LMFDB - Embedded newform 459.3.i.a.152.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,3,Mod(152,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.152"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	459.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.5068441341$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			152.31
Character	$\chi$	$=$	459.152
Dual form			459.3.i.a.305.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.82816 - 1.63284i) q^{2} +(3.33234 - 5.77179i) q^{4} +(-4.76697 + 8.25663i) q^{5} +(-0.760673 + 0.439175i) q^{7} -8.70203i q^{8} +31.1348i q^{10} +(4.44606 + 7.70081i) q^{11} +(-6.16052 + 10.6703i) q^{13} +(-1.43421 + 2.48412i) q^{14} +(-0.879664 - 1.52362i) q^{16} +(-2.43582 + 16.8246i) q^{17} +15.8202 q^{19} +(31.7703 + 55.0279i) q^{20} +(25.1484 + 14.5194i) q^{22} +(14.4724 - 25.0670i) q^{23} +(-32.9479 - 57.0675i) q^{25} +40.2366i q^{26} +5.85392i q^{28} +(5.73079 + 9.92603i) q^{29} +(-25.0398 - 14.4567i) q^{31} +(25.1691 + 14.5314i) q^{32} +(20.5830 + 51.5600i) q^{34} -8.37412i q^{35} +8.23116i q^{37} +(44.7422 - 25.8319i) q^{38} +(71.8494 + 41.4823i) q^{40} +(-31.0218 + 53.7314i) q^{41} +(1.16315 + 2.01464i) q^{43} +59.2633 q^{44} -94.5248i q^{46} +(42.2981 - 24.4208i) q^{47} +(-24.1143 + 41.7671i) q^{49} +(-186.364 - 107.598i) q^{50} +(41.0580 + 71.1145i) q^{52} +3.88416i q^{53} -84.7770 q^{55} +(3.82171 + 6.61940i) q^{56} +(32.4153 + 18.7150i) q^{58} +(-41.3195 - 23.8559i) q^{59} +(51.8668 - 29.9453i) q^{61} -94.4223 q^{62} +101.947 q^{64} +(-58.7340 - 101.730i) q^{65} +(45.1498 - 78.2017i) q^{67} +(88.9910 + 70.1244i) q^{68} +(-13.6736 - 23.6834i) q^{70} -0.732287 q^{71} -37.0254i q^{73} +(13.4402 + 23.2791i) q^{74} +(52.7185 - 91.3111i) q^{76} +(-6.76400 - 3.90520i) q^{77} +(91.8886 - 53.0519i) q^{79} +16.7733 q^{80} +202.615i q^{82} +(113.589 - 65.5804i) q^{83} +(-127.303 - 100.314i) q^{85} +(6.57916 + 3.79848i) q^{86} +(67.0127 - 38.6898i) q^{88} +110.840i q^{89} -10.8222i q^{91} +(-96.4543 - 167.064i) q^{92} +(79.7506 - 138.132i) q^{94} +(-75.4145 + 130.622i) q^{95} +(-35.1889 + 20.3163i) q^{97} +157.499i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.82816	−	1.63284i	1.41408	−	0.816421i	0.418313	−	0.908303i	$-0.362622\pi$
$2$	2.82816	−	1.63284i	1.41408	−	0.816421i	0.995770	+	0.0918822i	$0.0292883\pi$
$3$		0			0
$3$		0			0
$4$	3.33234	−	5.77179i	0.833086	−	1.44295i
$5$	−4.76697	+	8.25663i	−0.953393	+	1.65133i	−0.215390	+	0.976528i	$0.569102\pi$
$5$	−4.76697	+	8.25663i	−0.953393	+	1.65133i	−0.738003	+	0.674797i	$0.764231\pi$
$6$		0			0
$7$	−0.760673	+	0.439175i	−0.108668	+	0.0627392i	−0.553349	−	0.832950i	$-0.686650\pi$
$7$	−0.760673	+	0.439175i	−0.108668	+	0.0627392i	0.444681	+	0.895689i	$0.353317\pi$
$8$		−	8.70203i		−	1.08775i
$9$		0			0
$10$			31.1348i			3.11348i
$11$	4.44606	+	7.70081i	0.404188	+	0.700074i	0.994227	−	0.107301i	$-0.0342209\pi$
$11$	4.44606	+	7.70081i	0.404188	+	0.700074i	−0.590039	+	0.807375i	$0.700888\pi$
$12$		0			0
$13$	−6.16052	+	10.6703i	−0.473886	+	0.820795i	−0.999553	−	0.0298955i	$-0.990483\pi$
$13$	−6.16052	+	10.6703i	−0.473886	+	0.820795i	0.525667	+	0.850691i	$0.323816\pi$
$14$	−1.43421	+	2.48412i	−0.102443	+	0.177437i
$15$		0			0
$16$	−0.879664	−	1.52362i	−0.0549790	−	0.0952265i
$17$	−2.43582	+	16.8246i	−0.143283	+	0.989682i
$17$	−2.43582	+	16.8246i	−0.143283	+	0.989682i
$18$		0			0
$19$	15.8202			0.832644			0.416322	−	0.909217i	$-0.363319\pi$
$19$	15.8202			0.832644			0.416322	+	0.909217i	$0.363319\pi$
$20$	31.7703	+	55.0279i	1.58852	+	2.75139i
$21$		0			0
$22$	25.1484	+	14.5194i	1.14311	+	0.659975i
$23$	14.4724	−	25.0670i	0.629236	−	1.08987i	−0.358469	−	0.933542i	$-0.616701\pi$
$23$	14.4724	−	25.0670i	0.629236	−	1.08987i	0.987705	−	0.156327i	$-0.0499655\pi$
$24$		0			0
$25$	−32.9479	−	57.0675i	−1.31792	−	2.28270i
$26$			40.2366i			1.54756i
$27$		0			0
$28$			5.85392i			0.209069i
$29$	5.73079	+	9.92603i	0.197614	+	0.342277i	0.947754	−	0.319002i	$-0.103348\pi$
$29$	5.73079	+	9.92603i	0.197614	+	0.342277i	−0.750141	+	0.661278i	$0.770014\pi$
$30$		0			0
$31$	−25.0398	−	14.4567i	−0.807736	−	0.466347i	0.0384328	−	0.999261i	$-0.487763\pi$
$31$	−25.0398	−	14.4567i	−0.807736	−	0.466347i	−0.846169	+	0.532914i	$0.821097\pi$
$32$	25.1691	+	14.5314i	0.786533	+	0.454105i
$33$		0			0
$34$	20.5830	+	51.5600i	0.605382	+	1.51647i
$35$		−	8.37412i		−	0.239261i
$36$		0			0
$37$			8.23116i			0.222464i	0.993794	+	0.111232i	$0.0354796\pi$
$37$			8.23116i			0.222464i	−0.993794	+	0.111232i	$0.964520\pi$
$38$	44.7422	−	25.8319i	1.17743	−	0.679788i
$39$		0			0
$40$	71.8494	+	41.4823i	1.79624	+	1.03706i
$41$	−31.0218	+	53.7314i	−0.756630	+	1.31052i	0.187929	+	0.982183i	$0.439822\pi$
$41$	−31.0218	+	53.7314i	−0.756630	+	1.31052i	−0.944560	+	0.328340i	$0.893511\pi$
$42$		0			0
$43$	1.16315	+	2.01464i	0.0270500	+	0.0468520i	0.879234	−	0.476391i	$-0.158055\pi$
$43$	1.16315	+	2.01464i	0.0270500	+	0.0468520i	−0.852184	+	0.523243i	$0.824722\pi$
$44$	59.2633			1.34689
$45$		0			0
$46$		−	94.5248i		−	2.05489i
$47$	42.2981	−	24.4208i	0.899959	−	0.519592i	0.0227721	−	0.999741i	$-0.492751\pi$
$47$	42.2981	−	24.4208i	0.899959	−	0.519592i	0.877187	+	0.480149i	$0.159417\pi$
$48$		0			0
$49$	−24.1143	+	41.7671i	−0.492128	+	0.852390i
$50$	−186.364	−	107.598i	−3.72729	−	2.15195i
$51$		0			0
$52$	41.0580	+	71.1145i	0.789576	+	1.36759i
$53$			3.88416i			0.0732859i	0.999328	+	0.0366430i	$0.0116664\pi$
$53$			3.88416i			0.0732859i	−0.999328	+	0.0366430i	$0.988334\pi$
$54$		0			0
$55$	−84.7770			−1.54140
$56$	3.82171	+	6.61940i	0.0682448	+	0.118204i
$57$		0			0
$58$	32.4153	+	18.7150i	0.558884	+	0.322672i
$59$	−41.3195	−	23.8559i	−0.700331	−	0.404336i	0.107139	−	0.994244i	$-0.465831\pi$
$59$	−41.3195	−	23.8559i	−0.700331	−	0.404336i	−0.807471	+	0.589908i	$0.799164\pi$
$60$		0			0
$61$	51.8668	−	29.9453i	0.850276	−	0.490907i	−0.0104682	−	0.999945i	$-0.503332\pi$
$61$	51.8668	−	29.9453i	0.850276	−	0.490907i	0.860744	+	0.509038i	$0.169999\pi$
$62$	−94.4223			−1.52294
$63$		0			0
$64$	101.947			1.59292
$65$	−58.7340	−	101.730i	−0.903600	−	1.56508i
$66$		0			0
$67$	45.1498	−	78.2017i	0.673877	−	1.16719i	−0.302919	−	0.953016i	$-0.597961\pi$
$67$	45.1498	−	78.2017i	0.673877	−	1.16719i	0.976796	−	0.214173i	$-0.0687056\pi$
$68$	88.9910	+	70.1244i	1.30869	+	1.03124i
$69$		0			0
$70$	−13.6736	−	23.6834i	−0.195337	−	0.338334i
$71$	−0.732287			−0.0103139			−0.00515695	−	0.999987i	$-0.501642\pi$
$71$	−0.732287			−0.0103139			−0.00515695	+	0.999987i	$0.501642\pi$
$72$		0			0
$73$		−	37.0254i		−	0.507197i	−0.967310	−	0.253598i	$-0.918386\pi$
$73$		−	37.0254i		−	0.507197i	0.967310	−	0.253598i	$-0.0816142\pi$
$74$	13.4402	+	23.2791i	0.181624	+	0.314582i
$75$		0			0
$76$	52.7185	−	91.3111i	0.693664	−	1.20146i
$77$	−6.76400	−	3.90520i	−0.0878442	−	0.0507168i
$78$		0			0
$79$	91.8886	−	53.0519i	1.16315	−	0.671543i	0.211090	−	0.977467i	$-0.432299\pi$
$79$	91.8886	−	53.0519i	1.16315	−	0.671543i	0.952056	+	0.305924i	$0.0989652\pi$
$80$	16.7733			0.209666
$81$		0			0
$82$			202.615i			2.47092i
$83$	113.589	−	65.5804i	1.36854	−	0.790126i	0.377796	−	0.925889i	$-0.376682\pi$
$83$	113.589	−	65.5804i	1.36854	−	0.790126i	0.990741	+	0.135763i	$0.0433486\pi$
$84$		0			0
$85$	−127.303	−	100.314i	−1.49768	−	1.18016i
$86$	6.57916	+	3.79848i	0.0765019	+	0.0441684i
$87$		0			0
$88$	67.0127	−	38.6898i	0.761508	−	0.439657i
$89$			110.840i			1.24539i	0.782465	+	0.622694i	$0.213962\pi$
$89$			110.840i			1.24539i	−0.782465	+	0.622694i	$0.786038\pi$
$90$		0			0
$91$		−	10.8222i		−	0.118925i
$92$	−96.4543	−	167.064i	−1.04842	−	1.81591i
$93$		0			0
$94$	79.7506	−	138.132i	0.848411	−	1.46949i
$95$	−75.4145	+	130.622i	−0.793837	+	1.37497i
$96$		0			0
$97$	−35.1889	+	20.3163i	−0.362772	+	0.209447i	−0.670296	−	0.742094i	$-0.733833\pi$
$97$	−35.1889	+	20.3163i	−0.362772	+	0.209447i	0.307524	+	0.951540i	$0.400500\pi$
$98$			157.499i			1.60713i
$99$		0			0
$100$	−439.175			−4.39175
$101$	−49.3626	+	28.4995i	−0.488739	+	0.282173i	−0.724051	−	0.689746i	$-0.757722\pi$
$101$	−49.3626	+	28.4995i	−0.488739	+	0.282173i	0.235312	+	0.971920i	$0.424389\pi$
$102$		0			0
$103$	−69.8551	+	120.993i	−0.678205	+	1.17469i	0.297316	+	0.954779i	$0.403909\pi$
$103$	−69.8551	+	120.993i	−0.678205	+	1.17469i	−0.975521	+	0.219907i	$0.929425\pi$
$104$	92.8536	+	53.6091i	0.892823	+	0.515472i
$105$		0			0
$106$	6.34221	+	10.9850i	0.0598322	+	0.103632i
$107$	−80.1687			−0.749240			−0.374620	−	0.927178i	$-0.622227\pi$
$107$	−80.1687			−0.749240			−0.374620	+	0.927178i	$0.622227\pi$
$108$		0			0
$109$		−	116.611i		−	1.06982i	−0.844908	−	0.534911i	$-0.820345\pi$
$109$		−	116.611i		−	1.06982i	0.844908	−	0.534911i	$-0.179655\pi$
$110$	−239.763	+	138.427i	−2.17967	+	1.25843i
$111$		0			0
$112$	1.33827	+	0.772652i	0.0119489	+	0.00689868i
$113$	−19.2459	+	33.3349i	−0.170318	+	0.294999i	−0.938531	−	0.345195i	$-0.887813\pi$
$113$	−19.2459	+	33.3349i	−0.170318	+	0.294999i	0.768213	+	0.640194i	$0.221146\pi$
$114$		0			0
$115$	137.979	+	238.987i	1.19982	+	2.07815i
$116$	76.3879			0.658517
$117$		0			0
$118$	−155.811			−1.32044
$119$	−5.53607	−	13.8678i	−0.0465216	−	0.116536i
$120$		0			0
$121$	20.9650	−	36.3125i	0.173265	−	0.300103i
$122$	97.7919	−	169.381i	0.801573	−	1.38837i
$123$		0			0
$124$	−166.883	+	96.3498i	−1.34583	+	0.777014i
$125$	389.898			3.11919
$126$		0			0
$127$	180.664			1.42255			0.711274	−	0.702914i	$-0.248118\pi$
$127$	180.664			1.42255			0.711274	+	0.702914i	$0.248118\pi$
$128$	187.647	−	108.338i	1.46599	−	0.846389i
$129$		0			0
$130$	−332.219	−	191.807i	−2.55553	−	1.47544i
$131$	59.0158	−	102.218i	0.450502	−	0.780293i	−0.547915	−	0.836534i	$-0.684578\pi$
$131$	59.0158	−	102.218i	0.450502	−	0.780293i	0.998417	+	0.0562412i	$0.0179116\pi$
$132$		0			0
$133$	−12.0340	+	6.94785i	−0.0904814	+	0.0522394i
$134$		−	294.890i		−	2.20067i
$135$		0			0
$136$	146.408	+	21.1966i	1.07653	+	0.155857i
$137$	−151.448	+	87.4388i	−1.10546	+	0.638239i	−0.937651	−	0.347579i	$-0.887004\pi$
$137$	−151.448	+	87.4388i	−1.10546	+	0.638239i	−0.167813	+	0.985819i	$0.553670\pi$
$138$		0			0
$139$	156.687	+	90.4634i	1.12725	+	0.650816i	0.943241	−	0.332110i	$-0.107760\pi$
$139$	156.687	+	90.4634i	1.12725	+	0.650816i	0.184005	+	0.982925i	$0.441094\pi$
$140$	−48.3337	−	27.9055i	−0.345240	−	0.199325i
$141$		0			0
$142$	−2.07103	+	1.19571i	−0.0145847	+	0.00842048i
$143$	−109.560			−0.766156
$144$		0			0
$145$	−109.274			−0.753614
$146$	−60.4566	−	104.714i	−0.414086	−	0.717218i
$147$		0			0
$148$	47.5085	+	27.4291i	0.321004	+	0.185331i
$149$	−7.92913	−	4.57788i	−0.0532156	−	0.0307241i	0.473156	−	0.880979i	$-0.343115\pi$
$149$	−7.92913	−	4.57788i	−0.0532156	−	0.0307241i	−0.526372	+	0.850255i	$0.676448\pi$
$150$		0			0
$151$	3.49995	+	6.06209i	0.0231785	+	0.0401463i	0.877382	−	0.479793i	$-0.159288\pi$
$151$	3.49995	+	6.06209i	0.0231785	+	0.0401463i	−0.854203	+	0.519939i	$0.825955\pi$
$152$		−	137.668i		−	0.905712i
$153$		0			0
$154$	−25.5063			−0.165625
$155$	238.728	−	137.830i	1.54018	−	0.889224i
$156$		0			0
$157$	−1.20198	+	2.08189i	−0.00765591	+	0.0132604i	−0.869828	−	0.493355i	$-0.835770\pi$
$157$	−1.20198	+	2.08189i	−0.00765591	+	0.0132604i	0.862172	+	0.506616i	$0.169104\pi$
$158$	173.251	−	300.079i	1.09652	−	1.89923i
$159$		0			0
$160$	−239.960	+	138.541i	−1.49975	+	0.865881i
$161$			25.4237i			0.157911i
$162$		0			0
$163$		−	89.2950i		−	0.547822i	−0.961755	−	0.273911i	$-0.911683\pi$
$163$		−	89.2950i		−	0.547822i	0.961755	−	0.273911i	$-0.0883174\pi$
$164$	206.751	+	358.103i	1.26068	+	2.18356i
$165$		0			0
$166$	214.165	−	370.945i	1.29015	−	2.23461i
$167$	−48.0053	+	83.1476i	−0.287457	+	0.497890i	−0.973202	−	0.229952i	$-0.926143\pi$
$167$	−48.0053	+	83.1476i	−0.287457	+	0.497890i	0.685745	+	0.727842i	$0.259476\pi$
$168$		0			0
$169$	8.59597	+	14.8886i	0.0508637	+	0.0880985i
$170$	−523.830	−	75.8387i	−3.08135	−	0.446110i
$171$		0			0
$172$	15.5041			0.0901400
$173$	106.189	+	183.925i	0.613811	+	1.06315i	0.990592	+	0.136850i	$0.0436977\pi$
$173$	106.189	+	183.925i	0.613811	+	1.06315i	−0.376781	+	0.926303i	$0.622969\pi$
$174$		0			0
$175$	50.1252	+	28.9398i	0.286430	+	0.165370i
$176$	7.82209	−	13.5483i	0.0444437	−	0.0769787i
$177$		0			0
$178$	180.983	+	313.473i	1.01676	+	1.76108i
$179$			89.6762i			0.500984i	0.968119	+	0.250492i	$0.0805924\pi$
$179$			89.6762i			0.500984i	−0.968119	+	0.250492i	$0.919408\pi$
$180$		0			0
$181$		−	137.630i		−	0.760387i	−0.924907	−	0.380193i	$-0.875857\pi$
$181$		−	137.630i		−	0.760387i	0.924907	−	0.380193i	$-0.124143\pi$
$182$	−17.6709	−	30.6069i	−0.0970929	−	0.168170i
$183$		0			0
$184$	−218.134	−	125.940i	−1.18551	−	0.684454i
$185$	−67.9616	−	39.2377i	−0.367360	−	0.212095i
$186$		0			0
$187$	−140.393	+	56.0454i	−0.750764	+	0.299708i
$188$		−	325.514i		−	1.73146i
$189$		0			0
$190$			492.560i			2.59242i
$191$	−23.3318	+	13.4706i	−0.122156	+	0.0705267i	−0.559833	−	0.828606i	$-0.689135\pi$
$191$	−23.3318	+	13.4706i	−0.122156	+	0.0705267i	0.437677	+	0.899132i	$0.355801\pi$
$192$		0			0
$193$	305.903	+	176.613i	1.58499	+	0.915094i	0.994115	+	0.108331i	$0.0345508\pi$
$193$	305.903	+	176.613i	1.58499	+	0.915094i	0.590875	+	0.806763i	$0.298783\pi$
$194$	−66.3467	+	114.916i	−0.341993	+	0.592350i
$195$		0			0
$196$	160.714	+	278.365i	0.819969	+	1.42023i
$197$	72.8379			0.369735			0.184868	−	0.982763i	$-0.440814\pi$
$197$	72.8379			0.369735			0.184868	+	0.982763i	$0.440814\pi$
$198$		0			0
$199$		−	179.774i		−	0.903389i	−0.892173	−	0.451695i	$-0.850820\pi$
$199$		−	179.774i		−	0.903389i	0.892173	−	0.451695i	$-0.149180\pi$
$200$	−496.603	+	286.714i	−2.48302	+	1.43357i
$201$		0			0
$202$	−93.0704	+	161.203i	−0.460745	+	0.798033i
$203$	−8.71852	−	5.03364i	−0.0429484	−	0.0247962i
$204$		0			0
$205$	−295.760	−	512.272i	−1.44273	−	2.49889i
$206$			456.250i			2.21480i
$207$		0			0
$208$	21.6768			0.104215
$209$	70.3378	+	121.829i	0.336545	+	0.582912i
$210$		0			0
$211$	−137.194	−	79.2092i	−0.650210	−	0.375399i	0.138327	−	0.990387i	$-0.455828\pi$
$211$	−137.194	−	79.2092i	−0.650210	−	0.375399i	−0.788537	+	0.614988i	$0.789161\pi$
$212$	22.4185	+	12.9433i	0.105748	+	0.0610535i
$213$		0			0
$214$	−226.730	+	130.903i	−1.05949	+	0.611695i
$215$	−22.1788			−0.103157
$216$		0			0
$217$	25.3961			0.117033
$218$	−190.407	−	329.794i	−0.873425	−	1.51282i
$219$		0			0
$220$	−282.506	+	489.315i	−1.28412	+	2.22416i
$221$	−164.518	−	129.639i	−0.744426	−	0.586603i
$222$		0			0
$223$	−69.7050	−	120.733i	−0.312578	−	0.541402i	0.666341	−	0.745647i	$-0.267859\pi$
$223$	−69.7050	−	120.733i	−0.312578	−	0.541402i	−0.978920	+	0.204245i	$0.934526\pi$
$224$	−25.5272			−0.113961
$225$		0			0
$226$			125.702i			0.556205i
$227$	77.3081	+	133.902i	0.340564	+	0.589875i	0.984538	−	0.175173i	$-0.0560485\pi$
$227$	77.3081	+	133.902i	0.340564	+	0.589875i	−0.643973	+	0.765048i	$0.722715\pi$
$228$		0			0
$229$	69.3263	−	120.077i	0.302735	−	0.524352i	−0.674019	−	0.738714i	$-0.735434\pi$
$229$	69.3263	−	120.077i	0.302735	−	0.524352i	0.976754	+	0.214361i	$0.0687670\pi$
$230$	780.456	+	450.596i	3.39329	+	1.95911i
$231$		0			0
$232$	86.3766	−	49.8696i	0.372313	−	0.214955i
$233$	228.603			0.981127			0.490563	−	0.871406i	$-0.336791\pi$
$233$	228.603			0.981127			0.490563	+	0.871406i	$0.336791\pi$
$234$		0			0
$235$			465.653i			1.98150i
$236$	−275.382	+	158.992i	−1.16687	+	0.673694i
$237$		0			0
$238$	−38.3008	−	30.1808i	−0.160928	−	0.126810i
$239$	0.520502	+	0.300512i	0.00217783	+	0.00125737i	0.501089	−	0.865396i	$-0.332933\pi$
$239$	0.520502	+	0.300512i	0.00217783	+	0.00125737i	−0.498911	+	0.866653i	$0.666266\pi$
$240$		0			0
$241$	160.180	−	92.4798i	0.664646	−	0.383734i	−0.129399	−	0.991593i	$-0.541305\pi$
$241$	160.180	−	92.4798i	0.664646	−	0.383734i	0.794045	+	0.607859i	$0.207971\pi$
$242$		−	136.930i		−	0.565827i
$243$		0			0
$244$		−	399.153i		−	1.63587i
$245$	−229.904	−	398.205i	−0.938382	−	1.62533i
$246$		0			0
$247$	−97.4609	+	168.807i	−0.394579	+	0.683430i
$248$	−125.803	+	217.897i	−0.507271	+	0.878619i
$249$		0			0
$250$	1102.70	−	636.642i	4.41079	−	2.54657i
$251$		−	457.444i		−	1.82249i	−0.411869	−	0.911243i	$-0.635124\pi$
$251$		−	457.444i		−	1.82249i	0.411869	−	0.911243i	$-0.364876\pi$
$252$		0			0
$253$	257.381			1.01732
$254$	510.947	−	294.995i	2.01160	−	1.16140i
$255$		0			0
$256$	149.903	−	259.640i	0.585559	−	1.01422i
$257$	220.223	+	127.146i	0.856901	+	0.494732i	0.862973	−	0.505250i	$-0.168600\pi$
$257$	220.223	+	127.146i	0.856901	+	0.494732i	−0.00607253	+	0.999982i	$0.501933\pi$
$258$		0			0
$259$	−3.61491	−	6.26122i	−0.0139572	−	0.0241746i
$260$	−782.888			−3.01111
$261$		0			0
$262$		−	385.454i		−	1.47120i
$263$	153.715	−	88.7471i	0.584466	−	0.337442i	−0.178440	−	0.983951i	$-0.557105\pi$
$263$	153.715	−	88.7471i	0.584466	−	0.337442i	0.762906	+	0.646509i	$0.223772\pi$
$264$		0			0
$265$	−32.0700	−	18.5156i	−0.121019	−	0.0698703i
$266$	−22.6895	+	39.2993i	−0.0852987	+	0.147742i
$267$		0			0
$268$	−300.909	−	521.190i	−1.12280	−	1.94474i
$269$	82.9631			0.308413			0.154206	−	0.988039i	$-0.450718\pi$
$269$	82.9631			0.308413			0.154206	+	0.988039i	$0.450718\pi$
$270$		0			0
$271$	127.621			0.470926			0.235463	−	0.971883i	$-0.424339\pi$
$271$	127.621			0.470926			0.235463	+	0.971883i	$0.424339\pi$
$272$	27.7770	−	11.0887i	0.102121	−	0.0407674i
$273$		0			0
$274$	−285.547	+	494.583i	−1.04214	+	1.80505i
$275$	292.977	−	507.452i	1.06537	−	1.84528i
$276$		0			0
$277$	−239.752	+	138.421i	−0.865529	+	0.499714i	−0.865860	−	0.500286i	$-0.833228\pi$
$277$	−239.752	+	138.421i	−0.865529	+	0.499714i	0.000330781		1.00000i	$0.499895\pi$
$278$	590.849			2.12536
$279$		0			0
$280$	−72.8719			−0.260257
$281$	−395.521	+	228.354i	−1.40755	+	0.812648i	−0.995151	−	0.0983557i	$-0.968642\pi$
$281$	−395.521	+	228.354i	−1.40755	+	0.812648i	−0.412397	+	0.911004i	$0.635308\pi$
$282$		0			0
$283$	162.926	+	94.0654i	0.575710	+	0.332387i	0.759427	−	0.650593i	$-0.225479\pi$
$283$	162.926	+	94.0654i	0.575710	+	0.332387i	−0.183716	+	0.982979i	$0.558813\pi$
$284$	−2.44023	+	4.22661i	−0.00859237	+	0.0148824i
$285$		0			0
$286$	−309.855	+	178.895i	−1.08341	+	0.625506i
$287$		−	54.4960i		−	0.189882i
$288$		0			0
$289$	−277.134	−	81.9633i	−0.958940	−	0.283610i
$290$	−309.045	+	178.427i	−1.06567	+	0.615266i
$291$		0			0
$292$	−213.703	−	123.381i	−0.731858	−	0.422539i
$293$	−468.026	−	270.215i	−1.59736	−	0.922235i	−0.991994	−	0.126287i	$-0.959694\pi$
$293$	−468.026	−	270.215i	−1.59736	−	0.922235i	−0.605365	−	0.795948i	$-0.706973\pi$
$294$		0			0
$295$	393.938	−	227.440i	1.33538	−	0.770983i
$296$	71.6278			0.241986
$297$		0			0
$298$	−29.8998			−0.100335
$299$	178.315	+	308.851i	0.596373	+	1.03295i
$300$		0			0
$301$	−1.76955	−	1.02165i	−0.00587892	−	0.00339419i
$302$	19.7969	+	11.4297i	0.0655526	+	0.0378468i
$303$		0			0
$304$	−13.9165	−	24.1041i	−0.0457780	−	0.0792898i
$305$			570.993i			1.87211i
$306$		0			0
$307$	−75.1841			−0.244899			−0.122450	−	0.992475i	$-0.539075\pi$
$307$	−75.1841			−0.244899			−0.122450	+	0.992475i	$0.539075\pi$
$308$	−45.0800	+	26.0269i	−0.146363	+	0.0845030i
$309$		0			0
$310$	450.108	−	779.610i	1.45196	−	2.51487i
$311$	161.009	−	278.877i	0.517715	−	0.896709i	−0.482073	−	0.876131i	$-0.660116\pi$
$311$	161.009	−	278.877i	0.517715	−	0.896709i	0.999788	−	0.0205782i	$-0.00655069\pi$
$312$		0			0
$313$	372.141	−	214.856i	1.18895	−	0.686441i	0.230882	−	0.972982i	$-0.425839\pi$
$313$	372.141	−	214.856i	1.18895	−	0.686441i	0.958068	+	0.286541i	$0.0925055\pi$
$314$			7.85056i			0.0250018i
$315$		0			0
$316$		−	707.149i		−	2.23781i
$317$	−176.843	−	306.301i	−0.557865	−	0.966251i	−0.997674	−	0.0681595i	$-0.978287\pi$
$317$	−176.843	−	306.301i	−0.557865	−	0.966251i	0.439809	−	0.898091i	$-0.355046\pi$
$318$		0			0
$319$	−50.9590	+	88.2635i	−0.159746	+	0.276688i
$320$	−485.978	+	841.738i	−1.51868	+	2.63043i
$321$		0			0
$322$	41.5129	+	71.9024i	0.128922	+	0.223299i
$323$	−38.5352	+	266.169i	−0.119304	+	0.824053i
$324$		0			0
$325$	811.906			2.49817
$326$	−145.805	−	252.541i	−0.447253	−	0.774666i
$327$		0			0
$328$	467.573	+	269.953i	1.42553	+	0.823028i
$329$	−21.4500	+	37.1525i	−0.0651975	+	0.112925i
$330$		0			0
$331$	−29.2504	−	50.6631i	−0.0883697	−	0.153061i	0.818452	−	0.574574i	$-0.194832\pi$
$331$	−29.2504	−	50.6631i	−0.0883697	−	0.153061i	−0.906822	+	0.421513i	$0.861499\pi$
$332$		−	874.146i		−	2.63297i
$333$		0			0
$334$			313.540i			0.938743i
$335$	430.455	+	745.570i	1.28494	+	2.22558i
$336$		0			0
$337$	64.0122	+	36.9575i	0.189947	+	0.109666i	0.591958	−	0.805969i	$-0.298355\pi$
$337$	64.0122	+	36.9575i	0.189947	+	0.109666i	−0.402011	+	0.915635i	$0.631689\pi$
$338$	48.6216	+	28.0717i	0.143851	+	0.0830524i
$339$		0			0
$340$	−1003.21	+	400.485i	−2.95061	+	1.17790i
$341$		−	257.103i		−	0.753967i
$342$		0			0
$343$		−	85.4006i		−	0.248981i
$344$	17.5314	−	10.1218i	0.0509635	−	0.0294238i
$345$		0			0
$346$	600.642	+	346.781i	1.73596	+	1.00226i
$347$	−230.091	+	398.529i	−0.663086	+	1.14850i	0.316714	+	0.948521i	$0.397420\pi$
$347$	−230.091	+	398.529i	−0.663086	+	1.14850i	−0.979800	+	0.199978i	$0.935913\pi$
$348$		0			0
$349$	81.1272	+	140.517i	0.232456	+	0.402626i	0.958530	−	0.284990i	$-0.0919904\pi$
$349$	81.1272	+	140.517i	0.232456	+	0.402626i	−0.726074	+	0.687616i	$0.758657\pi$
$350$	189.016			0.540047
$351$		0			0
$352$			258.429i			0.734175i
$353$	143.865	−	83.0607i	0.407550	−	0.235299i	−0.282186	−	0.959360i	$-0.591060\pi$
$353$	143.865	−	83.0607i	0.407550	−	0.235299i	0.689737	+	0.724060i	$0.257726\pi$
$354$		0			0
$355$	3.49079	−	6.04622i	0.00983320	−	0.0170316i
$356$	639.743	+	369.356i	1.79703	+	1.03752i
$357$		0			0
$358$	146.427	+	253.619i	0.409014	+	0.708433i
$359$		−	273.618i		−	0.762166i	−0.924541	−	0.381083i	$-0.875551\pi$
$359$		−	273.618i		−	0.762166i	0.924541	−	0.381083i	$-0.124449\pi$
$360$		0			0
$361$	−110.720			−0.306704
$362$	−224.728	−	389.240i	−0.620796	−	1.07525i
$363$		0			0
$364$	−62.4633	−	36.0632i	−0.171603	−	0.0990748i
$365$	305.705	+	176.499i	0.837547	+	0.483558i
$366$		0			0
$367$	−444.098	+	256.400i	−1.21008	+	0.698638i	−0.962776	−	0.270301i	$-0.912877\pi$
$367$	−444.098	+	256.400i	−1.21008	+	0.698638i	−0.247301	+	0.968939i	$0.579544\pi$
$368$	−50.9235			−0.138379
$369$		0			0
$370$	−256.276			−0.692636
$371$	−1.70582	−	2.95457i	−0.00459790	−	0.00796380i
$372$		0			0
$373$	−6.62533	+	11.4754i	−0.0177623	+	0.0307652i	−0.874770	−	0.484539i	$-0.838988\pi$
$373$	−6.62533	+	11.4754i	−0.0177623	+	0.0307652i	0.857008	+	0.515304i	$0.172321\pi$
$374$	−305.541	+	387.745i	−0.816953	+	1.03675i
$375$		0			0
$376$	−212.511	−	368.079i	−0.565188	−	0.978934i
$377$	−141.219			−0.374585
$378$		0			0
$379$			193.185i			0.509723i	0.966978	+	0.254862i	$0.0820299\pi$
$379$			193.185i			0.509723i	−0.966978	+	0.254862i	$0.917970\pi$
$380$	502.615	+	870.554i	1.32267	+	2.29093i
$381$		0			0
$382$	−43.9907	+	76.1941i	−0.115159	+	0.199461i
$383$	−513.258	−	296.330i	−1.34010	−	0.773706i	−0.353277	−	0.935519i	$-0.614933\pi$
$383$	−513.258	−	296.330i	−1.34010	−	0.773706i	−0.986822	+	0.161812i	$0.948266\pi$
$384$		0			0
$385$	64.4875	−	37.2319i	0.167500	−	0.0967062i
$386$	1153.53			2.98841
$387$		0			0
$388$			270.804i			0.697949i
$389$	555.852	−	320.921i	1.42892	−	0.824990i	0.431888	−	0.901927i	$-0.357847\pi$
$389$	555.852	−	320.921i	1.42892	−	0.824990i	0.997036	+	0.0769373i	$0.0245141\pi$
$390$		0			0
$391$	386.489	+	304.551i	0.988464	+	0.778904i
$392$	363.459	+	209.843i	0.927191	+	0.535314i
$393$		0			0
$394$	205.997	−	118.933i	0.522836	−	0.301860i
$395$			1011.59i			2.56098i
$396$		0			0
$397$			82.8506i			0.208692i	0.994541	+	0.104346i	$0.0332749\pi$
$397$			82.8506i			0.208692i	−0.994541	+	0.104346i	$0.966725\pi$
$398$	−293.543	−	508.432i	−0.737546	−	1.27747i
$399$		0			0
$400$	−57.9662	+	100.400i	−0.144916	+	0.251001i
$401$	131.632	−	227.993i	0.328259	−	0.568561i	−0.653908	−	0.756574i	$-0.726872\pi$
$401$	131.632	−	227.993i	0.328259	−	0.568561i	0.982166	+	0.188014i	$0.0602049\pi$
$402$		0			0
$403$	308.517	−	178.122i	0.765550	−	0.441991i
$404$			379.881i			0.940299i
$405$		0			0
$406$	−32.8765			−0.0809767
$407$	−63.3866	+	36.5963i	−0.155741	+	0.0899171i
$408$		0			0
$409$	−262.484	+	454.636i	−0.641771	+	1.11158i	0.343266	+	0.939238i	$0.388467\pi$
$409$	−262.484	+	454.636i	−0.641771	+	1.11158i	−0.985037	+	0.172342i	$0.944867\pi$
$410$	−1672.92	−	965.859i	−4.08029	−	2.35575i
$411$		0			0
$412$	465.563	+	806.378i	1.13001	+	1.95723i
$413$	41.9075			0.101471
$414$		0			0
$415$			1250.48i			3.01320i
$416$	−310.109	+	179.042i	−0.745454	+	0.430388i
$417$		0			0
$418$	397.854	+	229.701i	0.951804	+	0.549524i
$419$	−228.233	+	395.311i	−0.544709	+	0.943464i	0.453916	+	0.891045i	$0.350027\pi$
$419$	−228.233	+	395.311i	−0.544709	+	0.943464i	−0.998625	+	0.0524196i	$0.983307\pi$
$420$		0			0
$421$	245.380	+	425.010i	0.582850	+	1.00953i	0.995140	+	0.0984726i	$0.0313957\pi$
$421$	245.380	+	425.010i	0.582850	+	1.00953i	−0.412290	+	0.911053i	$0.635271\pi$
$422$	−517.344			−1.22593
$423$		0			0
$424$	33.8000			0.0797171
$425$	1040.39	−	415.329i	2.44798	−	0.977246i
$426$		0			0
$427$	−26.3024	+	45.5572i	−0.0615982	+	0.106691i
$428$	−267.150	+	462.717i	−0.624182	+	1.08111i
$429$		0			0
$430$	−62.7253	+	36.2145i	−0.145873	+	0.0842197i
$431$	−472.289			−1.09580			−0.547899	−	0.836544i	$-0.684572\pi$
$431$	−472.289			−1.09580			−0.547899	+	0.836544i	$0.684572\pi$
$432$		0			0
$433$	43.2832			0.0999611			0.0499806	−	0.998750i	$-0.484084\pi$
$433$	43.2832			0.0999611			0.0499806	+	0.998750i	$0.484084\pi$
$434$	71.8245	−	41.4679i	0.165494	−	0.0955481i
$435$		0			0
$436$	−673.052	−	388.587i	−1.54370	−	0.891254i
$437$	228.957	−	396.566i	0.523930	−	0.907473i
$438$		0			0
$439$	−547.444	+	316.067i	−1.24702	+	0.719970i	−0.970515	−	0.241042i	$-0.922511\pi$
$439$	−547.444	+	316.067i	−1.24702	+	0.719970i	−0.276509	+	0.961011i	$0.589178\pi$
$440$			737.732i			1.67666i
$441$		0			0
$442$	−676.965	−	98.0091i	−1.53159	−	0.221740i
$443$	−65.6955	+	37.9293i	−0.148297	+	0.0856192i	−0.572312	−	0.820036i	$-0.693954\pi$
$443$	−65.6955	+	37.9293i	−0.148297	+	0.0856192i	0.424016	+	0.905655i	$0.360620\pi$
$444$		0			0
$445$	−915.161	−	528.368i	−2.05654	−	1.18734i
$446$	−394.274	−	227.634i	−0.884023	−	0.510391i
$447$		0			0
$448$	−77.5483	+	44.7725i	−0.173099	+	0.0999386i
$449$	205.960			0.458708			0.229354	−	0.973343i	$-0.426339\pi$
$449$	205.960			0.458708			0.229354	+	0.973343i	$0.426339\pi$
$450$		0			0
$451$	−551.701			−1.22328
$452$	128.268	+	222.167i	0.283779	+	0.491520i
$453$		0			0
$454$	437.280	+	252.464i	0.963172	+	0.556088i
$455$	89.3547	+	51.5889i	0.196384	+	0.113382i
$456$		0			0
$457$	66.3571	+	114.934i	0.145201	+	0.251496i	0.929448	−	0.368953i	$-0.120284\pi$
$457$	66.3571	+	114.934i	0.145201	+	0.251496i	−0.784247	+	0.620449i	$0.786950\pi$
$458$		−	452.796i		−	0.988637i
$459$		0			0
$460$	1839.18			3.99821
$461$	28.9527	−	16.7158i	0.0628041	−	0.0362600i	−0.468269	−	0.883586i	$-0.655122\pi$
$461$	28.9527	−	16.7158i	0.0628041	−	0.0362600i	0.531073	+	0.847326i	$0.321789\pi$
$462$		0			0
$463$	−215.524	+	373.299i	−0.465495	+	0.806260i	−0.999224	−	0.0393952i	$-0.987457\pi$
$463$	−215.524	+	373.299i	−0.465495	+	0.806260i	0.533729	+	0.845656i	$0.320790\pi$
$464$	10.0823	−	17.4631i	0.0217292	−	0.0376361i
$465$		0			0
$466$	646.526	−	373.272i	1.38739	−	0.801012i
$467$			151.083i			0.323517i	0.986830	+	0.161759i	$0.0517166\pi$
$467$			151.083i			0.323517i	−0.986830	+	0.161759i	$0.948283\pi$
$468$		0			0
$469$			79.3145i			0.169114i
$470$	760.337	+	1316.94i	1.61774	+	2.80200i
$471$		0			0
$472$	−207.594	+	359.564i	−0.439819	+	0.761788i
$473$	−10.3429	+	17.9144i	−0.0218666	+	0.0378740i
$474$		0			0
$475$	−521.244	−	902.821i	−1.09736	−	1.90068i
$476$	−98.4899	−	14.2591i	−0.206911	−	0.0299561i
$477$		0			0
$478$	1.96275			0.00410618
$479$	4.46879	+	7.74018i	0.00932942	+	0.0161590i	0.870652	−	0.491899i	$-0.163697\pi$
$479$	4.46879	+	7.74018i	0.00932942	+	0.0161590i	−0.861323	+	0.508058i	$0.830364\pi$
$480$		0			0
$481$	−87.8292	−	50.7082i	−0.182597	−	0.105422i
$482$	302.010	−	523.097i	0.626577	−	1.08526i
$483$		0			0
$484$	−139.725	−	242.011i	−0.288689	−	0.500023i
$485$		−	387.389i		−	0.798741i
$486$		0			0
$487$		−	565.088i		−	1.16035i	−0.814493	−	0.580173i	$-0.802985\pi$
$487$		−	565.088i		−	1.16035i	0.814493	−	0.580173i	$-0.197015\pi$
$488$	−260.585	−	451.347i	−0.533986	−	0.924891i
$489$		0			0
$490$	−1300.41	−	750.793i	−2.65390	−	1.53223i
$491$	419.975	+	242.472i	0.855345	+	0.493834i	0.862451	−	0.506141i	$-0.168928\pi$
$491$	419.975	+	242.472i	0.855345	+	0.493834i	−0.00710548	+	0.999975i	$0.502262\pi$
$492$		0			0
$493$	−180.960	+	72.2403i	−0.367060	+	0.146532i
$494$			636.553i			1.28857i
$495$		0			0
$496$			50.8683i			0.102557i
$497$	0.557031	−	0.321602i	0.00112079	−	0.000647086i
$498$		0			0
$499$	−554.670	−	320.239i	−1.11156	−	0.641762i	−0.172330	−	0.985039i	$-0.555129\pi$
$499$	−554.670	−	320.239i	−1.11156	−	0.641762i	−0.939234	+	0.343278i	$0.888463\pi$
$500$	1299.28	−	2250.41i	2.59855	−	4.50082i
$501$		0			0
$502$	−746.934	−	1293.73i	−1.48792	−	2.57715i
$503$	−404.960			−0.805090			−0.402545	−	0.915400i	$-0.631874\pi$
$503$	−404.960			−0.805090			−0.402545	+	0.915400i	$0.631874\pi$
$504$		0			0
$505$		−	543.425i		−	1.07609i
$506$	727.917	−	420.263i	1.43857	−	0.830560i
$507$		0			0
$508$	602.034	−	1042.75i	1.18511	−	2.05266i
$509$	−491.624	−	283.839i	−0.965863	−	0.557641i	−0.0678907	−	0.997693i	$-0.521627\pi$
$509$	−491.624	−	283.839i	−0.965863	−	0.557641i	−0.897973	+	0.440051i	$0.854960\pi$
$510$		0			0
$511$	16.2606	+	28.1642i	0.0318211	+	0.0551158i
$512$		−	112.370i		−	0.219472i
$513$		0			0
$514$	830.438			1.61564
$515$	−665.994	−	1153.54i	−1.29319	−	2.23987i
$516$		0			0
$517$	376.120	+	217.153i	0.727505	+	0.420025i
$518$	−20.4472	−	11.8052i	−0.0394733	−	0.0227899i
$519$		0			0
$520$	−885.260	+	511.105i	−1.70242	+	0.982894i
$521$	857.106			1.64512			0.822558	−	0.568681i	$-0.192546\pi$
$521$	857.106			1.64512			0.822558	+	0.568681i	$0.192546\pi$
$522$		0			0
$523$	−142.429			−0.272332			−0.136166	−	0.990686i	$-0.543478\pi$
$523$	−142.429			−0.272332			−0.136166	+	0.990686i	$0.543478\pi$
$524$	−393.322	−	681.254i	−0.750614	−	1.30010i
$525$		0			0
$526$	289.820	−	501.983i	0.550989	−	0.954341i
$527$	304.221	−	386.071i	0.577270	−	0.732582i
$528$		0			0
$529$	−154.402	−	267.433i	−0.291876	−	0.505544i
$530$	−120.932			−0.228174
$531$		0			0
$532$			92.6105i			0.174080i
$533$	−382.221	−	662.027i	−0.717113	−	1.24208i
$534$		0			0
$535$	382.161	−	661.923i	0.714320	−	1.23724i
$536$	−680.514	−	392.895i	−1.26962	−	0.733013i
$537$		0			0
$538$	234.633	−	135.466i	0.436121	−	0.251795i
$539$	−428.854			−0.795648
$540$		0			0
$541$		−	279.116i		−	0.515927i	−0.966155	−	0.257963i	$-0.916949\pi$
$541$		−	279.116i		−	0.515927i	0.966155	−	0.257963i	$-0.0830514\pi$
$542$	360.933	−	208.385i	0.665928	−	0.384474i
$543$		0			0
$544$	−305.791	+	388.063i	−0.562117	+	0.713352i
$545$	962.811	+	555.879i	1.76663	+	1.01996i
$546$		0			0
$547$	44.0215	−	25.4158i	0.0804780	−	0.0464640i	−0.459221	−	0.888322i	$-0.651871\pi$
$547$	44.0215	−	25.4158i	0.0804780	−	0.0464640i	0.539699	+	0.841858i	$0.318538\pi$
$548$			1165.50i			2.12683i
$549$		0			0
$550$		−	1913.54i		−	3.47917i
$551$	90.6625	+	157.032i	0.164542	+	0.284995i
$552$		0			0
$553$	−46.5981	+	80.7102i	−0.0842642	+	0.145950i
$554$	−452.038	+	782.953i	−0.815953	+	1.41327i
$555$		0			0
$556$	1044.27	−	602.910i	1.87819	−	1.08437i
$557$		−	245.097i		−	0.440031i	−0.975496	−	0.220016i	$-0.929389\pi$
$557$		−	245.097i		−	0.440031i	0.975496	−	0.220016i	$-0.0706109\pi$
$558$		0			0
$559$	−28.6625			−0.0512745
$560$	−12.7590	+	7.36641i	−0.0227839	+	0.0131543i
$561$		0			0
$562$	−745.733	+	1291.65i	−1.32693	+	2.29830i
$563$	13.2728	+	7.66308i	0.0235752	+	0.0136112i	0.511741	−	0.859140i	$-0.329001\pi$
$563$	13.2728	+	7.66308i	0.0235752	+	0.0136112i	−0.488166	+	0.872751i	$0.662334\pi$
$564$		0			0
$565$	−183.489	−	317.813i	−0.324760	−	0.562501i
$566$	614.376			1.08547
$567$		0			0
$568$			6.37239i			0.0112190i
$569$	−498.322	+	287.707i	−0.875786	+	0.505635i	−0.869267	−	0.494343i	$-0.835409\pi$
$569$	−498.322	+	287.707i	−0.875786	+	0.505635i	−0.00651941	+	0.999979i	$0.502075\pi$
$570$		0			0
$571$	436.016	+	251.734i	0.763601	+	0.440865i	0.830587	−	0.556889i	$-0.188005\pi$
$571$	436.016	+	251.734i	0.763601	+	0.440865i	−0.0669862	+	0.997754i	$0.521338\pi$
$572$	−365.093	+	632.359i	−0.638274	+	1.10552i
$573$		0			0
$574$	−88.9834	−	154.124i	−0.155023	−	0.268508i
$575$	−1907.35			−3.31712
$576$		0			0
$577$	702.293			1.21715			0.608573	−	0.793498i	$-0.291742\pi$
$577$	702.293			1.21715			0.608573	+	0.793498i	$0.291742\pi$
$578$	−917.613	+	220.710i	−1.58756	+	0.381851i
$579$		0			0
$580$	−364.139	+	630.707i	−0.627825	+	1.08743i
$581$	−57.6025	+	99.7705i	−0.0991437	+	0.171722i
$582$		0			0
$583$	−29.9111	+	17.2692i	−0.0513056	+	0.0296213i
$584$	−322.196			−0.551705
$585$		0			0
$586$	−1764.87			−3.01173
$587$	−814.714	+	470.375i	−1.38793	+	0.801321i	−0.993082	−	0.117427i	$-0.962536\pi$
$587$	−814.714	+	470.375i	−1.38793	+	0.801321i	−0.394846	+	0.918747i	$0.629202\pi$
$588$		0			0
$589$	−396.136	−	228.709i	−0.672557	−	0.388301i
$590$	742.747	−	1286.48i	1.25889	−	2.18047i
$591$		0			0
$592$	12.5412	−	7.24066i	0.0211844	−	0.0122308i
$593$			313.881i			0.529311i	0.964343	+	0.264655i	$0.0852582\pi$
$593$			313.881i			0.529311i	−0.964343	+	0.264655i	$0.914742\pi$
$594$		0			0
$595$	140.891	+	20.3978i	0.236792	+	0.0342821i
$596$	−52.8452	+	30.5102i	−0.0886664	+	0.0511916i
$597$		0			0
$598$	1008.61	+	582.322i	1.68664	+	0.973782i
$599$	−697.940	−	402.956i	−1.16518	−	0.672714i	−0.212637	−	0.977131i	$-0.568205\pi$
$599$	−697.940	−	402.956i	−1.16518	−	0.672714i	−0.952539	+	0.304417i	$0.901538\pi$
$600$		0			0
$601$	−466.199	+	269.160i	−0.775705	+	0.447853i	−0.834906	−	0.550393i	$-0.814478\pi$
$601$	−466.199	+	269.160i	−0.775705	+	0.447853i	0.0592011	+	0.998246i	$0.481145\pi$
$602$	−6.67279			−0.0110844
$603$		0			0
$604$	46.6522			0.0772387
$605$	199.879	+	346.201i	0.330379	+	0.572232i
$606$		0			0
$607$	450.953	+	260.358i	0.742921	+	0.428925i	0.823130	−	0.567853i	$-0.192226\pi$
$607$	450.953	+	260.358i	0.742921	+	0.428925i	−0.0802096	+	0.996778i	$0.525559\pi$
$608$	398.180	+	229.890i	0.654902	+	0.378108i
$609$		0			0
$610$	932.342	+	1614.86i	1.52843	+	2.64732i
$611$			601.779i			0.984909i
$612$		0			0
$613$	398.338			0.649817			0.324908	−	0.945745i	$-0.394667\pi$
$613$	398.338			0.649817			0.324908	+	0.945745i	$0.394667\pi$
$614$	−212.633	+	122.764i	−0.346308	+	0.199941i
$615$		0			0
$616$	−33.9832	+	58.8605i	−0.0551675	+	0.0955528i
$617$	−467.483	+	809.703i	−0.757670	+	1.31232i	0.186366	+	0.982480i	$0.440329\pi$
$617$	−467.483	+	809.703i	−0.757670	+	1.31232i	−0.944036	+	0.329843i	$0.893004\pi$
$618$		0			0
$619$	−946.839	+	546.658i	−1.52963	+	0.883131i	−0.530250	+	0.847841i	$0.677902\pi$
$619$	−946.839	+	546.658i	−1.52963	+	0.883131i	−0.999377	+	0.0352896i	$0.988765\pi$
$620$		−	1837.18i		−	2.96320i
$621$		0			0
$622$		−	1051.61i		−	1.69069i
$623$	−48.6779	−	84.3126i	−0.0781347	−	0.135333i
$624$		0			0
$625$	−1034.93	+	1792.56i	−1.65589	+	2.86809i
$626$	701.651	−	1215.30i	1.12085	−	1.94137i
$627$		0			0
$628$	8.01081	+	13.8751i	0.0127561	+	0.0220942i
$629$	−138.486	−	20.0496i	−0.220168	−	0.0318754i
$630$		0			0
$631$	127.975			0.202814			0.101407	−	0.994845i	$-0.467666\pi$
$631$	127.975			0.202814			0.101407	+	0.994845i	$0.467666\pi$
$632$	−461.659	−	799.617i	−0.730474	−	1.26522i
$633$		0			0
$634$	−1000.28	−	577.514i	−1.57773	−	0.910905i
$635$	−861.218	+	1491.67i	−1.35625	+	2.34909i
$636$		0			0
$637$	−297.113	−	514.614i	−0.466425	−	0.807872i
$638$			332.832i			0.521680i
$639$		0			0
$640$			2065.77i			3.22777i
$641$	−534.465	−	925.721i	−0.833799	−	1.44418i	−0.895004	−	0.446058i	$-0.852828\pi$
$641$	−534.465	−	925.721i	−0.833799	−	1.44418i	0.0612048	−	0.998125i	$-0.480506\pi$
$642$		0			0
$643$	−113.768	−	65.6838i	−0.176933	−	0.102152i	0.408918	−	0.912571i	$-0.365906\pi$
$643$	−113.768	−	65.6838i	−0.176933	−	0.102152i	−0.585851	+	0.810419i	$0.699239\pi$
$644$	146.740	+	84.7205i	0.227857	+	0.131554i
$645$		0			0
$646$	325.628	+	815.692i	0.504068	+	1.26268i
$647$		−	437.023i		−	0.675461i	−0.941243	−	0.337731i	$-0.890341\pi$
$647$		−	437.023i		−	0.675461i	0.941243	−	0.337731i	$-0.109659\pi$
$648$		0			0
$649$		−	424.259i		−	0.653711i
$650$	2296.20	−	1325.71i	3.53262	−	2.03956i
$651$		0			0
$652$	−515.392	−	297.562i	−0.790479	−	0.456383i
$653$	86.3726	−	149.602i	0.132270	−	0.229099i	−0.792281	−	0.610156i	$-0.791107\pi$
$653$	86.3726	−	149.602i	0.132270	−	0.229099i	0.924551	+	0.381057i	$0.124440\pi$
$654$		0			0
$655$	562.653	+	974.543i	0.859012	+	1.48785i
$656$	109.155			0.166395
$657$		0			0
$658$			140.098i			0.212915i
$659$	184.210	−	106.353i	0.279529	−	0.161386i	−0.353681	−	0.935366i	$-0.615070\pi$
$659$	184.210	−	106.353i	0.279529	−	0.161386i	0.633210	+	0.773980i	$0.281737\pi$
$660$		0			0
$661$	414.459	−	717.865i	0.627019	−	1.08603i	−0.361128	−	0.932516i	$-0.617608\pi$
$661$	414.459	−	717.865i	0.627019	−	1.08603i	0.988147	−	0.153512i	$-0.0490585\pi$
$662$	−165.450	−	95.5225i	−0.249924	−	0.144294i
$663$		0			0
$664$	−570.683	−	988.452i	−0.859462	−	1.48863i
$665$		−	132.481i		−	0.199219i
$666$		0			0
$667$	331.754			0.497382
$668$	319.940	+	554.153i	0.478952	+	0.829570i
$669$		0			0
$670$	2434.79	+	1405.73i	3.63402	+	2.09810i
$671$	461.206	+	266.278i	0.687342	+	0.396837i
$672$		0			0
$673$	58.9517	−	34.0358i	0.0875954	−	0.0505733i	−0.455562	−	0.890204i	$-0.650562\pi$
$673$	58.9517	−	34.0358i	0.0875954	−	0.0505733i	0.543158	+	0.839631i	$0.317228\pi$
$674$	241.383			0.358135
$675$		0			0
$676$	114.579			0.169495
$677$	170.933	+	296.065i	0.252486	+	0.437319i	0.964210	−	0.265141i	$-0.0854184\pi$
$677$	170.933	+	296.065i	0.252486	+	0.437319i	−0.711723	+	0.702460i	$0.752085\pi$
$678$		0			0
$679$	17.8448	−	30.9082i	0.0262811	−	0.0455201i
$680$	−872.935	+	1107.79i	−1.28373	+	1.62911i
$681$		0			0
$682$	−419.808	−	727.129i	−0.615554	−	1.06617i
$683$	−224.819			−0.329165			−0.164582	−	0.986363i	$-0.552628\pi$
$683$	−224.819			−0.329165			−0.164582	+	0.986363i	$0.552628\pi$
$684$		0			0
$685$		−	1667.27i		−	2.43397i
$686$	−139.446	−	241.527i	−0.203273	−	0.352080i
$687$		0			0
$688$	2.04636	−	3.54441i	0.00297437	−	0.00515175i
$689$	−41.4452	−	23.9284i	−0.0601527	−	0.0347292i
$690$		0			0
$691$	36.0581	−	20.8182i	0.0521825	−	0.0301276i	−0.473682	−	0.880696i	$-0.657075\pi$
$691$	36.0581	−	20.8182i	0.0521825	−	0.0301276i	0.525864	+	0.850568i	$0.323742\pi$
$692$	1415.44			2.04543
$693$		0			0
$694$			1502.81i			2.16543i
$695$	−1493.84	+	862.472i	−2.14942	+	1.24097i
$696$		0			0
$697$	−828.445	−	652.810i	−1.18859	−	0.936599i
$698$	458.882	+	264.936i	0.657425	+	0.379564i
$699$		0			0
$700$	334.069	−	192.875i	0.477241	−	0.275535i
$701$		−	742.107i		−	1.05864i	−0.848422	−	0.529320i	$-0.822447\pi$
$701$		−	742.107i		−	1.05864i	0.848422	−	0.529320i	$-0.177553\pi$
$702$		0			0
$703$			130.219i			0.185233i
$704$	453.263	+	785.074i	0.643839	+	1.11516i
$705$		0			0
$706$	271.250	−	469.819i	0.384207	−	0.665465i
$707$	25.0325	−	43.3576i	0.0354067	−	0.0613262i
$708$		0			0
$709$	−365.285	+	210.898i	−0.515212	+	0.297458i	−0.734974	−	0.678096i	$-0.762805\pi$
$709$	−365.285	+	210.898i	−0.515212	+	0.297458i	0.219761	+	0.975554i	$0.429472\pi$
$710$		−	22.7996i		−	0.0321121i
$711$		0			0
$712$	964.530			1.35468
$713$	−724.774	+	418.449i	−1.01651	+	0.586884i
$714$		0			0
$715$	522.270	−	904.599i	0.730448	−	1.26517i
$716$	517.592	+	298.832i	0.722894	+	0.417363i
$717$		0			0
$718$	−446.774	−	773.836i	−0.622249	−	1.07777i
$719$	805.388			1.12015			0.560075	−	0.828442i	$-0.310772\pi$
$719$	805.388			1.12015			0.560075	+	0.828442i	$0.310772\pi$
$720$		0			0
$721$		−	122.714i		−	0.170200i
$722$	−313.135	+	180.788i	−0.433704	+	0.250399i
$723$		0			0
$724$	−794.371	−	458.631i	−1.09720	−	0.633468i
$725$	377.636	−	654.084i	0.520877	−	0.902185i
$726$		0			0
$727$	−557.548	−	965.701i	−0.766916	−	1.32834i	−0.939228	−	0.343295i	$-0.888457\pi$
$727$	−557.548	−	965.701i	−0.766916	−	1.32834i	0.172312	−	0.985042i	$-0.444876\pi$
$728$	−94.1749			−0.129361
$729$		0			0
$730$	1152.78			1.57915
$731$	−36.7286	+	14.6622i	−0.0502444	+	0.0200578i
$732$		0			0
$733$	−283.568	+	491.155i	−0.386860	+	0.670061i	−0.992025	−	0.126039i	$-0.959774\pi$
$733$	−283.568	+	491.155i	−0.386860	+	0.670061i	0.605166	+	0.796100i	$0.293107\pi$
$734$	−837.322	+	1450.28i	−1.14077	+	1.97586i
$735$		0			0
$736$	728.515	−	420.608i	0.989830	−	0.571479i
$737$	802.955			1.08949
$738$		0			0
$739$	231.813			0.313684			0.156842	−	0.987624i	$-0.449869\pi$
$739$	231.813			0.313684			0.156842	+	0.987624i	$0.449869\pi$
$740$	−452.943	+	261.507i	−0.612085	+	0.353388i
$741$		0			0
$742$	−9.64869	−	5.57068i	−0.0130036	−	0.00750765i
$743$	−125.933	+	218.122i	−0.169492	+	0.293569i	−0.938241	−	0.345981i	$-0.887546\pi$
$743$	−125.933	+	218.122i	−0.169492	+	0.293569i	0.768749	+	0.639550i	$0.220879\pi$
$744$		0			0
$745$	75.5958	−	43.6452i	0.101471	−	0.0585842i
$746$			43.2725i			0.0580060i
$747$		0			0
$748$	−144.355	+	997.080i	−0.192987	+	1.33300i
$749$	60.9821	−	35.2080i	0.0814181	−	0.0470067i
$750$		0			0
$751$	−453.273	−	261.697i	−0.603559	−	0.348465i	0.166881	−	0.985977i	$-0.446630\pi$
$751$	−453.273	−	261.697i	−0.603559	−	0.348465i	−0.770440	+	0.637512i	$0.779964\pi$
$752$	−74.4162	−	42.9642i	−0.0989577	−	0.0571333i
$753$		0			0
$754$	−399.390	+	230.588i	−0.529695	+	0.305819i
$755$	−66.7366			−0.0883929
$756$		0			0
$757$	329.893			0.435790			0.217895	−	0.975972i	$-0.430081\pi$
$757$	329.893			0.435790			0.217895	+	0.975972i	$0.430081\pi$
$758$	315.441	+	546.359i	0.416149	+	0.720791i
$759$		0			0
$760$	1136.68	+	656.260i	1.49563	+	0.863500i
$761$	−839.259	−	484.546i	−1.10284	−	0.636723i	−0.165872	−	0.986147i	$-0.553044\pi$
$761$	−839.259	−	484.546i	−1.10284	−	0.636723i	−0.936965	+	0.349424i	$0.886377\pi$
$762$		0			0
$763$	51.2124	+	88.7025i	0.0671198	+	0.116255i
$764$			179.555i			0.235019i
$765$		0			0
$766$	−1935.44			−2.52668
$767$	509.100	−	293.929i	0.663755	−	0.383219i
$768$		0			0
$769$	−154.348	+	267.338i	−0.200712	+	0.347644i	−0.948758	−	0.316003i	$-0.897659\pi$
$769$	−154.348	+	267.338i	−0.200712	+	0.347644i	0.748046	+	0.663647i	$0.230992\pi$
$770$	121.588	−	210.596i	0.157906	−	0.273501i
$771$		0			0
$772$	2038.75	−	1177.07i	2.64087	−	1.52471i
$773$		−	1477.85i		−	1.91183i	−0.293640	−	0.955916i	$-0.594867\pi$
$773$		−	1477.85i		−	1.91183i	0.293640	−	0.955916i	$-0.405133\pi$
$774$		0			0
$775$			1905.28i			2.45843i
$776$	176.793	+	306.215i	0.227827	+	0.394607i
$777$		0			0
$778$	1048.03	−	1815.24i	1.34708	−	2.33321i
$779$	−490.773	+	850.044i	−0.630004	+	1.09120i
$780$		0			0
$781$	−3.25580	−	5.63920i	−0.00416875	−	0.00722049i
$782$	1590.34	+	230.245i	2.03368	+	0.294431i
$783$		0			0
$784$	84.8498			0.108227
$785$	−11.4596	−	19.8486i	−0.0145982	−	0.0252848i
$786$		0			0
$787$	752.691	+	434.566i	0.956405	+	0.552181i	0.895065	−	0.445936i	$-0.147129\pi$
$787$	752.691	+	434.566i	0.956405	+	0.552181i	0.0613402	+	0.998117i	$0.480463\pi$
$788$	242.721	−	420.405i	0.308021	−	0.533509i
$789$		0			0
$790$	1651.76	+	2860.93i	2.09084	+	3.62143i
$791$		−	33.8093i		−	0.0427425i
$792$		0			0
$793$			737.915i			0.930536i
$794$	135.282	+	234.315i	0.170380	+	0.295107i
$795$		0			0
$796$	−1037.62	−	599.070i	−1.30354	−	0.752601i
$797$	54.9556	+	31.7287i	0.0689531	+	0.0398101i	0.534080	−	0.845434i	$-0.320658\pi$
$797$	54.9556	+	31.7287i	0.0689531	+	0.0398101i	−0.465127	+	0.885244i	$0.653991\pi$
$798$		0			0
$799$	307.840	+	771.132i	0.385281	+	0.965122i
$800$		−	1915.11i		−	2.39389i
$801$		0			0
$802$		−	859.735i		−	1.07199i
$803$	285.125	−	164.617i	0.355075	−	0.205003i
$804$		0			0
$805$	−209.914	−	121.194i	−0.260763	−	0.150551i
$806$	581.691	−	1007.52i	0.721701	−	1.25002i
$807$		0			0
$808$	248.004	+	429.555i	0.306935	+	0.531628i
$809$	−1330.12			−1.64415			−0.822076	−	0.569378i	$-0.807184\pi$
$809$	−1330.12			−1.64415			−0.822076	+	0.569378i	$0.807184\pi$
$810$		0			0
$811$		−	295.474i		−	0.364333i	−0.983268	−	0.182166i	$-0.941689\pi$
$811$		−	295.474i		−	0.364333i	0.983268	−	0.182166i	$-0.0583109\pi$
$812$	−58.1062	+	33.5476i	−0.0715594	+	0.0413148i
$813$		0			0
$814$	−119.512	+	207.001i	−0.146820	+	0.254300i
$815$	737.276	+	425.666i	0.904633	+	0.522290i
$816$		0			0
$817$	18.4013	+	31.8720i	0.0225230	+	0.0390110i
$818$			1714.38i			2.09582i
$819$		0			0
$820$	−3942.30			−4.80768
$821$	−428.265	−	741.776i	−0.521638	−	0.903504i	−0.999683	−	0.0251683i	$-0.991988\pi$
$821$	−428.265	−	741.776i	−0.521638	−	0.903504i	0.478045	−	0.878335i	$-0.341345\pi$
$822$		0			0
$823$	−29.1469	−	16.8280i	−0.0354155	−	0.0204471i	0.482188	−	0.876068i	$-0.339842\pi$
$823$	−29.1469	−	16.8280i	−0.0354155	−	0.0204471i	−0.517603	+	0.855621i	$0.673176\pi$
$824$	1052.88	+	607.882i	1.27777	+	0.737720i
$825$		0			0
$826$	118.521	−	68.4284i	0.143488	−	0.0828431i
$827$	948.705			1.14716			0.573582	−	0.819148i	$-0.305553\pi$
$827$	948.705			1.14716			0.573582	+	0.819148i	$0.305553\pi$
$828$		0			0
$829$	804.088			0.969949			0.484974	−	0.874528i	$-0.338829\pi$
$829$	804.088			0.969949			0.484974	+	0.874528i	$0.338829\pi$
$830$	2041.83	+	3536.56i	2.46004	+	4.26092i
$831$		0			0
$832$	−628.046	+	1087.81i	−0.754863	+	1.30746i
$833$	−643.976	−	507.449i	−0.773081	−	0.609183i
$834$		0			0
$835$	−457.679	−	792.723i	−0.548118	−	0.949369i
$836$	937.559			1.12148
$837$		0			0
$838$			1490.67i			1.77885i
$839$	127.234	+	220.375i	0.151649	+	0.262664i	0.931834	−	0.362885i	$-0.118208\pi$
$839$	127.234	+	220.375i	0.151649	+	0.262664i	−0.780185	+	0.625549i	$0.784875\pi$
$840$		0			0
$841$	354.816	−	614.559i	0.421898	−	0.730748i
$842$	1387.95	+	801.332i	1.64839	+	0.951701i
$843$		0			0
$844$	−914.357	+	527.904i	−1.08336	+	0.625479i
$845$	−163.907			−0.193972
$846$		0			0
$847$			36.8292i			0.0434819i
$848$	5.91799	−	3.41675i	0.00697876	−	0.00402919i
$849$		0			0
$850$	2264.23	−	2873.42i	2.66380	−	3.38049i
$851$	206.330	+	119.125i	0.242456	+	0.139982i
$852$		0			0
$853$	151.777	−	87.6286i	0.177933	−	0.102730i	−0.408388	−	0.912808i	$-0.633909\pi$
$853$	151.777	−	87.6286i	0.177933	−	0.102730i	0.586321	+	0.810079i	$0.300576\pi$
$854$			171.791i			0.201160i
$855$		0			0
$856$			697.631i			0.814989i
$857$	421.152	+	729.456i	0.491425	+	0.851174i	0.999951	−	0.00987289i	$-0.00314269\pi$
$857$	421.152	+	729.456i	0.491425	+	0.851174i	−0.508526	+	0.861047i	$0.669809\pi$
$858$		0			0
$859$	−127.044	+	220.047i	−0.147898	+	0.256166i	−0.930450	−	0.366418i	$-0.880584\pi$
$859$	−127.044	+	220.047i	−0.147898	+	0.256166i	0.782553	+	0.622584i	$0.213917\pi$
$860$	−73.9074	+	128.011i	−0.0859388	+	0.148850i
$861$		0			0
$862$	−1335.71	+	771.173i	−1.54955	+	0.894632i
$863$			78.9314i			0.0914617i	0.998954	+	0.0457308i	$0.0145617\pi$
$863$			78.9314i			0.0914617i	−0.998954	+	0.0457308i	$0.985438\pi$
$864$		0			0
$865$	−2024.80			−2.34081
$866$	122.412	−	70.6746i	0.141353	−	0.0816103i
$867$		0			0
$868$	84.6287	−	146.581i	0.0974985	−	0.168872i
$869$	817.085	+	471.744i	0.940259	+	0.542859i
$870$		0			0
$871$	556.292	+	963.526i	0.638682	+	1.10623i
$872$	−1014.75			−1.16370
$873$		0			0
$874$		−	1495.40i		−	1.71099i
$875$	−296.585	+	171.233i	−0.338954	+	0.195695i
$876$		0			0
$877$	655.371	+	378.379i	0.747288	+	0.431447i	0.824713	−	0.565551i	$-0.191337\pi$
$877$	655.371	+	378.379i	0.747288	+	0.431447i	−0.0774253	+	0.996998i	$0.524670\pi$
$878$	−1032.17	+	1787.78i	−1.17560	+	2.03619i
$879$		0			0
$880$	74.5753	+	129.168i	0.0847446	+	0.146782i
$881$	−762.067			−0.865002			−0.432501	−	0.901633i	$-0.642369\pi$
$881$	−762.067			−0.865002			−0.432501	+	0.901633i	$0.642369\pi$
$882$		0			0
$883$	464.583			0.526142			0.263071	−	0.964776i	$-0.415265\pi$
$883$	464.583			0.526142			0.263071	+	0.964776i	$0.415265\pi$
$884$	−1296.48	+	517.561i	−1.46661	+	0.585477i
$885$		0			0
$886$	−123.865	+	214.541i	−0.139803	+	0.242145i
$887$	561.347	−	972.282i	0.632860	−	1.09615i	−0.354104	−	0.935206i	$-0.615214\pi$
$887$	561.347	−	972.282i	0.632860	−	1.09615i	0.986964	−	0.160940i	$-0.0514526\pi$
$888$		0			0
$889$	−137.426	+	79.3429i	−0.154585	+	0.0892496i
$890$	−3450.97			−3.87749
$891$		0			0
$892$	−929.124			−1.04162
$893$	669.166	−	386.343i	0.749346	−	0.432635i
$894$		0			0
$895$	−740.423	−	427.483i	−0.827288	−	0.477635i
$896$	−95.1584	+	164.819i	−0.106204	+	0.183950i
$897$		0			0
$898$	582.488	−	336.300i	0.648651	−	0.374499i
$899$		−	331.395i		−	0.368626i
$900$		0			0
$901$	−65.3493	−	9.46110i	−0.0725298	−	0.0105007i
$902$	−1560.30	+	900.840i	−1.72982	+	0.998714i
$903$		0			0
$904$	290.082	+	167.479i	0.320887	+	0.185264i
$905$	1136.36	+	656.077i	1.25565	+	0.724947i
$906$		0			0
$907$	473.660	−	273.468i	0.522227	−	0.301508i	−0.215618	−	0.976478i	$-0.569177\pi$
$907$	473.660	−	273.468i	0.522227	−	0.301508i	0.737845	+	0.674970i	$0.235843\pi$
$908$	1030.47			1.13488
$909$		0			0
$910$	336.946			0.370271
$911$	331.911	+	574.887i	0.364337	+	0.631051i	0.988670	−	0.150108i	$-0.0479622\pi$
$911$	331.911	+	574.887i	0.364337	+	0.631051i	−0.624332	+	0.781159i	$0.714629\pi$
$912$		0			0
$913$	1010.04	+	583.150i	1.10629	+	0.638718i
$914$	375.338	+	216.701i	0.410654	+	0.237091i
$915$		0			0
$916$	−462.038	−	800.274i	−0.504409	−	0.873661i
$917$			103.673i			0.113057i
$918$		0			0
$919$	560.444			0.609841			0.304920	−	0.952378i	$-0.401370\pi$
$919$	560.444			0.609841			0.304920	+	0.952378i	$0.401370\pi$
$920$	2079.67	−	1200.70i	2.26051	−	1.30511i
$921$		0			0
$922$	54.5887	−	94.5503i	0.0592068	−	0.102549i
$923$	4.51127	−	7.81375i	0.00488762	−	0.00846560i
$924$		0			0
$925$	469.732	−	271.200i	0.507818	−	0.293189i
$926$			1407.67i			1.52016i
$927$		0			0
$928$			333.105i			0.358949i
$929$	−340.702	−	590.113i	−0.366741	−	0.635213i	0.622313	−	0.782768i	$-0.286193\pi$
$929$	−340.702	−	590.113i	−0.366741	−	0.635213i	−0.989054	+	0.147555i	$0.952860\pi$
$930$		0			0
$931$	−381.493	+	660.766i	−0.409767	+	0.709738i
$932$	761.782	−	1319.45i	0.817363	−	1.41571i
$933$		0			0
$934$	246.694	+	427.287i	0.264126	+	0.457480i
$935$	206.501	−	1426.34i	0.220857	−	1.52549i
$936$		0			0
$937$	−748.388			−0.798707			−0.399353	−	0.916797i	$-0.630765\pi$
$937$	−748.388			−0.798707			−0.399353	+	0.916797i	$0.630765\pi$
$938$	129.508	+	224.315i	0.138068	+	0.239141i
$939$		0			0
$940$	2687.65	+	1551.71i	2.85920	+	1.65076i
$941$	286.717	−	496.608i	0.304693	−	0.527745i	−0.672500	−	0.740098i	$-0.734779\pi$
$941$	286.717	−	496.608i	0.304693	−	0.527745i	0.977193	+	0.212353i	$0.0681126\pi$
$942$		0			0
$943$	897.923	+	1555.25i	0.952198	+	1.64926i
$944$			83.9406i			0.0889201i
$945$		0			0
$946$			67.5532i			0.0714093i
$947$	381.495	+	660.768i	0.402846	+	0.697749i	0.994068	−	0.108760i	$-0.0346879\pi$
$947$	381.495	+	660.768i	0.402846	+	0.697749i	−0.591223	+	0.806508i	$0.701355\pi$
$948$		0			0
$949$	395.073	+	228.096i	0.416305	+	0.240354i
$950$	−2948.33	−	1702.22i	−3.10350	−	1.79181i
$951$		0			0
$952$	−120.678	+	48.1751i	−0.126762	+	0.0506041i
$953$			672.823i			0.706005i	0.935622	+	0.353002i	$0.114839\pi$
$953$			672.823i			0.706005i	−0.935622	+	0.353002i	$0.885161\pi$
$954$		0			0
$955$		−	256.855i		−	0.268959i
$956$	3.46898	−	2.00282i	0.00362864	−	0.00209500i
$957$		0			0
$958$	25.2770	+	14.5937i	0.0263851	+	0.0152335i
$959$	76.8018	−	133.025i	0.0800853	−	0.138712i
$960$		0			0
$961$	−62.5048	−	108.261i	−0.0650414	−	0.112655i
$962$	−331.194			−0.344277
$963$		0			0
$964$		−	1232.70i		−	1.27873i
$965$	−2916.46	+	1683.82i	−3.02224	+	1.74489i
$966$		0			0
$967$	429.853	−	744.528i	0.444523	−	0.769936i	−0.553496	−	0.832852i	$-0.686707\pi$
$967$	429.853	−	744.528i	0.444523	−	0.769936i	0.998019	+	0.0629160i	$0.0200400\pi$
$968$	−315.992	−	182.438i	−0.326438	−	0.188469i
$969$		0			0
$970$	−632.545	−	1095.60i	−0.652108	−	1.12949i
$971$		−	238.263i		−	0.245379i	−0.992445	−	0.122689i	$-0.960848\pi$
$971$		−	238.263i		−	0.245379i	0.992445	−	0.122689i	$-0.0391519\pi$
$972$		0			0
$973$	−158.917			−0.163327
$974$	−922.700	−	1598.16i	−0.947330	−	1.64082i
$975$		0			0
$976$	−91.2508	−	52.6837i	−0.0934946	−	0.0539792i
$977$	1257.67	+	726.115i	1.28727	+	0.743208i	0.978167	−	0.207819i	$-0.0666364\pi$
$977$	1257.67	+	726.115i	1.28727	+	0.743208i	0.309107	+	0.951027i	$0.399970\pi$
$978$		0			0
$979$	−853.554	+	492.800i	−0.871864	+	0.503371i
$980$	−3064.47			−3.12701
$981$		0			0
$982$	1583.68			1.61271
$983$	−422.965	−	732.597i	−0.430280	−	0.745266i	0.566618	−	0.823981i	$-0.308252\pi$
$983$	−422.965	−	732.597i	−0.430280	−	0.745266i	−0.996897	+	0.0787148i	$0.974918\pi$
$984$		0			0
$985$	−347.216	+	601.395i	−0.352503	+	0.610553i
$986$	−393.829	+	499.787i	−0.399421	+	0.506884i
$987$		0			0
$988$	649.547	+	1125.05i	0.657436	+	1.13871i
$989$	67.3345			0.0680834
$990$		0			0
$991$		−	1269.61i		−	1.28114i	−0.767899	−	0.640571i	$-0.778698\pi$
$991$		−	1269.61i		−	1.28114i	0.767899	−	0.640571i	$-0.221302\pi$
$992$	−420.152	−	727.725i	−0.423541	−	0.733594i
$993$		0			0
$994$	1.05025	−	1.81909i	0.00105659	−	0.00183007i
$995$	1484.33	+	856.979i	1.49179	+	0.861285i
$996$		0			0
$997$	1371.59	−	791.888i	1.37572	−	0.794271i	0.384078	−	0.923301i	$-0.374520\pi$
$997$	1371.59	−	791.888i	1.37572	−	0.794271i	0.991641	+	0.129030i	$0.0411862\pi$
$998$	−2091.60			−2.09579
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.3.i.a.152.31		68
3.2	odd	2		153.3.i.a.50.3	✓	68
9.2	odd	6	inner	459.3.i.a.305.32		68
9.7	even	3		153.3.i.a.101.4	yes	68
17.16	even	2	inner	459.3.i.a.152.32		68
51.50	odd	2		153.3.i.a.50.4	yes	68
153.16	even	6		153.3.i.a.101.3	yes	68
153.101	odd	6	inner	459.3.i.a.305.31		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.3	✓	68	3.2	odd	2
153.3.i.a.50.4	yes	68	51.50	odd	2
153.3.i.a.101.3	yes	68	153.16	even	6
153.3.i.a.101.4	yes	68	9.7	even	3
459.3.i.a.152.31		68	1.1	even	1	trivial
459.3.i.a.152.32		68	17.16	even	2	inner
459.3.i.a.305.31		68	153.101	odd	6	inner
459.3.i.a.305.32		68	9.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	459.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.82816 - 1.63284i) q^{2} +(3.33234 - 5.77179i) q^{4} +(-4.76697 + 8.25663i) q^{5} +(-0.760673 + 0.439175i) q^{7} -8.70203i q^{8} +31.1348i q^{10} +(4.44606 + 7.70081i) q^{11} +(-6.16052 + 10.6703i) q^{13} +(-1.43421 + 2.48412i) q^{14} +(-0.879664 - 1.52362i) q^{16} +(-2.43582 + 16.8246i) q^{17} +15.8202 q^{19} +(31.7703 + 55.0279i) q^{20} +(25.1484 + 14.5194i) q^{22} +(14.4724 - 25.0670i) q^{23} +(-32.9479 - 57.0675i) q^{25} +40.2366i q^{26} +5.85392i q^{28} +(5.73079 + 9.92603i) q^{29} +(-25.0398 - 14.4567i) q^{31} +(25.1691 + 14.5314i) q^{32} +(20.5830 + 51.5600i) q^{34} -8.37412i q^{35} +8.23116i q^{37} +(44.7422 - 25.8319i) q^{38} +(71.8494 + 41.4823i) q^{40} +(-31.0218 + 53.7314i) q^{41} +(1.16315 + 2.01464i) q^{43} +59.2633 q^{44} -94.5248i q^{46} +(42.2981 - 24.4208i) q^{47} +(-24.1143 + 41.7671i) q^{49} +(-186.364 - 107.598i) q^{50} +(41.0580 + 71.1145i) q^{52} +3.88416i q^{53} -84.7770 q^{55} +(3.82171 + 6.61940i) q^{56} +(32.4153 + 18.7150i) q^{58} +(-41.3195 - 23.8559i) q^{59} +(51.8668 - 29.9453i) q^{61} -94.4223 q^{62} +101.947 q^{64} +(-58.7340 - 101.730i) q^{65} +(45.1498 - 78.2017i) q^{67} +(88.9910 + 70.1244i) q^{68} +(-13.6736 - 23.6834i) q^{70} -0.732287 q^{71} -37.0254i q^{73} +(13.4402 + 23.2791i) q^{74} +(52.7185 - 91.3111i) q^{76} +(-6.76400 - 3.90520i) q^{77} +(91.8886 - 53.0519i) q^{79} +16.7733 q^{80} +202.615i q^{82} +(113.589 - 65.5804i) q^{83} +(-127.303 - 100.314i) q^{85} +(6.57916 + 3.79848i) q^{86} +(67.0127 - 38.6898i) q^{88} +110.840i q^{89} -10.8222i q^{91} +(-96.4543 - 167.064i) q^{92} +(79.7506 - 138.132i) q^{94} +(-75.4145 + 130.622i) q^{95} +(-35.1889 + 20.3163i) q^{97} +157.499i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 6 q^{2} + 62 q^{4} - 2 q^{13} - 106 q^{16} - 32 q^{19} - 132 q^{25} - 27 q^{34} + 102 q^{38} + 58 q^{43} + 312 q^{47} + 152 q^{49} + 90 q^{50} + 70 q^{52} + 92 q^{55} + 258 q^{59} - 16 q^{64} + 82 q^{67}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q + 6 * q^2 + 62 * q^4 - 2 * q^13 - 106 * q^16 - 32 * q^19 - 132 * q^25 - 27 * q^34 + 102 * q^38 + 58 * q^43 + 312 * q^47 + 152 * q^49 + 90 * q^50 + 70 * q^52 + 92 * q^55 + 258 * q^59 - 16 * q^64 + 82 * q^67 + 333 * q^68 + 204 * q^70 + 34 * q^76 + 60 * q^77 + 690 * q^83 - 44 * q^85 + 1248 * q^86 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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