LMFDB - Embedded newform 504.3.l.h.181.21

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)

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")

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);

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

$q$-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	$-0.816486\pi$
$11$		−	11.9925i		−	1.09023i	0.838361	−	0.545115i	$-0.183514\pi$
$12$		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	$-0.887960\pi$
$17$		−	11.7219i		−	0.689523i	0.938690	−	0.344762i	$-0.112040\pi$
$18$		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	$-0.708357\pi$
$29$		−	46.0119i		−	1.58662i	0.608819	−	0.793309i	$-0.291643\pi$
$30$		0			0
$31$			37.9501i			1.22420i	0.790781	+	0.612099i	$0.209674\pi$
$31$			37.9501i			1.22420i	−0.790781	+	0.612099i	$0.790326\pi$
$32$	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	$0.0848993\pi$
$37$			19.5040i			0.527136i	−0.964641	+	0.263568i	$0.915101\pi$
$38$	−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	$0.166837\pi$
$41$			41.0379i			1.00092i	−0.865758	+	0.500462i	$0.833163\pi$
$42$		0			0
$43$		−	23.0681i		−	0.536468i	−0.963354	−	0.268234i	$-0.913560\pi$
$43$		−	23.0681i		−	0.536468i	0.963354	−	0.268234i	$-0.0864400\pi$
$44$	−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	$-0.793953\pi$
$47$		−	56.6865i		−	1.20610i	0.797705	−	0.603048i	$-0.206047\pi$
$48$		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	$0.178150\pi$
$53$			56.2765i			1.06182i	−0.847428	+	0.530910i	$0.821850\pi$
$54$		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	$-0.864982\pi$
$67$		−	55.1497i		−	0.823130i	0.911380	−	0.411565i	$-0.135018\pi$
$68$	−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	$-0.702621\pi$
$73$		−	117.406i		−	1.60830i	0.594426	−	0.804150i	$-0.297379\pi$
$74$	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	$-0.934363\pi$
$89$		−	36.4448i		−	0.409492i	0.978815	−	0.204746i	$-0.0656368\pi$
$90$		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	$-0.682064\pi$
$97$		−	163.122i		−	1.68167i	0.541292	−	0.840835i	$-0.317936\pi$
$98$	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	$0.0367014\pi$
$103$			23.6994i			0.230091i	−0.993360	+	0.115046i	$0.963299\pi$
$104$	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	$-0.850729\pi$
$107$		−	96.7170i		−	0.903898i	0.892044	−	0.451949i	$-0.149271\pi$
$108$		0			0
$109$			89.7670i			0.823550i	0.911285	+	0.411775i	$0.135091\pi$
$109$			89.7670i			0.823550i	−0.911285	+	0.411775i	$0.864909\pi$
$110$	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	$0.0425019\pi$
$149$			39.6719i			0.266255i	−0.991099	+	0.133127i	$0.957498\pi$
$150$		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	$0.00900379\pi$
$163$			9.22009i			0.0565650i	−0.999600	+	0.0282825i	$0.990996\pi$
$164$	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	$-0.787508\pi$
$167$		−	206.771i		−	1.23815i	0.785332	−	0.619075i	$-0.212492\pi$
$168$		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	$0.0173382\pi$
$179$			19.4905i			0.108886i	−0.998517	+	0.0544428i	$0.982662\pi$
$180$		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	$0.0230604\pi$
$197$			28.5190i			0.144766i	−0.997377	+	0.0723832i	$0.976940\pi$
$198$		0			0
$199$		−	330.734i		−	1.66198i	−0.556288	−	0.830990i	$-0.687775\pi$
$199$		−	330.734i		−	1.66198i	0.556288	−	0.830990i	$-0.312225\pi$
$200$	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	$-0.756027\pi$
$211$		−	292.696i		−	1.38719i	0.720367	−	0.693593i	$-0.243973\pi$
$212$	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	$0.132284\pi$
$223$			180.060i			0.807444i	−0.914882	+	0.403722i	$0.867716\pi$
$224$	−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	$0.0587371\pi$
$241$			88.4386i			0.366965i	−0.983023	+	0.183483i	$0.941263\pi$
$242$	−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	$-0.831741\pi$
$257$		−	259.224i		−	1.00865i	0.863513	−	0.504326i	$-0.168259\pi$
$258$		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	$0.353435\pi$
$271$			485.553i			1.79171i	−0.444350	+	0.895853i	$0.646565\pi$
$272$	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	$0.250650\pi$
$277$			392.536i			1.41710i	−0.705662	+	0.708548i	$0.749350\pi$
$278$	−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	$0.154201\pi$
$311$			289.672i			0.931421i	−0.884937	+	0.465710i	$0.845799\pi$
$312$		0			0
$313$		−	205.294i		−	0.655891i	−0.944697	−	0.327945i	$-0.893644\pi$
$313$		−	205.294i		−	0.655891i	0.944697	−	0.327945i	$-0.106356\pi$
$314$	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	$0.185205\pi$
$317$			348.421i			1.09912i	−0.835454	+	0.549560i	$0.814795\pi$
$318$		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	$0.0826947\pi$
$331$			170.055i			0.513761i	−0.966443	+	0.256881i	$0.917305\pi$
$332$	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	$0.0146421\pi$
$347$			31.9124i			0.0919666i	−0.998942	+	0.0459833i	$0.985358\pi$
$348$		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	$0.0705166\pi$
$353$			155.127i			0.439454i	−0.975561	+	0.219727i	$0.929483\pi$
$354$		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	$-0.771208\pi$
$367$		−	483.310i		−	1.31692i	0.752615	−	0.658461i	$-0.228792\pi$
$368$	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	$0.0133532\pi$
$373$			31.2857i			0.0838758i	−0.999120	+	0.0419379i	$0.986647\pi$
$374$	−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	$0.158639\pi$
$379$			362.325i			0.956003i	−0.878359	+	0.478002i	$0.841361\pi$
$380$	−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	$-0.961692\pi$
$383$		−	91.9648i		−	0.240117i	0.992767	−	0.120058i	$-0.0383082\pi$
$384$		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	$-0.986122\pi$
$389$		−	33.9094i		−	0.0871706i	0.999050	−	0.0435853i	$-0.0138780\pi$
$390$		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	$0.264807\pi$
$409$			604.684i			1.47845i	−0.673461	+	0.739223i	$0.735193\pi$
$410$	−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	$-0.743773\pi$
$421$		−	606.917i		−	1.44161i	0.693139	−	0.720804i	$-0.256227\pi$
$422$	−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	$-0.817411\pi$
$433$		−	469.957i		−	1.08535i	0.839942	−	0.542676i	$-0.182589\pi$
$434$	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	$-0.993028\pi$
$439$		−	19.2308i		−	0.0438060i	0.999760	−	0.0219030i	$-0.00697250\pi$
$440$	−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	$0.291258\pi$
$443$			702.218i			1.58514i	−0.609779	+	0.792572i	$0.708742\pi$
$444$		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	$-0.832907\pi$
$479$		−	480.110i		−	1.00232i	0.865356	−	0.501158i	$-0.167093\pi$
$480$		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	$-0.682981\pi$
$491$		−	824.167i		−	1.67855i	0.543709	−	0.839274i	$-0.317019\pi$
$492$		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	$0.212309\pi$
$499$			617.384i			1.23724i	−0.785689	+	0.618621i	$0.787691\pi$
$500$	−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	$-0.546853\pi$
$503$		−	995.122i		−	1.97837i	0.146663	−	0.989187i	$-0.453147\pi$
$504$		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	$-0.839320\pi$
$521$		−	503.937i		−	0.967249i	0.875276	−	0.483624i	$-0.160680\pi$
$522$		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	$0.219424\pi$
$541$			688.182i			1.27206i	−0.771666	+	0.636028i	$0.780576\pi$
$542$	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	$-0.865466\pi$
$547$		−	448.735i		−	0.820357i	0.912005	−	0.410178i	$-0.134534\pi$
$548$	−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	$-0.838672\pi$
$557$		−	540.742i		−	0.970811i	0.874289	−	0.485405i	$-0.161328\pi$
$558$		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	$0.171467\pi$
$571$			585.849i			1.02601i	−0.858387	+	0.513003i	$0.828533\pi$
$572$	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	$0.0371031\pi$
$577$			134.209i			0.232598i	−0.993214	+	0.116299i	$0.962897\pi$
$578$	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	$0.115818\pi$
$593$			422.070i			0.711754i	−0.934533	+	0.355877i	$0.884182\pi$
$594$		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	$-0.970243\pi$
$601$		−	112.203i		−	0.186694i	0.995634	−	0.0933471i	$-0.0297566\pi$
$602$	−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	$-0.883957\pi$
$607$		−	432.839i		−	0.713078i	0.934280	−	0.356539i	$-0.116043\pi$
$608$	−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	$-0.992294\pi$
$613$		−	29.6778i		−	0.0484141i	0.999707	−	0.0242070i	$-0.00770610\pi$
$614$	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	$0.138298\pi$
$647$			544.689i			0.841868i	−0.907091	+	0.420934i	$0.861702\pi$
$648$		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	$-0.958251\pi$
$653$		−	170.803i		−	0.261567i	0.991411	−	0.130784i	$-0.0417493\pi$
$654$		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	$-0.892078\pi$
$659$		−	438.353i		−	0.665180i	0.943072	−	0.332590i	$-0.107922\pi$
$660$		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	$-0.824338\pi$
$683$		−	716.152i		−	1.04854i	0.851552	−	0.524269i	$-0.175662\pi$
$684$		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	$-0.960732\pi$
$701$		−	172.520i		−	0.246106i	0.992400	−	0.123053i	$-0.0392685\pi$
$702$		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	$-0.760917\pi$
$709$		−	967.706i		−	1.36489i	0.730937	−	0.682444i	$-0.239083\pi$
$710$	−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	$-0.944780\pi$
$719$		−	248.215i		−	0.345222i	0.984990	−	0.172611i	$-0.0552204\pi$
$720$		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	$-0.922582\pi$
$727$		−	350.160i		−	0.481651i	0.970568	−	0.240825i	$-0.0774181\pi$
$728$	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	$-0.899480\pi$
$739$		−	459.023i		−	0.621141i	0.950550	−	0.310571i	$-0.100520\pi$
$740$	−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	$-0.917088\pi$
$757$		−	389.915i		−	0.515079i	0.966268	−	0.257540i	$-0.0829118\pi$
$758$	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	$0.191001\pi$
$761$			859.447i			1.12937i	−0.825308	+	0.564683i	$0.808999\pi$
$762$		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	$0.0647361\pi$
$769$			310.638i			0.403951i	−0.979391	+	0.201975i	$0.935264\pi$
$770$	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	$-0.954595\pi$
$821$		−	233.428i		−	0.284321i	0.989844	−	0.142160i	$-0.0454049\pi$
$822$		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	$-0.934636\pi$
$827$		−	337.263i		−	0.407815i	0.978990	−	0.203908i	$-0.0653642\pi$
$828$		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	$0.291412\pi$
$839$			1330.43i			1.58573i	−0.609396	+	0.792866i	$0.708588\pi$
$840$		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	$0.174983\pi$
$857$			895.486i			1.04491i	−0.852668	+	0.522454i	$0.825017\pi$
$858$		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	$-0.591461\pi$
$877$		−	1682.09i		−	1.91801i	0.283396	−	0.959003i	$-0.408539\pi$
$878$	−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	$0.0705325\pi$
$881$			387.244i			0.439551i	−0.975550	+	0.219775i	$0.929468\pi$
$882$		0			0
$883$			848.009i			0.960373i	0.877166	+	0.480187i	$0.159431\pi$
$883$			848.009i			0.960373i	−0.877166	+	0.480187i	$0.840569\pi$
$884$	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	$0.0421556\pi$
$887$			234.255i			0.264098i	−0.991243	+	0.132049i	$0.957844\pi$
$888$		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	$-0.632935\pi$
$907$		−	1658.09i		−	1.82811i	0.405593	−	0.914054i	$-0.367065\pi$
$908$	−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	$-0.871626\pi$
$929$		−	729.180i		−	0.784909i	0.919772	−	0.392454i	$-0.128374\pi$
$930$		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	$0.0633197\pi$
$937$			370.331i			0.395231i	−0.980280	+	0.197615i	$0.936680\pi$
$938$	−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	$0.116273\pi$
$947$			676.560i			0.714425i	−0.934023	+	0.357212i	$0.883727\pi$
$948$		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	$-0.717632\pi$
$983$		−	1524.11i		−	1.55047i	0.631675	−	0.775234i	$-0.282368\pi$
$984$		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.181.21		32
3.2	odd	2		168.3.l.a.13.11	yes	32
4.3	odd	2		2016.3.l.h.433.13		32
7.6	odd	2	inner	504.3.l.h.181.22		32
8.3	odd	2		2016.3.l.h.433.20		32
8.5	even	2	inner	504.3.l.h.181.24		32
12.11	even	2		672.3.l.a.433.21		32
21.20	even	2		168.3.l.a.13.12	yes	32
24.5	odd	2		168.3.l.a.13.10	yes	32
24.11	even	2		672.3.l.a.433.12		32
28.27	even	2		2016.3.l.h.433.19		32
56.13	odd	2	inner	504.3.l.h.181.23		32
56.27	even	2		2016.3.l.h.433.14		32
84.83	odd	2		672.3.l.a.433.5		32
168.83	odd	2		672.3.l.a.433.28		32
168.125	even	2		168.3.l.a.13.9	✓	32

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

Fields

Representations

Groups

Database

Properties

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