i	−0.999345	−	0.0362014i	$-0.988474\pi$
$811$		−	58.7187i		−	0.0724029i	0.999345	−	0.0362014i	$-0.0115258\pi$
$812$		0			0
$813$	−882.435			−1.08541
$814$		0			0
$815$	42.7258	−	24.6678i	0.0524243	−	0.0302672i
$816$		0			0
$817$	−123.562	−	71.3386i	−0.151239	−	0.0873177i
$818$		0			0
$819$	180.711	−	459.158i	0.220648	−	0.560633i
$820$		0			0
$821$	397.231	−	688.024i	0.483838	−	0.838032i	−0.515990	−	0.856595i	$-0.672576\pi$
$821$	397.231	−	688.024i	0.483838	−	0.838032i	0.999828	+	0.0185627i	$0.00590903\pi$
$822$		0			0
$823$	−461.687	−	799.666i	−0.560981	−	0.971648i	−0.997411	−	0.0719094i	$-0.977091\pi$
$823$	−461.687	−	799.666i	−0.560981	−	0.971648i	0.436430	−	0.899738i	$-0.356243\pi$
$824$		0			0
$825$			67.5085i			0.0818285i
$826$		0			0
$827$	−616.087			−0.744967			−0.372483	−	0.928039i	$-0.621494\pi$
$827$	−616.087			−0.744967			−0.372483	+	0.928039i	$0.621494\pi$
$828$		0			0
$829$	−119.347	+	68.9050i	−0.143965	+	0.0831182i	−0.570252	−	0.821470i	$-0.693155\pi$
$829$	−119.347	+	68.9050i	−0.143965	+	0.0831182i	0.426287	+	0.904588i	$0.359821\pi$
$830$		0			0
$831$	−37.0777	−	21.4068i	−0.0446182	−	0.0257603i
$832$		0			0
$833$	137.699	−	147.838i	0.165304	−	0.177477i
$834$		0			0
$835$	60.9331	−	105.539i	0.0729738	−	0.126394i
$836$		0			0
$837$	−58.1197	−	100.666i	−0.0694381	−	0.120270i
$838$		0			0
$839$			971.400i			1.15781i	0.815396	+	0.578903i	$0.196519\pi$
$839$			971.400i			1.15781i	−0.815396	+	0.578903i	$0.803481\pi$
$840$		0			0
$841$	262.006			0.311541
$842$		0			0
$843$	718.526	−	414.841i	0.852344	−	0.492101i
$844$		0			0
$845$	69.0689	+	39.8770i	0.0817384	+	0.0471917i
$846$		0			0
$847$	−778.170	−	306.264i	−0.918736	−	0.361587i
$848$		0			0
$849$	214.766	−	371.986i	0.252964	−	0.438146i
$850$		0			0
$851$	−802.808	−	1390.50i	−0.943370	−	1.63397i
$852$		0			0
$853$		−	1327.35i		−	1.55610i	−0.628202	−	0.778050i	$-0.716209\pi$
$853$		−	1327.35i		−	1.55610i	0.628202	−	0.778050i	$-0.283791\pi$
$854$		0			0
$855$	−20.6609			−0.0241648
$856$		0			0
$857$	−845.824	+	488.337i	−0.986959	+	0.569821i	−0.904364	−	0.426762i	$-0.859654\pi$
$857$	−845.824	+	488.337i	−0.986959	+	0.569821i	−0.0825950	+	0.996583i	$0.526321\pi$
$858$		0			0
$859$	1095.78	+	632.646i	1.27564	+	0.736492i	0.976044	−	0.217574i	$-0.0698143\pi$
$859$	1095.78	+	632.646i	1.27564	+	0.736492i	0.299597	+	0.954066i	$0.403148\pi$
$860$		0			0
$861$	230.017	−	183.075i	0.267151	−	0.212630i
$862$		0			0
$863$	−170.310	+	294.986i	−0.197347	+	0.341814i	−0.947667	−	0.319260i	$-0.896566\pi$
$863$	−170.310	+	294.986i	−0.197347	+	0.341814i	0.750321	+	0.661074i	$0.229899\pi$
$864$		0			0
$865$	−68.7009	−	118.993i	−0.0794230	−	0.137565i
$866$		0			0
$867$		−	37.6628i		−	0.0434404i
$868$		0			0
$869$	124.230			0.142957
$870$		0			0
$871$	−1054.63	+	608.889i	−1.21082	+	0.699069i
$872$		0			0
$873$	−240.236	−	138.700i	−0.275184	−	0.158877i
$874$		0			0
$875$	214.335	−	32.0971i	0.244954	−	0.0366824i
$876$		0			0
$877$	450.172	−	779.721i	0.513309	−	0.889078i	−0.486571	−	0.873641i	$-0.661753\pi$
$877$	450.172	−	779.721i	0.513309	−	0.889078i	0.999881	−	0.0154372i	$-0.00491400\pi$
$878$		0			0
$879$	−542.280	−	939.257i	−0.616928	−	1.06855i
$880$		0			0
$881$		−	423.593i		−	0.480809i	−0.970673	−	0.240404i	$-0.922720\pi$
$881$		−	423.593i		−	0.480809i	0.970673	−	0.240404i	$-0.0772801\pi$
$882$		0			0
$883$	1511.11			1.71134			0.855668	−	0.517526i	$-0.173147\pi$
$883$	1511.11			1.71134			0.855668	+	0.517526i	$0.173147\pi$
$884$		0			0
$885$	−52.4489	+	30.2814i	−0.0592643	+	0.0342163i
$886$		0			0
$887$	906.365	+	523.290i	1.02183	+	0.589955i	0.914634	−	0.404283i	$-0.132479\pi$
$887$	906.365	+	523.290i	1.02183	+	0.589955i	0.107198	+	0.994238i	$0.465812\pi$
$888$		0			0
$889$	−242.256	−	1617.71i	−0.272504	−	1.81970i
$890$		0			0
$891$	16.9826	−	29.4146i	0.0190601	−	0.0330131i
$892$		0			0
$893$	73.0391	+	126.507i	0.0817907	+	0.141666i
$894$		0			0
$895$		−	186.259i		−	0.208111i
$896$		0			0
$897$	−1155.21			−1.28786
$898$		0			0
$899$	115.269	−	66.5504i	0.128219	−	0.0740272i
$900$		0			0
$901$	−91.5131	−	52.8351i	−0.101568	−	0.0586405i
$902$		0			0
$903$	−170.302	−	213.970i	−0.188596	−	0.236955i
$904$		0			0
$905$	44.7058	−	77.4327i	0.0493987	−	0.0855610i
$906$		0			0
$907$	338.511	+	586.317i	0.373220	+	0.646436i	0.990059	−	0.140653i	$-0.0449203\pi$
$907$	338.511	+	586.317i	0.373220	+	0.646436i	−0.616839	+	0.787089i	$0.711587\pi$
$908$		0			0
$909$			623.379i			0.685785i
$910$		0			0
$911$	6.67095			0.00732267			0.00366133	−	0.999993i	$-0.498835\pi$
$911$	6.67095			0.00732267			0.00366133	+	0.999993i	$0.498835\pi$
$912$		0			0
$913$	62.2262	−	35.9263i	0.0681557	−	0.0393497i
$914$		0			0
$915$	29.1043	+	16.8034i	0.0318080	+	0.0183643i
$916$		0			0
$917$	−345.566	+	878.029i	−0.376844	+	0.957501i
$918$		0			0
$919$	183.534	−	317.890i	0.199711	−	0.345909i	−0.748724	−	0.662882i	$-0.769333\pi$
$919$	183.534	−	317.890i	0.199711	−	0.345909i	0.948435	+	0.316973i	$0.102666\pi$
$920$		0			0
$921$	−180.509	−	312.650i	−0.195992	−	0.339468i
$922$		0			0
$923$		−	759.814i		−	0.823201i
$924$		0			0
$925$	−1305.55			−1.41140
$926$		0			0
$927$	−50.4843	+	29.1471i	−0.0544598	+	0.0314424i
$928$		0			0
$929$	−427.815	−	246.999i	−0.460511	−	0.265876i	0.251748	−	0.967793i	$-0.418995\pi$
$929$	−427.815	−	246.999i	−0.460511	−	0.265876i	−0.712259	+	0.701916i	$0.752328\pi$
$930$		0			0
$931$	386.354	+	88.9570i	0.414988	+	0.0955500i
$932$		0			0
$933$	−444.656	+	770.166i	−0.476587	+	0.825473i
$934$		0			0
$935$	−1.59296	−	2.75908i	−0.00170370	−	0.00295089i
$936$		0			0
$937$		−	261.731i		−	0.279328i	−0.990199	−	0.139664i	$-0.955398\pi$
$937$		−	261.731i		−	0.279328i	0.990199	−	0.139664i	$-0.0446023\pi$
$938$		0			0
$939$	−731.433			−0.778949
$940$		0			0
$941$	643.565	−	371.563i	0.683916	−	0.394859i	−0.117413	−	0.993083i	$-0.537460\pi$
$941$	643.565	−	371.563i	0.683916	−	0.394859i	0.801329	+	0.598224i	$0.204127\pi$
$942$		0			0
$943$	496.885	+	286.877i	0.526920	+	0.304217i
$944$		0			0
$945$	−117.903	−	46.4030i	−0.124765	−	0.0491037i
$946$		0			0
$947$	−846.095	+	1465.48i	−0.893448	+	1.54750i	−0.0577341	+	0.998332i	$0.518388\pi$
$947$	−846.095	+	1465.48i	−0.893448	+	1.54750i	−0.835714	+	0.549165i	$0.814946\pi$
$948$		0			0
$949$	−800.928	−	1387.25i	−0.843970	−	1.46180i
$950$		0			0
$951$		−	647.929i		−	0.681313i
$952$		0			0
$953$	−1620.20			−1.70010			−0.850051	−	0.526700i	$-0.823429\pi$
$953$	−1620.20			−1.70010			−0.850051	+	0.526700i	$0.823429\pi$
$954$		0			0
$955$	53.5953	−	30.9432i	0.0561207	−	0.0324013i
$956$		0			0
$957$	78.8964	+	45.5508i	0.0824414	+	0.0475975i
$958$		0			0
$959$	737.233	−	586.776i	0.768752	−	0.611863i
$960$		0			0
$961$	−472.469	+	818.341i	−0.491643	+	0.851551i
$962$		0			0
$963$	34.8410	+	60.3464i	0.0361797	+	0.0626650i
$964$		0			0
$965$			133.657i			0.138504i
$966$		0			0
$967$	623.072			0.644335			0.322167	−	0.946683i	$-0.395589\pi$
$967$	623.072			0.644335			0.322167	+	0.946683i	$0.395589\pi$
$968$		0			0
$969$	64.0067	−	36.9543i	0.0660544	−	0.0381365i
$970$		0			0
$971$	−365.911	−	211.259i	−0.376840	−	0.217569i	0.299603	−	0.954064i	$-0.403146\pi$
$971$	−365.911	−	211.259i	−0.376840	−	0.217569i	−0.676442	+	0.736496i	$0.736479\pi$
$972$		0			0
$973$	1857.44	−	278.156i	1.90898	−	0.285874i
$974$		0			0
$975$	−469.660	+	813.475i	−0.481703	+	0.834334i
$976$		0			0
$977$	31.7155	+	54.9329i	0.0324621	+	0.0562261i	0.881800	−	0.471623i	$-0.156332\pi$
$977$	31.7155	+	54.9329i	0.0324621	+	0.0562261i	−0.849338	+	0.527850i	$0.822998\pi$
$978$		0			0
$979$			68.1368i			0.0695984i
$980$		0			0
$981$	152.037			0.154982
$982$		0			0
$983$	−530.845	+	306.483i	−0.540025	+	0.311784i	−0.745089	−	0.666965i	$-0.767593\pi$
$983$	−530.845	+	306.483i	−0.540025	+	0.311784i	0.205064	+	0.978749i	$0.434260\pi$
$984$		0			0
$985$	−140.165	−	80.9244i	−0.142300	−	0.0821567i
$986$		0			0
$987$	41.4666	+	276.902i	0.0420128	+	0.280549i
$988$		0			0
$989$	266.863	−	462.220i	0.269831	−	0.467361i
$990$		0			0
$991$	−539.330	−	934.147i	−0.544228	−	0.942631i	−0.998655	−	0.0518468i	$-0.983489\pi$
$991$	−539.330	−	934.147i	−0.544228	−	0.942631i	0.454427	−	0.890784i	$-0.349844\pi$
$992$		0			0
$993$		−	236.577i		−	0.238245i
$994$		0			0
$995$	27.0445			0.0271804
$996$		0			0
$997$	685.303	−	395.660i	0.687365	−	0.396850i	−0.115259	−	0.993335i	$-0.536770\pi$
$997$	685.303	−	395.660i	0.687365	−	0.396850i	0.802624	+	0.596485i	$0.203436\pi$
$998$		0			0
$999$	1332.49	+	769.313i	1.33382	+	0.770084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.3.s.a.341.15	✓	44
7.3	odd	6	inner	476.3.s.a.409.15	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.3.s.a.341.15	✓	44	1.1	even	1	trivial
476.3.s.a.409.15	yes	44	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	476.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.91865 - 1.10773i) q^{3} +(-0.540464 - 0.312037i) q^{5} +(-1.03671 - 6.92281i) q^{7} +(-2.04587 + 3.54354i) q^{9} +O(q^{10})\)	\(q+(1.91865 - 1.10773i) q^{3} +(-0.540464 - 0.312037i) q^{5} +(-1.03671 - 6.92281i) q^{7} +(-2.04587 + 3.54354i) q^{9} +(-0.619075 - 1.07227i) q^{11} -17.2278i q^{13} -1.38261 q^{15} +(-3.57071 + 2.06155i) q^{17} +(-7.00707 - 4.04554i) q^{19} +(-9.65767 - 12.1340i) q^{21} +(15.1335 - 26.2120i) q^{23} +(-12.3053 - 21.3133i) q^{25} +29.0042i q^{27} -33.2115 q^{29} +(-3.47074 + 2.00383i) q^{31} +(-2.37557 - 1.37154i) q^{33} +(-1.59987 + 4.06502i) q^{35} +(26.5242 - 45.9412i) q^{37} +(-19.0837 - 33.0540i) q^{39} +18.9564i q^{41} +17.6339 q^{43} +(2.21143 - 1.27677i) q^{45} +(-15.6354 - 9.02712i) q^{47} +(-46.8505 + 14.3538i) q^{49} +(-4.56729 + 7.91078i) q^{51} +(12.8144 + 22.1952i) q^{53} +0.772698i q^{55} -17.9255 q^{57} +(37.9347 - 21.9016i) q^{59} +(-21.0502 - 12.1533i) q^{61} +(26.6522 + 10.4895i) q^{63} +(-5.37570 + 9.31099i) q^{65} +(-35.3435 - 61.2167i) q^{67} -67.0554i q^{69} +44.1041 q^{71} +(80.5240 - 46.4905i) q^{73} +(-47.2189 - 27.2618i) q^{75} +(-6.78132 + 5.39736i) q^{77} +(-50.1676 + 86.8928i) q^{79} +(13.7161 + 23.7569i) q^{81} +58.0322i q^{83} +2.57312 q^{85} +(-63.7212 + 36.7894i) q^{87} +(-47.6584 - 27.5156i) q^{89} +(-119.264 + 17.8601i) q^{91} +(-4.43942 + 7.68930i) q^{93} +(2.52471 + 4.37293i) q^{95} +67.7953i q^{97} +5.06618 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9}+O(q^{10}) \) 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9	\( 44 q - 6 q^{3} + 22 q^{7} + 88 q^{9} + 8 q^{11} + 16 q^{15} - 54 q^{19} - 16 q^{21} - 52 q^{23} + 150 q^{25} + 8 q^{29} + 78 q^{31} - 6 q^{33} + 10 q^{35} - 34 q^{37} - 60 q^{39} - 76 q^{43} - 72 q^{45} - 6 q^{47} - 56 q^{49} - 172 q^{53} - 64 q^{57} + 30 q^{59} + 444 q^{61} + 206 q^{63} - 54 q^{65} - 56 q^{67} + 204 q^{71} - 48 q^{73} + 132 q^{75} - 494 q^{77} - 16 q^{79} - 342 q^{81} + 594 q^{87} - 252 q^{89} + 284 q^{91} - 146 q^{93} + 148 q^{95} - 180 q^{99}+O(q^{100}) \) 44 * q - 6 * q^3 + 22 * q^7 + 88 * q^9 + 8 * q^11 + 16 * q^15 - 54 * q^19 - 16 * q^21 - 52 * q^23 + 150 * q^25 + 8 * q^29 + 78 * q^31 - 6 * q^33 + 10 * q^35 - 34 * q^37 - 60 * q^39 - 76 * q^43 - 72 * q^45 - 6 * q^47 - 56 * q^49 - 172 * q^53 - 64 * q^57 + 30 * q^59 + 444 * q^61 + 206 * q^63 - 54 * q^65 - 56 * q^67 + 204 * q^71 - 48 * q^73 + 132 * q^75 - 494 * q^77 - 16 * q^79 - 342 * q^81 + 594 * q^87 - 252 * q^89 + 284 * q^91 - 146 * q^93 + 148 * q^95 - 180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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