LMFDB - Embedded newform 504.3.l.h.181.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(181,504)] 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("504.181"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,2,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.23
Character	$\chi$	$=$	504.181
Dual form			504.3.l.h.181.21

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.962692 + 1.75306i) q^{2} +(-2.14645 + 3.37532i) q^{4} -1.68264 q^{5} +(5.30913 - 4.56214i) q^{7} +(-7.98351 - 0.513465i) q^{8} +(-1.61986 - 2.94977i) q^{10} +11.9925i q^{11} -25.3039 q^{13} +(13.1088 + 4.91531i) q^{14} +(-6.78552 - 14.4899i) q^{16} +11.7219i q^{17} -0.0390239 q^{19} +(3.61170 - 5.67944i) q^{20} +(-21.0236 + 11.5451i) q^{22} -26.6539 q^{23} -22.1687 q^{25} +(-24.3598 - 44.3592i) q^{26} +(4.00287 + 27.7124i) q^{28} +46.0119i q^{29} -37.9501i q^{31} +(18.8693 - 25.8447i) q^{32} +(-20.5492 + 11.2846i) q^{34} +(-8.93335 + 7.67643i) q^{35} -19.5040i q^{37} +(-0.0375680 - 0.0684113i) q^{38} +(13.4334 + 0.863976i) q^{40} -41.0379i q^{41} +23.0681i q^{43} +(-40.4786 - 25.7413i) q^{44} +(-25.6595 - 46.7259i) q^{46} +56.6865i q^{47} +(7.37382 - 48.4420i) q^{49} +(-21.3417 - 38.8631i) q^{50} +(54.3134 - 85.4086i) q^{52} -56.2765i q^{53} -20.1791i q^{55} +(-44.7280 + 33.6958i) q^{56} +(-80.6617 + 44.2953i) q^{58} -64.4331 q^{59} +52.2895 q^{61} +(66.5289 - 36.5343i) q^{62} +(63.4727 + 8.19850i) q^{64} +42.5773 q^{65} +55.1497i q^{67} +(-39.5651 - 25.1604i) q^{68} +(-22.0573 - 8.27068i) q^{70} +8.38597 q^{71} +117.406i q^{73} +(34.1917 - 18.7764i) q^{74} +(0.0837628 - 0.131718i) q^{76} +(54.7115 + 63.6699i) q^{77} -13.2280 q^{79} +(11.4176 + 24.3812i) q^{80} +(71.9420 - 39.5069i) q^{82} -19.4050 q^{83} -19.7237i q^{85} +(-40.4398 + 22.2075i) q^{86} +(6.15774 - 95.7424i) q^{88} +36.4448i q^{89} +(-134.342 + 115.440i) q^{91} +(57.2112 - 89.9654i) q^{92} +(-99.3749 + 54.5717i) q^{94} +0.0656632 q^{95} +163.122i q^{97} +(92.0205 - 33.7080i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.962692	+	1.75306i	0.481346	+	0.876531i
$2$	0.962692	+	1.75306i	0.481346	+	0.876531i
$3$		0			0
$3$		0			0
$4$	−2.14645	+	3.37532i	−0.536612	+	0.843829i
$5$	−1.68264			−0.336528			−0.168264	−	0.985742i	$-0.553816\pi$
$5$	−1.68264			−0.336528			−0.168264	+	0.985742i	$0.553816\pi$
$6$		0			0
$7$	5.30913	−	4.56214i	0.758448	−	0.651734i
$7$	5.30913	−	4.56214i	0.758448	−	0.651734i
$8$	−7.98351	−	0.513465i	−0.997938	−	0.0641831i
$9$		0			0
$10$	−1.61986	−	2.94977i	−0.161986	−	0.294977i
$11$			11.9925i			1.09023i	0.838361	+	0.545115i	$0.183514\pi$
$11$			11.9925i			1.09023i	−0.838361	+	0.545115i	$0.816486\pi$
$12$		0			0
$13$	−25.3039			−1.94645			−0.973226	−	0.229851i	$-0.926176\pi$
$13$	−25.3039			−1.94645			−0.973226	+	0.229851i	$0.926176\pi$
$14$	13.1088	+	4.91531i	0.936340	+	0.351093i
$15$		0			0
$16$	−6.78552	−	14.4899i	−0.424095	−	0.905618i
$17$			11.7219i			0.689523i	0.938690	+	0.344762i	$0.112040\pi$
$17$			11.7219i			0.689523i	−0.938690	+	0.344762i	$0.887960\pi$
$18$		0			0
$19$	−0.0390239			−0.00205389			−0.00102695	−	0.999999i	$-0.500327\pi$
$19$	−0.0390239			−0.00205389			−0.00102695	+	0.999999i	$0.500327\pi$
$20$	3.61170	−	5.67944i	0.180585	−	0.283972i
$21$		0			0
$22$	−21.0236	+	11.5451i	−0.955619	+	0.524778i
$23$	−26.6539			−1.15887			−0.579433	−	0.815020i	$-0.696726\pi$
$23$	−26.6539			−1.15887			−0.579433	+	0.815020i	$0.696726\pi$
$24$		0			0
$25$	−22.1687			−0.886749
$26$	−24.3598	−	44.3592i	−0.936917	−	1.70612i
$27$		0			0
$28$	4.00287	+	27.7124i	0.142960	+	0.989729i
$29$			46.0119i			1.58662i	0.608819	+	0.793309i	$0.291643\pi$
$29$			46.0119i			1.58662i	−0.608819	+	0.793309i	$0.708357\pi$
$30$		0			0
$31$		−	37.9501i		−	1.22420i	−0.790781	−	0.612099i	$-0.790326\pi$
$31$		−	37.9501i		−	1.22420i	0.790781	−	0.612099i	$-0.209674\pi$
$32$	18.8693	−	25.8447i	0.589665	−	0.807648i
$33$		0			0
$34$	−20.5492	+	11.2846i	−0.604388	+	0.331899i
$35$	−8.93335	+	7.67643i	−0.255239	+	0.219326i
$36$		0			0
$37$		−	19.5040i		−	0.527136i	−0.964641	−	0.263568i	$-0.915101\pi$
$37$		−	19.5040i		−	0.527136i	0.964641	−	0.263568i	$-0.0848993\pi$
$38$	−0.0375680	−	0.0684113i	−0.000988632	−	0.00180030i
$39$		0			0
$40$	13.4334	+	0.863976i	0.335834	+	0.0215994i
$41$		−	41.0379i		−	1.00092i	−0.865758	−	0.500462i	$-0.833163\pi$
$41$		−	41.0379i		−	1.00092i	0.865758	−	0.500462i	$-0.166837\pi$
$42$		0			0
$43$			23.0681i			0.536468i	0.963354	+	0.268234i	$0.0864400\pi$
$43$			23.0681i			0.536468i	−0.963354	+	0.268234i	$0.913560\pi$
$44$	−40.4786	−	25.7413i	−0.919967	−	0.585030i
$45$		0			0
$46$	−25.6595	−	46.7259i	−0.557815	−	1.01578i
$47$			56.6865i			1.20610i	0.797705	+	0.603048i	$0.206047\pi$
$47$			56.6865i			1.20610i	−0.797705	+	0.603048i	$0.793953\pi$
$48$		0			0
$49$	7.37382	−	48.4420i	0.150486	−	0.988612i
$50$	−21.3417	−	38.8631i	−0.426833	−	0.777263i
$51$		0			0
$52$	54.3134	−	85.4086i	1.04449	−	1.64247i
$53$		−	56.2765i		−	1.06182i	−0.847428	−	0.530910i	$-0.821850\pi$
$53$		−	56.2765i		−	1.06182i	0.847428	−	0.530910i	$-0.178150\pi$
$54$		0			0
$55$		−	20.1791i		−	0.366892i
$56$	−44.7280	+	33.6958i	−0.798714	+	0.601710i
$57$		0			0
$58$	−80.6617	+	44.2953i	−1.39072	+	0.763712i
$59$	−64.4331			−1.09209			−0.546043	−	0.837757i	$-0.683867\pi$
$59$	−64.4331			−1.09209			−0.546043	+	0.837757i	$0.683867\pi$
$60$		0			0
$61$	52.2895			0.857205			0.428603	−	0.903493i	$-0.359006\pi$
$61$	52.2895			0.857205			0.428603	+	0.903493i	$0.359006\pi$
$62$	66.5289	−	36.5343i	1.07305	−	0.589262i
$63$		0			0
$64$	63.4727	+	8.19850i	0.991761	+	0.128102i
$65$	42.5773			0.655035
$66$		0			0
$67$			55.1497i			0.823130i	0.911380	+	0.411565i	$0.135018\pi$
$67$			55.1497i			0.823130i	−0.911380	+	0.411565i	$0.864982\pi$
$68$	−39.5651	−	25.1604i	−0.581840	−	0.370006i
$69$		0			0
$70$	−22.0573	−	8.27068i	−0.315105	−	0.118153i
$71$	8.38597			0.118112			0.0590561	−	0.998255i	$-0.481191\pi$
$71$	8.38597			0.118112			0.0590561	+	0.998255i	$0.481191\pi$
$72$		0			0
$73$			117.406i			1.60830i	0.594426	+	0.804150i	$0.297379\pi$
$73$			117.406i			1.60830i	−0.594426	+	0.804150i	$0.702621\pi$
$74$	34.1917	−	18.7764i	0.462051	−	0.253735i
$75$		0			0
$76$	0.0837628	−	0.131718i	0.00110214	−	0.00173313i
$77$	54.7115	+	63.6699i	0.710539	+	0.826882i
$78$		0			0
$79$	−13.2280			−0.167442			−0.0837212	−	0.996489i	$-0.526681\pi$
$79$	−13.2280			−0.167442			−0.0837212	+	0.996489i	$0.526681\pi$
$80$	11.4176	+	24.3812i	0.142720	+	0.304765i
$81$		0			0
$82$	71.9420	−	39.5069i	0.877341	−	0.481791i
$83$	−19.4050			−0.233795			−0.116897	−	0.993144i	$-0.537295\pi$
$83$	−19.4050			−0.233795			−0.116897	+	0.993144i	$0.537295\pi$
$84$		0			0
$85$		−	19.7237i		−	0.232044i
$86$	−40.4398	+	22.2075i	−0.470231	+	0.258227i
$87$		0			0
$88$	6.15774	−	95.7424i	0.0699743	−	1.08798i
$89$			36.4448i			0.409492i	0.978815	+	0.204746i	$0.0656368\pi$
$89$			36.4448i			0.409492i	−0.978815	+	0.204746i	$0.934363\pi$
$90$		0			0
$91$	−134.342	+	115.440i	−1.47628	+	1.26857i
$92$	57.2112	−	89.9654i	0.621861	−	0.977884i
$93$		0			0
$94$	−99.3749	+	54.5717i	−1.05718	+	0.580550i
$95$	0.0656632			0.000691191
$96$		0			0
$97$			163.122i			1.68167i	0.541292	+	0.840835i	$0.317936\pi$
$97$			163.122i			1.68167i	−0.541292	+	0.840835i	$0.682064\pi$
$98$	92.0205	−	33.7080i	0.938985	−	0.343959i
$99$		0			0
$100$	47.5840	−	74.8265i	0.475840	−	0.748265i
$101$	−115.558			−1.14414			−0.572072	−	0.820204i	$-0.693860\pi$
$101$	−115.558			−1.14414			−0.572072	+	0.820204i	$0.693860\pi$
$102$		0			0
$103$		−	23.6994i		−	0.230091i	−0.993360	−	0.115046i	$-0.963299\pi$
$103$		−	23.6994i		−	0.230091i	0.993360	−	0.115046i	$-0.0367014\pi$
$104$	202.014	+	12.9927i	1.94244	+	0.124929i
$105$		0			0
$106$	98.6561	−	54.1769i	0.930718	−	0.511103i
$107$			96.7170i			0.903898i	0.892044	+	0.451949i	$0.149271\pi$
$107$			96.7170i			0.903898i	−0.892044	+	0.451949i	$0.850729\pi$
$108$		0			0
$109$		−	89.7670i		−	0.823550i	−0.911285	−	0.411775i	$-0.864909\pi$
$109$		−	89.7670i		−	0.823550i	0.911285	−	0.411775i	$-0.135091\pi$
$110$	35.3752	−	19.4262i	0.321592	−	0.176602i
$111$		0			0
$112$	−102.130	−	45.9723i	−0.911876	−	0.410467i
$113$	219.679			1.94406			0.972032	−	0.234848i	$-0.0754594\pi$
$113$	219.679			1.94406			0.972032	+	0.234848i	$0.0754594\pi$
$114$		0			0
$115$	44.8489			0.389990
$116$	−155.305	−	98.7622i	−1.33883	−	0.851398i
$117$		0			0
$118$	−62.0292	−	112.955i	−0.525671	−	0.957247i
$119$	53.4769	+	62.2331i	0.449386	+	0.522967i
$120$		0			0
$121$	−22.8206			−0.188600
$122$	50.3387	+	91.6668i	0.412612	+	0.751367i
$123$		0			0
$124$	128.094	+	81.4579i	1.03301	+	0.656919i
$125$	79.3679			0.634943
$126$		0			0
$127$	47.5294			0.374247			0.187124	−	0.982336i	$-0.440084\pi$
$127$	47.5294			0.374247			0.187124	+	0.982336i	$0.440084\pi$
$128$	46.7322	+	119.164i	0.365095	+	0.930970i
$129$		0			0
$130$	40.9888	+	74.6406i	0.315298	+	0.574158i
$131$	−173.193			−1.32209			−0.661043	−	0.750348i	$-0.729886\pi$
$131$	−173.193			−1.32209			−0.661043	+	0.750348i	$0.729886\pi$
$132$		0			0
$133$	−0.207183	+	0.178032i	−0.00155777	+	0.00133859i
$134$	−96.6809	+	53.0922i	−0.721499	+	0.396211i
$135$		0			0
$136$	6.01878	−	93.5818i	0.0442558	−	0.688101i
$137$	22.7114			0.165777			0.0828884	−	0.996559i	$-0.473585\pi$
$137$	22.7114			0.165777			0.0828884	+	0.996559i	$0.473585\pi$
$138$		0			0
$139$	−73.1490			−0.526252			−0.263126	−	0.964761i	$-0.584753\pi$
$139$	−73.1490			−0.526252			−0.263126	+	0.964761i	$0.584753\pi$
$140$	−6.73539	−	46.6299i	−0.0481099	−	0.333071i
$141$		0			0
$142$	8.07311	+	14.7011i	0.0568529	+	0.103529i
$143$		−	303.457i		−	2.12208i
$144$		0			0
$145$		−	77.4214i		−	0.533941i
$146$	−205.820	+	113.026i	−1.40972	+	0.774149i
$147$		0			0
$148$	65.8322	+	41.8644i	0.444812	+	0.282867i
$149$		−	39.6719i		−	0.266255i	−0.991099	−	0.133127i	$-0.957498\pi$
$149$		−	39.6719i		−	0.266255i	0.991099	−	0.133127i	$-0.0425019\pi$
$150$		0			0
$151$	−75.6271			−0.500842			−0.250421	−	0.968137i	$-0.580569\pi$
$151$	−75.6271			−0.500842			−0.250421	+	0.968137i	$0.580569\pi$
$152$	0.311548	+	0.0200374i	0.00204966	+	0.000131825i
$153$		0			0
$154$	−58.9469	+	157.207i	−0.382772	+	1.02083i
$155$			63.8563i			0.411976i
$156$		0			0
$157$	148.998			0.949034			0.474517	−	0.880246i	$-0.342623\pi$
$157$	148.998			0.949034			0.474517	+	0.880246i	$0.342623\pi$
$158$	−12.7344	−	23.1894i	−0.0805978	−	0.146768i
$159$		0			0
$160$	−31.7502	+	43.4873i	−0.198439	+	0.271796i
$161$	−141.509	+	121.599i	−0.878939	+	0.755272i
$162$		0			0
$163$		−	9.22009i		−	0.0565650i	−0.999600	−	0.0282825i	$-0.990996\pi$
$163$		−	9.22009i		−	0.0565650i	0.999600	−	0.0282825i	$-0.00900379\pi$
$164$	138.516	+	88.0858i	0.844610	+	0.537108i
$165$		0			0
$166$	−18.6810	−	34.0181i	−0.112536	−	0.204928i
$167$			206.771i			1.23815i	0.785332	+	0.619075i	$0.212492\pi$
$167$			206.771i			1.23815i	−0.785332	+	0.619075i	$0.787508\pi$
$168$		0			0
$169$	471.286			2.78867
$170$	34.5769	−	18.9879i	0.203393	−	0.111693i
$171$		0			0
$172$	−77.8622	−	49.5145i	−0.452687	−	0.287875i
$173$	−16.2366			−0.0938532			−0.0469266	−	0.998898i	$-0.514943\pi$
$173$	−16.2366			−0.0938532			−0.0469266	+	0.998898i	$0.514943\pi$
$174$		0			0
$175$	−117.697	+	101.137i	−0.672553	+	0.577924i
$176$	173.770	−	81.3755i	0.987331	−	0.462361i
$177$		0			0
$178$	−63.8899	+	35.0851i	−0.358932	+	0.197107i
$179$		−	19.4905i		−	0.108886i	−0.998517	−	0.0544428i	$-0.982662\pi$
$179$		−	19.4905i		−	0.108886i	0.998517	−	0.0544428i	$-0.0173382\pi$
$180$		0			0
$181$	94.8825			0.524212			0.262106	−	0.965039i	$-0.415583\pi$
$181$	94.8825			0.524212			0.262106	+	0.965039i	$0.415583\pi$
$182$	−331.703	−	124.376i	−1.82254	−	0.683386i
$183$		0			0
$184$	212.792	+	13.6858i	1.15648	+	0.0743796i
$185$			32.8182i			0.177396i
$186$		0			0
$187$	−140.575			−0.751738
$188$	−191.335	−	121.675i	−1.01774	−	0.647206i
$189$		0			0
$190$	0.0632134	+	0.115112i	0.000332702	+	0.000605850i
$191$	−59.6646			−0.312380			−0.156190	−	0.987727i	$-0.549921\pi$
$191$	−59.6646			−0.312380			−0.156190	+	0.987727i	$0.549921\pi$
$192$		0			0
$193$	100.790			0.522228			0.261114	−	0.965308i	$-0.415910\pi$
$193$	100.790			0.522228			0.261114	+	0.965308i	$0.415910\pi$
$194$	−285.963	+	157.036i	−1.47404	+	0.809465i
$195$		0			0
$196$	147.680	+	128.867i	0.753467	+	0.657486i
$197$		−	28.5190i		−	0.144766i	−0.997377	−	0.0723832i	$-0.976940\pi$
$197$		−	28.5190i		−	0.144766i	0.997377	−	0.0723832i	$-0.0230604\pi$
$198$		0			0
$199$			330.734i			1.66198i	0.556288	+	0.830990i	$0.312225\pi$
$199$			330.734i			1.66198i	−0.556288	+	0.830990i	$0.687775\pi$
$200$	176.984	+	11.3829i	0.884921	+	0.0569143i
$201$		0			0
$202$	−111.247	−	202.581i	−0.550729	−	1.00288i
$203$	209.913	+	244.283i	1.03405	+	1.20337i
$204$		0			0
$205$			69.0520i			0.336839i
$206$	41.5465	−	22.8152i	0.201682	−	0.110754i
$207$		0			0
$208$	171.700	+	366.650i	0.825480	+	1.76274i
$209$		−	0.467995i		−	0.00223921i
$210$		0			0
$211$			292.696i			1.38719i	0.720367	+	0.693593i	$0.243973\pi$
$211$			292.696i			1.38719i	−0.720367	+	0.693593i	$0.756027\pi$
$212$	189.951	+	120.794i	0.895995	+	0.569785i
$213$		0			0
$214$	−169.551	+	93.1087i	−0.792294	+	0.435087i
$215$		−	38.8153i		−	0.180536i
$216$		0			0
$217$	−173.134	−	201.482i	−0.797851	−	0.928490i
$218$	157.367	−	86.4180i	0.721867	−	0.396413i
$219$		0			0
$220$	68.1108	+	43.3134i	0.309594	+	0.196879i
$221$		−	296.609i		−	1.34212i
$222$		0			0
$223$		−	180.060i		−	0.807444i	−0.914882	−	0.403722i	$-0.867716\pi$
$223$		−	180.060i		−	0.807444i	0.914882	−	0.403722i	$-0.132284\pi$
$224$	−17.7276	−	223.297i	−0.0791411	−	0.996863i
$225$		0			0
$226$	211.483	+	385.111i	0.935767	+	1.70403i
$227$	80.3777			0.354087			0.177043	−	0.984203i	$-0.443347\pi$
$227$	80.3777			0.354087			0.177043	+	0.984203i	$0.443347\pi$
$228$		0			0
$229$	−25.1773			−0.109944			−0.0549722	−	0.998488i	$-0.517507\pi$
$229$	−25.1773			−0.109944			−0.0549722	+	0.998488i	$0.517507\pi$
$230$	43.1757	+	78.6229i	0.187720	+	0.341838i
$231$		0			0
$232$	23.6255	−	367.336i	0.101834	−	1.58335i
$233$	−266.112			−1.14211			−0.571056	−	0.820911i	$-0.693466\pi$
$233$	−266.112			−1.14211			−0.571056	+	0.820911i	$0.693466\pi$
$234$		0			0
$235$		−	95.3829i		−	0.405885i
$236$	138.302	−	217.482i	0.586027	−	0.921534i
$237$		0			0
$238$	−57.6167	+	153.660i	−0.242087	+	0.645628i
$239$	171.348			0.716937			0.358469	−	0.933542i	$-0.383299\pi$
$239$	171.348			0.716937			0.358469	+	0.933542i	$0.383299\pi$
$240$		0			0
$241$		−	88.4386i		−	0.366965i	−0.983023	−	0.183483i	$-0.941263\pi$
$241$		−	88.4386i		−	0.366965i	0.983023	−	0.183483i	$-0.0587371\pi$
$242$	−21.9692	−	40.0059i	−0.0907819	−	0.165314i
$243$		0			0
$244$	−112.237	+	176.494i	−0.459987	+	0.723335i
$245$	−12.4075	+	81.5104i	−0.0506427	+	0.332695i
$246$		0			0
$247$	0.987456			0.00399780
$248$	−19.4861	+	302.975i	−0.0785728	+	1.22167i
$249$		0			0
$250$	76.4069	+	139.137i	0.305627	+	0.556547i
$251$	−250.857			−0.999428			−0.499714	−	0.866190i	$-0.666562\pi$
$251$	−250.857			−0.999428			−0.499714	+	0.866190i	$0.666562\pi$
$252$		0			0
$253$		−	319.648i		−	1.26343i
$254$	45.7562	+	83.3219i	0.180142	+	0.328039i
$255$		0			0
$256$	−163.913	+	196.643i	−0.640287	+	0.768136i
$257$			259.224i			1.00865i	0.863513	+	0.504326i	$0.168259\pi$
$257$			259.224i			1.00865i	−0.863513	+	0.504326i	$0.831741\pi$
$258$		0			0
$259$	−88.9800	−	103.549i	−0.343552	−	0.399805i
$260$	−91.3899	+	143.712i	−0.351500	+	0.552737i
$261$		0			0
$262$	−166.732	−	303.618i	−0.636381	−	1.15885i
$263$	−16.9363			−0.0643964			−0.0321982	−	0.999482i	$-0.510251\pi$
$263$	−16.9363			−0.0643964			−0.0321982	+	0.999482i	$0.510251\pi$
$264$		0			0
$265$			94.6929i			0.357332i
$266$	−0.511556	−	0.191815i	−0.00192314	−	0.000721107i
$267$		0			0
$268$	−186.148	−	118.376i	−0.694581	−	0.441702i
$269$	−46.9302			−0.174462			−0.0872308	−	0.996188i	$-0.527802\pi$
$269$	−46.9302			−0.174462			−0.0872308	+	0.996188i	$0.527802\pi$
$270$		0			0
$271$		−	485.553i		−	1.79171i	−0.444350	−	0.895853i	$-0.646565\pi$
$271$		−	485.553i		−	1.79171i	0.444350	−	0.895853i	$-0.353435\pi$
$272$	169.849	−	79.5391i	0.624444	−	0.292423i
$273$		0			0
$274$	21.8641	+	39.8145i	0.0797960	+	0.145308i
$275$		−	265.859i		−	0.966760i
$276$		0			0
$277$		−	392.536i		−	1.41710i	−0.705662	−	0.708548i	$-0.749350\pi$
$277$		−	392.536i		−	1.41710i	0.705662	−	0.708548i	$-0.250650\pi$
$278$	−70.4200	−	128.235i	−0.253309	−	0.461276i
$279$		0			0
$280$	75.2611	−	56.6978i	0.268789	−	0.202492i
$281$	−193.018			−0.686898			−0.343449	−	0.939171i	$-0.611595\pi$
$281$	−193.018			−0.686898			−0.343449	+	0.939171i	$0.611595\pi$
$282$		0			0
$283$	−382.634			−1.35206			−0.676031	−	0.736873i	$-0.736302\pi$
$283$	−382.634			−1.35206			−0.676031	+	0.736873i	$0.736302\pi$
$284$	−18.0000	+	28.3053i	−0.0633805	+	0.0996666i
$285$		0			0
$286$	531.979	−	292.136i	1.86007	−	1.02145i
$287$	−187.221	−	217.876i	−0.652337	−	0.759149i
$288$		0			0
$289$	151.597			0.524558
$290$	135.724	−	74.5330i	0.468015	−	0.257010i
$291$		0			0
$292$	−396.282	−	252.006i	−1.35713	−	0.863034i
$293$	310.742			1.06055			0.530276	−	0.847825i	$-0.322088\pi$
$293$	310.742			1.06055			0.530276	+	0.847825i	$0.322088\pi$
$294$		0			0
$295$	108.418			0.367517
$296$	−10.0146	+	155.710i	−0.0338332	+	0.526049i
$297$		0			0
$298$	69.5473	−	38.1919i	0.233380	−	0.128161i
$299$	674.447			2.25568
$300$		0			0
$301$	105.240	+	122.472i	0.349634	+	0.406883i
$302$	−72.8056	−	132.579i	−0.241078	−	0.439003i
$303$		0			0
$304$	0.264798	+	0.565452i	0.000871045	+	0.00186004i
$305$	−87.9844			−0.288473
$306$		0			0
$307$	386.739			1.25974			0.629868	−	0.776702i	$-0.283109\pi$
$307$	386.739			1.25974			0.629868	+	0.776702i	$0.283109\pi$
$308$	−332.342	+	48.0046i	−1.07903	+	0.155859i
$309$		0			0
$310$	−111.944	+	61.4740i	−0.361110	+	0.198303i
$311$		−	289.672i		−	0.931421i	−0.884937	−	0.465710i	$-0.845799\pi$
$311$		−	289.672i		−	0.931421i	0.884937	−	0.465710i	$-0.154201\pi$
$312$		0			0
$313$			205.294i			0.655891i	0.944697	+	0.327945i	$0.106356\pi$
$313$			205.294i			0.655891i	−0.944697	+	0.327945i	$0.893644\pi$
$314$	143.439	+	261.203i	0.456814	+	0.831857i
$315$		0			0
$316$	28.3931	−	44.6485i	0.0898516	−	0.141293i
$317$		−	348.421i		−	1.09912i	−0.835454	−	0.549560i	$-0.814795\pi$
$317$		−	348.421i		−	1.09912i	0.835454	−	0.549560i	$-0.185205\pi$
$318$		0			0
$319$	−551.799			−1.72978
$320$	−106.802	−	13.7951i	−0.333755	−	0.0431097i
$321$		0			0
$322$	−349.400	−	131.012i	−1.08509	−	0.406870i
$323$		−	0.457434i		−	0.00141621i
$324$		0			0
$325$	560.955			1.72601
$326$	16.1634	−	8.87610i	0.0495809	−	0.0272273i
$327$		0			0
$328$	−21.0715	+	327.626i	−0.0642425	+	0.998861i
$329$	258.612	+	300.956i	0.786054	+	0.914761i
$330$		0			0
$331$		−	170.055i		−	0.513761i	−0.966443	−	0.256881i	$-0.917305\pi$
$331$		−	170.055i		−	0.513761i	0.966443	−	0.256881i	$-0.0826947\pi$
$332$	41.6518	−	65.4979i	0.125457	−	0.197283i
$333$		0			0
$334$	−362.482	+	199.057i	−1.08528	+	0.595979i
$335$		−	92.7971i		−	0.277006i
$336$		0			0
$337$	−216.000			−0.640949			−0.320475	−	0.947257i	$-0.603842\pi$
$337$	−216.000			−0.640949			−0.320475	+	0.947257i	$0.603842\pi$
$338$	453.703	+	826.193i	1.34232	+	2.44436i
$339$		0			0
$340$	66.5738	+	42.3359i	0.195805	+	0.124517i
$341$	455.118			1.33466
$342$		0			0
$343$	−181.850	−	290.825i	−0.530176	−	0.847888i
$344$	11.8447	−	184.164i	0.0344322	−	0.535362i
$345$		0			0
$346$	−15.6308	−	28.4638i	−0.0451759	−	0.0822652i
$347$		−	31.9124i		−	0.0919666i	−0.998942	−	0.0459833i	$-0.985358\pi$
$347$		−	31.9124i		−	0.0919666i	0.998942	−	0.0459833i	$-0.0146421\pi$
$348$		0			0
$349$	−27.2479			−0.0780743			−0.0390372	−	0.999238i	$-0.512429\pi$
$349$	−27.2479			−0.0780743			−0.0390372	+	0.999238i	$0.512429\pi$
$350$	−290.605	−	108.966i	−0.830299	−	0.311332i
$351$		0			0
$352$	309.944	+	226.290i	0.880521	+	0.642870i
$353$		−	155.127i		−	0.439454i	−0.975561	−	0.219727i	$-0.929483\pi$
$353$		−	155.127i		−	0.439454i	0.975561	−	0.219727i	$-0.0705166\pi$
$354$		0			0
$355$	−14.1106			−0.0397480
$356$	−123.013	−	78.2268i	−0.345541	−	0.219738i
$357$		0			0
$358$	34.1681	−	18.7634i	0.0954415	−	0.0524116i
$359$	−310.919			−0.866070			−0.433035	−	0.901377i	$-0.642557\pi$
$359$	−310.919			−0.866070			−0.433035	+	0.901377i	$0.642557\pi$
$360$		0			0
$361$	−360.998			−0.999996
$362$	91.3426	+	166.335i	0.252328	+	0.459488i
$363$		0			0
$364$	−101.288	−	701.231i	−0.278264	−	1.92646i
$365$		−	197.552i		−	0.541238i
$366$		0			0
$367$			483.310i			1.31692i	0.752615	+	0.658461i	$0.228792\pi$
$367$			483.310i			1.31692i	−0.752615	+	0.658461i	$0.771208\pi$
$368$	180.861	+	386.212i	0.491469	+	1.04949i
$369$		0			0
$370$	−57.5323	+	31.5938i	−0.155493	+	0.0853887i
$371$	−256.741	−	298.779i	−0.692024	−	0.805335i
$372$		0			0
$373$		−	31.2857i		−	0.0838758i	−0.999120	−	0.0419379i	$-0.986647\pi$
$373$		−	31.2857i		−	0.0838758i	0.999120	−	0.0419379i	$-0.0133532\pi$
$374$	−135.330	−	246.437i	−0.361846	−	0.658922i
$375$		0			0
$376$	29.1065	−	452.557i	0.0774110	−	1.20361i
$377$		−	1164.28i		−	3.08827i
$378$		0			0
$379$		−	362.325i		−	0.956003i	−0.878359	−	0.478002i	$-0.841361\pi$
$379$		−	362.325i		−	0.956003i	0.878359	−	0.478002i	$-0.158639\pi$
$380$	−0.140943	+	0.221634i	−0.000370901	+	0.000583247i
$381$		0			0
$382$	−57.4387	−	104.596i	−0.150363	−	0.273811i
$383$			91.9648i			0.240117i	0.992767	+	0.120058i	$0.0383082\pi$
$383$			91.9648i			0.240117i	−0.992767	+	0.120058i	$0.961692\pi$
$384$		0			0
$385$	−92.0597	−	107.133i	−0.239116	−	0.278269i
$386$	97.0298	+	176.691i	0.251373	+	0.457749i
$387$		0			0
$388$	−550.588	−	350.133i	−1.41904	−	0.902404i
$389$			33.9094i			0.0871706i	0.999050	+	0.0435853i	$0.0138780\pi$
$389$			33.9094i			0.0871706i	−0.999050	+	0.0435853i	$0.986122\pi$
$390$		0			0
$391$		−	312.434i		−	0.799064i
$392$	−83.7422	+	382.951i	−0.213628	+	0.976915i
$393$		0			0
$394$	49.9955	−	27.4550i	0.126892	−	0.0696827i
$395$	22.2579			0.0563490
$396$		0			0
$397$	−467.018			−1.17637			−0.588184	−	0.808727i	$-0.700157\pi$
$397$	−467.018			−1.17637			−0.588184	+	0.808727i	$0.700157\pi$
$398$	−579.797	+	318.395i	−1.45678	+	0.799987i
$399$		0			0
$400$	150.426	+	321.222i	0.376066	+	0.803056i
$401$	87.5191			0.218252			0.109126	−	0.994028i	$-0.465195\pi$
$401$	87.5191			0.218252			0.109126	+	0.994028i	$0.465195\pi$
$402$		0			0
$403$			960.285i			2.38284i
$404$	248.040	−	390.046i	0.613961	−	0.965461i
$405$		0			0
$406$	−226.163	+	603.159i	−0.557051	+	1.48561i
$407$	233.902			0.574699
$408$		0			0
$409$		−	604.684i		−	1.47845i	−0.673461	−	0.739223i	$-0.735193\pi$
$409$		−	604.684i		−	1.47845i	0.673461	−	0.739223i	$-0.264807\pi$
$410$	−121.052	+	66.4758i	−0.295250	+	0.162136i
$411$		0			0
$412$	79.9930	+	50.8695i	0.194158	+	0.123470i
$413$	−342.084	+	293.953i	−0.828290	+	0.711750i
$414$		0			0
$415$	32.6515			0.0786784
$416$	−477.466	+	653.972i	−1.14775	+	1.57205i
$417$		0			0
$418$	0.820424	−	0.450535i	0.00196274	−	0.00107784i
$419$	−484.795			−1.15703			−0.578514	−	0.815672i	$-0.696367\pi$
$419$	−484.795			−1.15703			−0.578514	+	0.815672i	$0.696367\pi$
$420$		0			0
$421$			606.917i			1.44161i	0.693139	+	0.720804i	$0.256227\pi$
$421$			606.917i			1.44161i	−0.693139	+	0.720804i	$0.743773\pi$
$422$	−513.115	+	281.776i	−1.21591	+	0.667717i
$423$		0			0
$424$	−28.8960	+	449.283i	−0.0681509	+	1.05963i
$425$		−	259.859i		−	0.611434i
$426$		0			0
$427$	277.612	−	238.552i	0.650146	−	0.558670i
$428$	−326.451	−	207.598i	−0.762735	−	0.485042i
$429$		0			0
$430$	68.0456	−	37.3672i	0.158246	−	0.0869004i
$431$	−774.667			−1.79737			−0.898685	−	0.438594i	$-0.855477\pi$
$431$	−774.667			−1.79737			−0.898685	+	0.438594i	$0.855477\pi$
$432$		0			0
$433$			469.957i			1.08535i	0.839942	+	0.542676i	$0.182589\pi$
$433$			469.957i			1.08535i	−0.839942	+	0.542676i	$0.817411\pi$
$434$	186.536	−	497.479i	0.429807	−	1.14627i
$435$		0			0
$436$	302.992	+	192.680i	0.694936	+	0.441927i
$437$	1.04014			0.00238018
$438$		0			0
$439$			19.2308i			0.0438060i	0.999760	+	0.0219030i	$0.00697250\pi$
$439$			19.2308i			0.0438060i	−0.999760	+	0.0219030i	$0.993028\pi$
$440$	−10.3613	+	161.100i	−0.0235483	+	0.366136i
$441$		0			0
$442$	519.974	−	285.543i	1.17641	−	0.646026i
$443$		−	702.218i		−	1.58514i	−0.609779	−	0.792572i	$-0.708742\pi$
$443$		−	702.218i		−	1.58514i	0.609779	−	0.792572i	$-0.291258\pi$
$444$		0			0
$445$		−	61.3234i		−	0.137805i
$446$	315.656	−	173.342i	0.707750	−	0.388660i
$447$		0			0
$448$	374.388	−	246.044i	0.835687	−	0.549206i
$449$	488.093			1.08707			0.543533	−	0.839388i	$-0.317086\pi$
$449$	488.093			1.08707			0.543533	+	0.839388i	$0.317086\pi$
$450$		0			0
$451$	492.148			1.09124
$452$	−471.530	+	741.487i	−1.04321	+	1.64046i
$453$		0			0
$454$	77.3790	+	140.907i	0.170438	+	0.310368i
$455$	226.048	−	194.243i	0.496810	−	0.426908i
$456$		0			0
$457$	−732.332			−1.60248			−0.801239	−	0.598344i	$-0.795825\pi$
$457$	−732.332			−1.60248			−0.801239	+	0.598344i	$0.795825\pi$
$458$	−24.2380	−	44.1373i	−0.0529213	−	0.0963697i
$459$		0			0
$460$	−96.2658	+	151.379i	−0.209274	+	0.329085i
$461$	−234.921			−0.509591			−0.254796	−	0.966995i	$-0.582008\pi$
$461$	−234.921			−0.509591			−0.254796	+	0.966995i	$0.582008\pi$
$462$		0			0
$463$	899.121			1.94195			0.970974	−	0.239187i	$-0.0768809\pi$
$463$	899.121			1.94195			0.970974	+	0.239187i	$0.0768809\pi$
$464$	666.707	−	312.215i	1.43687	−	0.672877i
$465$		0			0
$466$	−256.184	−	466.511i	−0.549751	−	1.00110i
$467$	−436.886			−0.935516			−0.467758	−	0.883857i	$-0.654938\pi$
$467$	−436.886			−0.935516			−0.467758	+	0.883857i	$0.654938\pi$
$468$		0			0
$469$	251.601	+	292.797i	0.536462	+	0.624301i
$470$	167.212	−	91.8244i	0.355770	−	0.195371i
$471$		0			0
$472$	514.402	+	33.0841i	1.08983	+	0.0700935i
$473$	−276.645			−0.584873
$474$		0			0
$475$	0.865111			0.00182129
$476$	−324.842	+	46.9213i	−0.682441	+	0.0985741i
$477$		0			0
$478$	164.955	+	300.384i	0.345095	+	0.628417i
$479$			480.110i			1.00232i	0.865356	+	0.501158i	$0.167093\pi$
$479$			480.110i			1.00232i	−0.865356	+	0.501158i	$0.832907\pi$
$480$		0			0
$481$			493.527i			1.02604i
$482$	155.038	−	85.1391i	0.321656	−	0.176637i
$483$		0			0
$484$	48.9833	−	77.0268i	0.101205	−	0.159146i
$485$		−	274.475i		−	0.565929i
$486$		0			0
$487$	−338.026			−0.694098			−0.347049	−	0.937847i	$-0.612816\pi$
$487$	−338.026			−0.694098			−0.347049	+	0.937847i	$0.612816\pi$
$488$	−417.454	−	26.8489i	−0.855438	−	0.0550181i
$489$		0			0
$490$	−154.837	+	56.7183i	−0.315994	+	0.115752i
$491$			824.167i			1.67855i	0.543709	+	0.839274i	$0.317019\pi$
$491$			824.167i			1.67855i	−0.543709	+	0.839274i	$0.682981\pi$
$492$		0			0
$493$	−539.347			−1.09401
$494$	0.950616	+	1.73107i	0.00192432	+	0.00350419i
$495$		0			0
$496$	−549.893	+	257.511i	−1.10865	+	0.519176i
$497$	44.5222	−	38.2579i	0.0895820	−	0.0769777i
$498$		0			0
$499$		−	617.384i		−	1.23724i	−0.785689	−	0.618621i	$-0.787691\pi$
$499$		−	617.384i		−	1.23724i	0.785689	−	0.618621i	$-0.212309\pi$
$500$	−170.359	+	267.892i	−0.340718	+	0.535784i
$501$		0			0
$502$	−241.498	−	439.767i	−0.481071	−	0.876030i
$503$			995.122i			1.97837i	0.146663	+	0.989187i	$0.453147\pi$
$503$			995.122i			1.97837i	−0.146663	+	0.989187i	$0.546853\pi$
$504$		0			0
$505$	194.443			0.385036
$506$	560.362	−	307.722i	1.10743	−	0.608147i
$507$		0			0
$508$	−102.019	+	160.427i	−0.200826	+	0.315801i
$509$	77.0714			0.151417			0.0757086	−	0.997130i	$-0.475878\pi$
$509$	77.0714			0.151417			0.0757086	+	0.997130i	$0.475878\pi$
$510$		0			0
$511$	535.622	+	623.324i	1.04818	+	1.21981i
$512$	−502.525	−	98.0438i	−0.981494	−	0.191492i
$513$		0			0
$514$	−454.435	+	249.552i	−0.884114	+	0.485511i
$515$			39.8775i			0.0774321i
$516$		0			0
$517$	−679.814			−1.31492
$518$	95.8682	−	255.674i	0.185074	−	0.493578i
$519$		0			0
$520$	−339.916	−	21.8619i	−0.653684	−	0.0420422i
$521$			503.937i			0.967249i	0.875276	+	0.483624i	$0.160680\pi$
$521$			503.937i			0.967249i	−0.875276	+	0.483624i	$0.839320\pi$
$522$		0			0
$523$	499.828			0.955694			0.477847	−	0.878443i	$-0.341417\pi$
$523$	499.828			0.955694			0.477847	+	0.878443i	$0.341417\pi$
$524$	371.750	−	584.582i	0.709447	−	1.11561i
$525$		0			0
$526$	−16.3044	−	29.6903i	−0.0309970	−	0.0564454i
$527$	444.847			0.844112
$528$		0			0
$529$	181.431			0.342969
$530$	−166.003	+	91.1601i	−0.313212	+	0.172000i
$531$		0			0
$532$	−0.156208	−	1.08145i	−0.000293624	−	0.00203279i
$533$			1038.42i			1.94825i
$534$		0			0
$535$		−	162.740i		−	0.304187i
$536$	28.3175	−	440.288i	0.0528311	−	0.821433i
$537$		0			0
$538$	−45.1793	−	82.2715i	−0.0839764	−	0.152921i
$539$	580.942	+	88.4307i	1.07781	+	0.164064i
$540$		0			0
$541$		−	688.182i		−	1.27206i	−0.771666	−	0.636028i	$-0.780576\pi$
$541$		−	688.182i		−	1.27206i	0.771666	−	0.636028i	$-0.219424\pi$
$542$	851.203	−	467.438i	1.57049	−	0.862431i
$543$		0			0
$544$	302.949	+	221.184i	0.556892	+	0.406588i
$545$			151.045i			0.277147i
$546$		0			0
$547$			448.735i			0.820357i	0.912005	+	0.410178i	$0.134534\pi$
$547$			448.735i			0.820357i	−0.912005	+	0.410178i	$0.865466\pi$
$548$	−48.7489	+	76.6582i	−0.0889578	+	0.139887i
$549$		0			0
$550$	466.067	−	255.940i	0.847395	−	0.465346i
$551$		−	1.79557i		−	0.00325874i
$552$		0			0
$553$	−70.2290	+	60.3477i	−0.126996	+	0.109128i
$554$	688.139	−	377.891i	1.24213	−	0.682114i
$555$		0			0
$556$	157.011	−	246.901i	0.282393	−	0.444067i
$557$			540.742i			0.970811i	0.874289	+	0.485405i	$0.161328\pi$
$557$			540.742i			0.970811i	−0.874289	+	0.485405i	$0.838672\pi$
$558$		0			0
$559$		−	583.713i		−	1.04421i
$560$	171.848	+	77.3547i	0.306871	+	0.138133i
$561$		0			0
$562$	−185.817	−	338.373i	−0.330636	−	0.602087i
$563$	506.381			0.899434			0.449717	−	0.893171i	$-0.351525\pi$
$563$	506.381			0.899434			0.449717	+	0.893171i	$0.351525\pi$
$564$		0			0
$565$	−369.641			−0.654231
$566$	−368.358	−	670.780i	−0.650810	−	1.18512i
$567$		0			0
$568$	−66.9494	−	4.30590i	−0.117869	−	0.00758081i
$569$	−704.539			−1.23821			−0.619103	−	0.785310i	$-0.712504\pi$
$569$	−704.539			−1.23821			−0.619103	+	0.785310i	$0.712504\pi$
$570$		0			0
$571$		−	585.849i		−	1.02601i	−0.858387	−	0.513003i	$-0.828533\pi$
$571$		−	585.849i		−	1.02601i	0.858387	−	0.513003i	$-0.171467\pi$
$572$	1024.26	+	651.355i	1.79067	+	1.13873i
$573$		0			0
$574$	201.714	−	537.957i	0.351418	−	0.937206i
$575$	590.883			1.02762
$576$		0			0
$577$		−	134.209i		−	0.232598i	−0.993214	−	0.116299i	$-0.962897\pi$
$577$		−	134.209i		−	0.232598i	0.993214	−	0.116299i	$-0.0371031\pi$
$578$	145.941	+	265.759i	0.252494	+	0.459791i
$579$		0			0
$580$	261.322	+	166.181i	0.450555	+	0.286519i
$581$	−103.024	+	88.5281i	−0.177321	+	0.152372i
$582$		0			0
$583$	674.897			1.15763
$584$	60.2839	−	937.311i	0.103226	−	1.60498i
$585$		0			0
$586$	299.149	+	544.750i	0.510493	+	0.929607i
$587$	540.615			0.920979			0.460489	−	0.887665i	$-0.347674\pi$
$587$	540.615			0.920979			0.460489	+	0.887665i	$0.347674\pi$
$588$		0			0
$589$			1.48096i			0.00251437i
$590$	104.373	+	190.063i	0.176903	+	0.322140i
$591$		0			0
$592$	−282.611	+	132.345i	−0.477383	+	0.223556i
$593$		−	422.070i		−	0.711754i	−0.934533	−	0.355877i	$-0.884182\pi$
$593$		−	422.070i		−	0.711754i	0.934533	−	0.355877i	$-0.115818\pi$
$594$		0			0
$595$	−89.9823	−	104.716i	−0.151231	−	0.175993i
$596$	133.905	+	85.1537i	0.224673	+	0.142875i
$597$		0			0
$598$	649.285	+	1182.35i	1.08576	+	1.97717i
$599$	−580.079			−0.968412			−0.484206	−	0.874954i	$-0.660891\pi$
$599$	−580.079			−0.968412			−0.484206	+	0.874954i	$0.660891\pi$
$600$		0			0
$601$			112.203i			0.186694i	0.995634	+	0.0933471i	$0.0297566\pi$
$601$			112.203i			0.186694i	−0.995634	+	0.0933471i	$0.970243\pi$
$602$	−113.387	+	302.395i	−0.188350	+	0.502317i
$603$		0			0
$604$	162.330	−	255.265i	0.268758	−	0.422625i
$605$	38.3988			0.0634692
$606$		0			0
$607$			432.839i			0.713078i	0.934280	+	0.356539i	$0.116043\pi$
$607$			432.839i			0.713078i	−0.934280	+	0.356539i	$0.883957\pi$
$608$	−0.736354	+	1.00856i	−0.00121111	+	0.00165882i
$609$		0			0
$610$	−84.7019	−	154.242i	−0.138856	−	0.252856i
$611$		−	1434.39i		−	2.34761i
$612$		0			0
$613$			29.6778i			0.0484141i	0.999707	+	0.0242070i	$0.00770610\pi$
$613$			29.6778i			0.0484141i	−0.999707	+	0.0242070i	$0.992294\pi$
$614$	372.310	+	677.977i	0.606369	+	1.10420i
$615$		0			0
$616$	−404.098	−	536.402i	−0.656002	−	0.870782i
$617$	465.733			0.754835			0.377417	−	0.926043i	$-0.376812\pi$
$617$	465.733			0.754835			0.377417	+	0.926043i	$0.376812\pi$
$618$		0			0
$619$	−903.672			−1.45989			−0.729945	−	0.683506i	$-0.760454\pi$
$619$	−903.672			−1.45989			−0.729945	+	0.683506i	$0.760454\pi$
$620$	−215.535	−	137.064i	−0.347638	−	0.221071i
$621$		0			0
$622$	507.813	−	278.865i	0.816419	−	0.448336i
$623$	166.266	+	193.490i	0.266880	+	0.310578i
$624$		0			0
$625$	420.671			0.673073
$626$	−359.893	+	197.635i	−0.574909	+	0.315710i
$627$		0			0
$628$	−319.817	+	502.916i	−0.509263	+	0.800822i
$629$	228.624			0.363472
$630$		0			0
$631$	−125.556			−0.198979			−0.0994897	−	0.995039i	$-0.531721\pi$
$631$	−125.556			−0.198979			−0.0994897	+	0.995039i	$0.531721\pi$
$632$	105.605	+	6.79209i	0.167097	+	0.0107470i
$633$		0			0
$634$	610.803	−	335.422i	0.963412	−	0.529057i
$635$	−79.9748			−0.125945
$636$		0			0
$637$	−186.586	+	1225.77i	−0.292914	+	1.92429i
$638$	−531.212	−	967.337i	−0.832621	−	1.51620i
$639$		0			0
$640$	−78.6334	−	200.510i	−0.122865	−	0.313297i
$641$	849.006			1.32450			0.662251	−	0.749282i	$-0.269601\pi$
$641$	849.006			1.32450			0.662251	+	0.749282i	$0.269601\pi$
$642$		0			0
$643$	756.458			1.17645			0.588225	−	0.808697i	$-0.299827\pi$
$643$	756.458			1.17645			0.588225	+	0.808697i	$0.299827\pi$
$644$	−106.692	−	738.644i	−0.165671	−	1.14696i
$645$		0			0
$646$	0.801910	−	0.440368i	0.00124135	−	0.000681685i
$647$		−	544.689i		−	0.841868i	−0.907091	−	0.420934i	$-0.861702\pi$
$647$		−	544.689i		−	0.841868i	0.907091	−	0.420934i	$-0.138298\pi$
$648$		0			0
$649$		−	772.715i		−	1.19062i
$650$	540.027	+	983.388i	0.830810	+	1.51290i
$651$		0			0
$652$	31.1207	+	19.7904i	0.0477312	+	0.0303534i
$653$			170.803i			0.261567i	0.991411	+	0.130784i	$0.0417493\pi$
$653$			170.803i			0.261567i	−0.991411	+	0.130784i	$0.958251\pi$
$654$		0			0
$655$	291.422			0.444918
$656$	−594.635	+	278.464i	−0.906455	+	0.424487i
$657$		0			0
$658$	−278.632	+	743.090i	−0.423452	+	1.12932i
$659$			438.353i			0.665180i	0.943072	+	0.332590i	$0.107922\pi$
$659$			438.353i			0.665180i	−0.943072	+	0.332590i	$0.892078\pi$
$660$		0			0
$661$	−433.173			−0.655330			−0.327665	−	0.944794i	$-0.606262\pi$
$661$	−433.173			−0.655330			−0.327665	+	0.944794i	$0.606262\pi$
$662$	298.117	−	163.711i	0.450328	−	0.247297i
$663$		0			0
$664$	154.920	+	9.96377i	0.233313	+	0.0150057i
$665$	0.348615	−	0.299564i	0.000524232	−	0.000450473i
$666$		0			0
$667$		−	1226.40i		−	1.83868i
$668$	−697.918	−	443.824i	−1.04479	−	0.664406i
$669$		0			0
$670$	162.679	−	89.3350i	0.242804	−	0.133336i
$671$			627.083i			0.934551i
$672$		0			0
$673$	800.284			1.18913			0.594565	−	0.804048i	$-0.297324\pi$
$673$	800.284			1.18913			0.594565	+	0.804048i	$0.297324\pi$
$674$	−207.941	−	378.661i	−0.308518	−	0.561812i
$675$		0			0
$676$	−1011.59	+	1590.74i	−1.49644	+	2.35316i
$677$	−1235.04			−1.82428			−0.912142	−	0.409875i	$-0.865572\pi$
$677$	−1235.04			−1.82428			−0.912142	+	0.409875i	$0.865572\pi$
$678$		0			0
$679$	744.185	+	866.037i	1.09600	+	1.27546i
$680$	−10.1274	+	157.464i	−0.0148933	+	0.231565i
$681$		0			0
$682$	438.138	+	797.849i	0.642431	+	1.16987i
$683$			716.152i			1.04854i	0.851552	+	0.524269i	$0.175662\pi$
$683$			716.152i			1.04854i	−0.851552	+	0.524269i	$0.824338\pi$
$684$		0			0
$685$	−38.2151			−0.0557885
$686$	334.769	−	598.770i	0.488001	−	0.872843i
$687$		0			0
$688$	334.254	−	156.529i	0.485835	−	0.227513i
$689$			1424.01i			2.06678i
$690$		0			0
$691$	−66.2153			−0.0958253			−0.0479126	−	0.998852i	$-0.515257\pi$
$691$	−66.2153			−0.0958253			−0.0479126	+	0.998852i	$0.515257\pi$
$692$	34.8510	−	54.8037i	0.0503628	−	0.0791961i
$693$		0			0
$694$	55.9444	−	30.7218i	0.0806115	−	0.0442677i
$695$	123.083			0.177098
$696$		0			0
$697$	481.042			0.690161
$698$	−26.2314	−	47.7673i	−0.0375808	−	0.0684345i
$699$		0			0
$700$	−88.7386	−	614.349i	−0.126769	−	0.877641i
$701$			172.520i			0.246106i	0.992400	+	0.123053i	$0.0392685\pi$
$701$			172.520i			0.246106i	−0.992400	+	0.123053i	$0.960732\pi$
$702$		0			0
$703$			0.761123i			0.00108268i
$704$	−98.3207	+	761.198i	−0.139660	+	1.08125i
$705$		0			0
$706$	271.947	−	149.340i	0.385195	−	0.211529i
$707$	−613.515	+	527.194i	−0.867773	+	0.745677i
$708$		0			0
$709$			967.706i			1.36489i	0.730937	+	0.682444i	$0.239083\pi$
$709$			967.706i			1.36489i	−0.730937	+	0.682444i	$0.760917\pi$
$710$	−13.5841	−	24.7367i	−0.0191326	−	0.0348404i
$711$		0			0
$712$	18.7131	−	290.957i	0.0262825	−	0.408647i
$713$			1011.52i			1.41868i
$714$		0			0
$715$			510.609i			0.714138i
$716$	65.7866	+	41.8354i	0.0918808	+	0.0584293i
$717$		0			0
$718$	−299.319	−	545.060i	−0.416879	−	0.759137i
$719$			248.215i			0.345222i	0.984990	+	0.172611i	$0.0552204\pi$
$719$			248.215i			0.345222i	−0.984990	+	0.172611i	$0.944780\pi$
$720$		0			0
$721$	−108.120	−	125.823i	−0.149958	−	0.174512i
$722$	−347.530	−	632.852i	−0.481344	−	0.876527i
$723$		0			0
$724$	−203.660	+	320.258i	−0.281299	+	0.442346i
$725$		−	1020.03i		−	1.40693i
$726$		0			0
$727$			350.160i			0.481651i	0.970568	+	0.240825i	$0.0774181\pi$
$727$			350.160i			0.481651i	−0.970568	+	0.240825i	$0.922582\pi$
$728$	1131.79	−	852.634i	1.55466	−	1.17120i
$729$		0			0
$730$	346.320	−	190.182i	0.474412	−	0.260523i
$731$	−270.402			−0.369907
$732$		0			0
$733$	1193.91			1.62880			0.814398	−	0.580306i	$-0.197067\pi$
$733$	1193.91			1.62880			0.814398	+	0.580306i	$0.197067\pi$
$734$	−847.272	+	465.279i	−1.15432	+	0.633895i
$735$		0			0
$736$	−502.940	+	688.863i	−0.683343	+	0.935955i
$737$	−661.384			−0.897401
$738$		0			0
$739$			459.023i			0.621141i	0.950550	+	0.310571i	$0.100520\pi$
$739$			459.023i			0.621141i	−0.950550	+	0.310571i	$0.899480\pi$
$740$	−110.772	−	70.4426i	−0.149692	−	0.0951927i
$741$		0			0
$742$	276.616	−	737.715i	0.372798	−	0.994225i
$743$	−115.842			−0.155911			−0.0779555	−	0.996957i	$-0.524839\pi$
$743$	−115.842			−0.155911			−0.0779555	+	0.996957i	$0.524839\pi$
$744$		0			0
$745$			66.7535i			0.0896020i
$746$	54.8457	−	30.1185i	0.0735197	−	0.0403733i
$747$		0			0
$748$	301.737	−	474.485i	0.403392	−	0.634339i
$749$	441.236	+	513.484i	0.589101	+	0.685559i
$750$		0			0
$751$	−995.994			−1.32622			−0.663112	−	0.748520i	$-0.730765\pi$
$751$	−995.994			−1.32622			−0.663112	+	0.748520i	$0.730765\pi$
$752$	821.381	−	384.648i	1.09226	−	0.511499i
$753$		0			0
$754$	2041.05	−	1120.84i	2.70697	−	1.48653i
$755$	127.253			0.168547
$756$		0			0
$757$			389.915i			0.515079i	0.966268	+	0.257540i	$0.0829118\pi$
$757$			389.915i			0.515079i	−0.966268	+	0.257540i	$0.917088\pi$
$758$	635.178	−	348.808i	0.837966	−	0.460168i
$759$		0			0
$760$	−0.524222	−	0.0337157i	−0.000689766	−	4.43628e-5i
$761$		−	859.447i		−	1.12937i	−0.825308	−	0.564683i	$-0.808999\pi$
$761$		−	859.447i		−	1.12937i	0.825308	−	0.564683i	$-0.191001\pi$
$762$		0			0
$763$	−409.529	−	476.585i	−0.536736	−	0.624620i
$764$	128.067	−	201.387i	0.167627	−	0.263596i
$765$		0			0
$766$	−161.220	+	88.5338i	−0.210470	+	0.115579i
$767$	1630.41			2.12569
$768$		0			0
$769$		−	310.638i		−	0.403951i	−0.979391	−	0.201975i	$-0.935264\pi$
$769$		−	310.638i		−	0.403951i	0.979391	−	0.201975i	$-0.0647361\pi$
$770$	99.1864	−	264.523i	0.128813	−	0.343536i
$771$		0			0
$772$	−216.341	+	340.198i	−0.280234	+	0.440672i
$773$	−968.383			−1.25276			−0.626380	−	0.779518i	$-0.715464\pi$
$773$	−968.383			−1.25276			−0.626380	+	0.779518i	$0.715464\pi$
$774$		0			0
$775$			841.306i			1.08556i
$776$	83.7574	−	1302.29i	0.107935	−	1.67820i
$777$		0			0
$778$	−59.4452	+	32.6443i	−0.0764077	+	0.0419592i
$779$			1.60146i			0.00205579i
$780$		0			0
$781$			100.569i			0.128769i
$782$	547.716	−	300.778i	0.700405	−	0.384626i
$783$		0			0
$784$	−751.954	+	221.858i	−0.959125	+	0.282983i
$785$	−250.710			−0.319376
$786$		0			0
$787$	705.562			0.896522			0.448261	−	0.893903i	$-0.352044\pi$
$787$	705.562			0.896522			0.448261	+	0.893903i	$0.352044\pi$
$788$	96.2606	+	61.2145i	0.122158	+	0.0776834i
$789$		0			0
$790$	21.4275	+	39.0194i	0.0271234	+	0.0493917i
$791$	1166.31	−	1002.21i	1.47447	−	1.26701i
$792$		0			0
$793$	−1323.13			−1.66851
$794$	−449.594	−	818.711i	−0.566240	−	1.03112i
$795$		0			0
$796$	−1116.33	−	709.903i	−1.40243	−	0.891838i
$797$	−53.1630			−0.0667039			−0.0333519	−	0.999444i	$-0.510618\pi$
$797$	−53.1630			−0.0667039			−0.0333519	+	0.999444i	$0.510618\pi$
$798$		0			0
$799$	−664.473			−0.831631
$800$	−418.308	+	572.945i	−0.522885	+	0.716181i
$801$		0			0
$802$	84.2540	+	153.426i	0.105055	+	0.191305i
$803$	−1407.99			−1.75342
$804$		0			0
$805$	238.109	−	204.607i	0.295787	−	0.254170i
$806$	−1683.44	+	924.458i	−2.08863	+	1.14697i
$807$		0			0
$808$	922.562	+	59.3352i	1.14178	+	0.0734347i
$809$	−1346.92			−1.66492			−0.832460	−	0.554086i	$-0.813068\pi$
$809$	−1346.92			−1.66492			−0.832460	+	0.554086i	$0.813068\pi$
$810$		0			0
$811$	−507.939			−0.626313			−0.313156	−	0.949702i	$-0.601386\pi$
$811$	−507.939			−0.626313			−0.313156	+	0.949702i	$0.601386\pi$
$812$	−1275.10	+	184.180i	−1.57032	+	0.226822i
$813$		0			0
$814$	225.176	+	410.045i	0.276629	+	0.503741i
$815$			15.5141i			0.0190357i
$816$		0			0
$817$		−	0.900208i		−	0.00110185i
$818$	1060.05	−	582.125i	1.29590	−	0.711644i
$819$		0			0
$820$	−233.072	−	148.217i	−0.284235	−	0.180752i
$821$			233.428i			0.284321i	0.989844	+	0.142160i	$0.0454049\pi$
$821$			233.428i			0.284321i	−0.989844	+	0.142160i	$0.954595\pi$
$822$		0			0
$823$	20.9805			0.0254928			0.0127464	−	0.999919i	$-0.495943\pi$
$823$	20.9805			0.0254928			0.0127464	+	0.999919i	$0.495943\pi$
$824$	−12.1688	+	189.204i	−0.0147680	+	0.229617i
$825$		0			0
$826$	−844.638	−	316.708i	−1.02256	−	0.383424i
$827$			337.263i			0.407815i	0.978990	+	0.203908i	$0.0653642\pi$
$827$			337.263i			0.407815i	−0.978990	+	0.203908i	$0.934636\pi$
$828$		0			0
$829$	−444.428			−0.536102			−0.268051	−	0.963405i	$-0.586379\pi$
$829$	−444.428			−0.536102			−0.268051	+	0.963405i	$0.586379\pi$
$830$	31.4334	+	57.2402i	0.0378715	+	0.0689641i
$831$		0			0
$832$	−1606.11	−	207.454i	−1.93041	−	0.249344i
$833$	567.832	+	86.4351i	0.681671	+	0.103764i
$834$		0			0
$835$		−	347.921i		−	0.416672i
$836$	1.57963	+	1.00453i	0.00188951	+	0.00120159i
$837$		0			0
$838$	−466.708	−	849.875i	−0.556931	−	1.01417i
$839$		−	1330.43i		−	1.58573i	−0.609396	−	0.792866i	$-0.708588\pi$
$839$		−	1330.43i		−	1.58573i	0.609396	−	0.792866i	$-0.291412\pi$
$840$		0			0
$841$	−1276.10			−1.51736
$842$	−1063.96	+	584.274i	−1.26361	+	0.693912i
$843$		0			0
$844$	−987.943	−	628.258i	−1.17055	−	0.744381i
$845$	−793.004			−0.938466
$846$		0			0
$847$	−121.158	+	104.111i	−0.143043	+	0.122917i
$848$	−815.439	+	381.865i	−0.961603	+	0.450313i
$849$		0			0
$850$	455.550	−	250.165i	0.535941	−	0.294311i
$851$			519.858i			0.610879i
$852$		0			0
$853$	−1439.08			−1.68708			−0.843540	−	0.537066i	$-0.819533\pi$
$853$	−1439.08			−1.68708			−0.843540	+	0.537066i	$0.819533\pi$
$854$	685.451	+	257.019i	0.802636	+	0.300959i
$855$		0			0
$856$	49.6608	−	772.141i	0.0580150	−	0.902034i
$857$		−	895.486i		−	1.04491i	−0.852668	−	0.522454i	$-0.825017\pi$
$857$		−	895.486i		−	1.04491i	0.852668	−	0.522454i	$-0.174983\pi$
$858$		0			0
$859$	530.971			0.618127			0.309064	−	0.951041i	$-0.399984\pi$
$859$	530.971			0.618127			0.309064	+	0.951041i	$0.399984\pi$
$860$	131.014	+	83.3150i	0.152342	+	0.0968780i
$861$		0			0
$862$	−745.765	−	1358.04i	−0.865157	−	1.57545i
$863$	−597.284			−0.692102			−0.346051	−	0.938216i	$-0.612478\pi$
$863$	−597.284			−0.692102			−0.346051	+	0.938216i	$0.612478\pi$
$864$		0			0
$865$	27.3203			0.0315842
$866$	−823.864	+	452.424i	−0.951344	+	0.522430i
$867$		0			0
$868$	1051.69	−	151.909i	1.21162	−	0.175011i
$869$		−	158.637i		−	0.182551i
$870$		0			0
$871$		−	1395.50i		−	1.60218i
$872$	−46.0922	+	716.655i	−0.0528580	+	0.821852i
$873$		0			0
$874$	1.00133	+	1.82343i	0.00114569	+	0.00208630i
$875$	421.375	−	362.087i	0.481571	−	0.413814i
$876$		0			0
$877$			1682.09i			1.91801i	0.283396	+	0.959003i	$0.408539\pi$
$877$			1682.09i			1.91801i	−0.283396	+	0.959003i	$0.591461\pi$
$878$	−33.7128	+	18.5134i	−0.0383973	+	0.0210858i
$879$		0			0
$880$	−292.393	+	136.926i	−0.332264	+	0.155597i
$881$		−	387.244i		−	0.439551i	−0.975550	−	0.219775i	$-0.929468\pi$
$881$		−	387.244i		−	0.439551i	0.975550	−	0.219775i	$-0.0705325\pi$
$882$		0			0
$883$		−	848.009i		−	0.960373i	−0.877166	−	0.480187i	$-0.840569\pi$
$883$		−	848.009i		−	0.960373i	0.877166	−	0.480187i	$-0.159431\pi$
$884$	1001.15	+	636.656i	1.13252	+	0.720199i
$885$		0			0
$886$	1231.03	−	676.020i	1.38943	−	0.763002i
$887$		−	234.255i		−	0.264098i	−0.991243	−	0.132049i	$-0.957844\pi$
$887$		−	234.255i		−	0.264098i	0.991243	−	0.132049i	$-0.0421556\pi$
$888$		0			0
$889$	252.340	−	216.836i	0.283847	−	0.243910i
$890$	107.504	−	59.0355i	0.120791	−	0.0663320i
$891$		0			0
$892$	607.760	+	386.490i	0.681345	+	0.433284i
$893$		−	2.21213i		−	0.00247719i
$894$		0			0
$895$			32.7955i			0.0366430i
$896$	791.751	+	419.460i	0.883650	+	0.468147i
$897$		0			0
$898$	469.883	+	855.657i	0.523255	+	0.952847i
$899$	1746.16			1.94233
$900$		0			0
$901$	659.667			0.732149
$902$	473.787	+	862.766i	0.525263	+	0.956503i
$903$		0			0
$904$	−1753.81	−	112.798i	−1.94006	−	0.124776i
$905$	−159.653			−0.176412
$906$		0			0
$907$			1658.09i			1.82811i	0.405593	+	0.914054i	$0.367065\pi$
$907$			1658.09i			1.82811i	−0.405593	+	0.914054i	$0.632935\pi$
$908$	−172.527	+	271.300i	−0.190007	+	0.298789i
$909$		0			0
$910$	558.135	+	209.280i	0.613336	+	0.229978i
$911$	−1227.41			−1.34732			−0.673662	−	0.739039i	$-0.735280\pi$
$911$	−1227.41			−1.34732			−0.673662	+	0.739039i	$0.735280\pi$
$912$		0			0
$913$		−	232.715i		−	0.254890i
$914$	−705.011	−	1283.82i	−0.771346	−	1.40462i
$915$		0			0
$916$	54.0417	−	84.9813i	0.0589975	−	0.0927743i
$917$	−919.506	+	790.131i	−1.00273	+	0.861648i
$918$		0			0
$919$	386.961			0.421067			0.210533	−	0.977587i	$-0.432480\pi$
$919$	386.961			0.421067			0.210533	+	0.977587i	$0.432480\pi$
$920$	−358.051	−	23.0283i	−0.389186	−	0.0250308i
$921$		0			0
$922$	−226.157	−	411.832i	−0.245290	−	0.446672i
$923$	−212.197			−0.229900
$924$		0			0
$925$			432.379i			0.467437i
$926$	865.577	+	1576.22i	0.934748	+	1.70218i
$927$		0			0
$928$	1189.17	+	868.212i	1.28143	+	0.935573i
$929$			729.180i			0.784909i	0.919772	+	0.392454i	$0.128374\pi$
$929$			729.180i			0.784909i	−0.919772	+	0.392454i	$0.871626\pi$
$930$		0			0
$931$	−0.287755	+	1.89040i	−0.000309082	+	0.00203050i
$932$	571.196	−	898.213i	0.612871	−	0.963748i
$933$		0			0
$934$	−420.586	−	765.888i	−0.450307	−	0.820008i
$935$	236.537			0.252981
$936$		0			0
$937$		−	370.331i		−	0.395231i	−0.980280	−	0.197615i	$-0.936680\pi$
$937$		−	370.331i		−	0.395231i	0.980280	−	0.197615i	$-0.0633197\pi$
$938$	−271.078	+	722.945i	−0.288996	+	0.770730i
$939$		0			0
$940$	321.948	+	204.734i	0.342497	+	0.217803i
$941$	929.751			0.988045			0.494023	−	0.869449i	$-0.335526\pi$
$941$	929.751			0.988045			0.494023	+	0.869449i	$0.335526\pi$
$942$		0			0
$943$			1093.82i			1.15994i
$944$	437.212	+	933.628i	0.463148	+	0.989013i
$945$		0			0
$946$	−266.324	−	484.976i	−0.281526	−	0.512659i
$947$		−	676.560i		−	0.714425i	−0.934023	−	0.357212i	$-0.883727\pi$
$947$		−	676.560i		−	0.714425i	0.934023	−	0.357212i	$-0.116273\pi$
$948$		0			0
$949$		−	2970.82i		−	3.13048i
$950$	0.832835	+	1.51659i	0.000876669	+	0.00159641i
$951$		0			0
$952$	−394.978	−	524.297i	−0.414893	−	0.550732i
$953$	194.019			0.203587			0.101794	−	0.994806i	$-0.467542\pi$
$953$	194.019			0.203587			0.101794	+	0.994806i	$0.467542\pi$
$954$		0			0
$955$	100.394			0.105125
$956$	−367.790	+	578.354i	−0.384717	+	0.604972i
$957$		0			0
$958$	−841.662	+	462.198i	−0.878561	+	0.482461i
$959$	120.578	−	103.613i	0.125733	−	0.108042i
$960$		0			0
$961$	−479.211			−0.498659
$962$	−865.183	+	475.115i	−0.899359	+	0.493882i
$963$		0			0
$964$	298.508	+	189.829i	0.309656	+	0.196918i
$965$	−169.593			−0.175744
$966$		0			0
$967$	−1251.92			−1.29465			−0.647324	−	0.762215i	$-0.724112\pi$
$967$	−1251.92			−1.29465			−0.647324	+	0.762215i	$0.724112\pi$
$968$	182.188	+	11.7176i	0.188211	+	0.0121049i
$969$		0			0
$970$	481.172	−	264.235i	0.496054	−	0.272407i
$971$	990.379			1.01996			0.509979	−	0.860187i	$-0.329653\pi$
$971$	990.379			1.01996			0.509979	+	0.860187i	$0.329653\pi$
$972$		0			0
$973$	−388.358	+	333.716i	−0.399135	+	0.342976i
$974$	−325.415	−	592.580i	−0.334101	−	0.608398i
$975$		0			0
$976$	−354.812	−	757.669i	−0.363537	−	0.776300i
$977$	1149.77			1.17684			0.588419	−	0.808556i	$-0.299751\pi$
$977$	1149.77			1.17684			0.588419	+	0.808556i	$0.299751\pi$
$978$		0			0
$979$	−437.065			−0.446440
$980$	−248.491	−	216.837i	−0.253563	−	0.221262i
$981$		0			0
$982$	−1444.81	+	793.419i	−1.47130	+	0.807962i
$983$			1524.11i			1.55047i	0.631675	+	0.775234i	$0.282368\pi$
$983$			1524.11i			1.55047i	−0.631675	+	0.775234i	$0.717632\pi$
$984$		0			0
$985$			47.9871i			0.0487179i
$986$	−519.225	−	945.508i	−0.526597	−	0.958933i
$987$		0			0
$988$	−2.11952	+	3.33298i	−0.00214527	+	0.00337346i
$989$		−	614.855i		−	0.621694i
$990$		0			0
$991$	−624.497			−0.630168			−0.315084	−	0.949064i	$-0.602033\pi$
$991$	−624.497			−0.630168			−0.315084	+	0.949064i	$0.602033\pi$
$992$	−980.810	−	716.092i	−0.988720	−	0.721866i
$993$		0			0
$994$	109.930	+	41.2196i	0.110593	+	0.0414684i
$995$		−	556.506i		−	0.559302i
$996$		0			0
$997$	−26.7499			−0.0268304			−0.0134152	−	0.999910i	$-0.504270\pi$
$997$	−26.7499			−0.0268304			−0.0134152	+	0.999910i	$0.504270\pi$
$998$	1082.31	−	594.351i	1.08448	−	0.595542i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.l.h.181.23		32
3.2	odd	2		168.3.l.a.13.9	✓	32
4.3	odd	2		2016.3.l.h.433.14		32
7.6	odd	2	inner	504.3.l.h.181.24		32
8.3	odd	2		2016.3.l.h.433.19		32
8.5	even	2	inner	504.3.l.h.181.22		32
12.11	even	2		672.3.l.a.433.28		32
21.20	even	2		168.3.l.a.13.10	yes	32
24.5	odd	2		168.3.l.a.13.12	yes	32
24.11	even	2		672.3.l.a.433.5		32
28.27	even	2		2016.3.l.h.433.20		32
56.13	odd	2	inner	504.3.l.h.181.21		32
56.27	even	2		2016.3.l.h.433.13		32
84.83	odd	2		672.3.l.a.433.12		32
168.83	odd	2		672.3.l.a.433.21		32
168.125	even	2		168.3.l.a.13.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.l.a.13.9	✓	32	3.2	odd	2
168.3.l.a.13.10	yes	32	21.20	even	2
168.3.l.a.13.11	yes	32	168.125	even	2
168.3.l.a.13.12	yes	32	24.5	odd	2
504.3.l.h.181.21		32	56.13	odd	2	inner
504.3.l.h.181.22		32	8.5	even	2	inner
504.3.l.h.181.23		32	1.1	even	1	trivial
504.3.l.h.181.24		32	7.6	odd	2	inner
672.3.l.a.433.5		32	24.11	even	2
672.3.l.a.433.12		32	84.83	odd	2
672.3.l.a.433.21		32	168.83	odd	2
672.3.l.a.433.28		32	12.11	even	2
2016.3.l.h.433.13		32	56.27	even	2
2016.3.l.h.433.14		32	4.3	odd	2
2016.3.l.h.433.19		32	8.3	odd	2
2016.3.l.h.433.20		32	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.962692 + 1.75306i) q^{2} +(-2.14645 + 3.37532i) q^{4} -1.68264 q^{5} +(5.30913 - 4.56214i) q^{7} +(-7.98351 - 0.513465i) q^{8} +(-1.61986 - 2.94977i) q^{10} +11.9925i q^{11} -25.3039 q^{13} +(13.1088 + 4.91531i) q^{14} +(-6.78552 - 14.4899i) q^{16} +11.7219i q^{17} -0.0390239 q^{19} +(3.61170 - 5.67944i) q^{20} +(-21.0236 + 11.5451i) q^{22} -26.6539 q^{23} -22.1687 q^{25} +(-24.3598 - 44.3592i) q^{26} +(4.00287 + 27.7124i) q^{28} +46.0119i q^{29} -37.9501i q^{31} +(18.8693 - 25.8447i) q^{32} +(-20.5492 + 11.2846i) q^{34} +(-8.93335 + 7.67643i) q^{35} -19.5040i q^{37} +(-0.0375680 - 0.0684113i) q^{38} +(13.4334 + 0.863976i) q^{40} -41.0379i q^{41} +23.0681i q^{43} +(-40.4786 - 25.7413i) q^{44} +(-25.6595 - 46.7259i) q^{46} +56.6865i q^{47} +(7.37382 - 48.4420i) q^{49} +(-21.3417 - 38.8631i) q^{50} +(54.3134 - 85.4086i) q^{52} -56.2765i q^{53} -20.1791i q^{55} +(-44.7280 + 33.6958i) q^{56} +(-80.6617 + 44.2953i) q^{58} -64.4331 q^{59} +52.2895 q^{61} +(66.5289 - 36.5343i) q^{62} +(63.4727 + 8.19850i) q^{64} +42.5773 q^{65} +55.1497i q^{67} +(-39.5651 - 25.1604i) q^{68} +(-22.0573 - 8.27068i) q^{70} +8.38597 q^{71} +117.406i q^{73} +(34.1917 - 18.7764i) q^{74} +(0.0837628 - 0.131718i) q^{76} +(54.7115 + 63.6699i) q^{77} -13.2280 q^{79} +(11.4176 + 24.3812i) q^{80} +(71.9420 - 39.5069i) q^{82} -19.4050 q^{83} -19.7237i q^{85} +(-40.4398 + 22.2075i) q^{86} +(6.15774 - 95.7424i) q^{88} +36.4448i q^{89} +(-134.342 + 115.440i) q^{91} +(57.2112 - 89.9654i) q^{92} +(-99.3749 + 54.5717i) q^{94} +0.0656632 q^{95} +163.122i q^{97} +(92.0205 - 33.7080i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 6 q^{4} + 2 q^{8} - 38 q^{14} - 46 q^{16} + 16 q^{22} - 64 q^{23} + 160 q^{25} - 122 q^{28} + 122 q^{32} + 216 q^{44} - 260 q^{46} - 16 q^{49} - 122 q^{50} - 98 q^{56} - 160 q^{58} - 174 q^{64}+ \cdots + 2 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 6 * q^4 + 2 * q^8 - 38 * q^14 - 46 * q^16 + 16 * q^22 - 64 * q^23 + 160 * q^25 - 122 * q^28 + 122 * q^32 + 216 * q^44 - 260 * q^46 - 16 * q^49 - 122 * q^50 - 98 * q^56 - 160 * q^58 - 174 * q^64 + 408 * q^70 + 640 * q^71 - 408 * q^74 - 64 * q^79 - 792 * q^86 - 592 * q^88 - 316 * q^92 + 768 * q^95 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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