LMFDB - Embedded newform 378.3.r.a.305.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(233,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 2])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.233"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			305.8
Character	$\chi$	$=$	378.305
Dual form			378.3.r.a.233.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421i q^{2} -2.00000 q^{4} +(7.41683 + 4.28211i) q^{5} +(-6.97339 - 0.609798i) q^{7} +2.82843i q^{8} +(6.05582 - 10.4890i) q^{10} +(6.10804 - 3.52648i) q^{11} +(7.43588 + 12.8793i) q^{13} +(-0.862384 + 9.86186i) q^{14} +4.00000 q^{16} +(-12.4500 - 7.18802i) q^{17} +(9.66453 + 16.7395i) q^{19} +(-14.8337 - 8.56422i) q^{20} +(-4.98720 - 8.63808i) q^{22} +(34.0962 + 19.6854i) q^{23} +(24.1729 + 41.8687i) q^{25} +(18.2141 - 10.5159i) q^{26} +(13.9468 + 1.21960i) q^{28} +(11.7844 + 6.80374i) q^{29} -24.1029 q^{31} -5.65685i q^{32} +(-10.1654 + 17.6070i) q^{34} +(-49.1092 - 34.3836i) q^{35} +(17.6184 + 30.5159i) q^{37} +(23.6732 - 13.6677i) q^{38} +(-12.1116 + 20.9780i) q^{40} +(-7.79426 + 4.50002i) q^{41} +(32.4531 - 56.2103i) q^{43} +(-12.2161 + 7.05296i) q^{44} +(27.8394 - 48.2192i) q^{46} -33.3805i q^{47} +(48.2563 + 8.50471i) q^{49} +(59.2113 - 34.1857i) q^{50} +(-14.8718 - 25.7586i) q^{52} +(52.4399 + 30.2762i) q^{53} +60.4031 q^{55} +(1.72477 - 19.7237i) q^{56} +(9.62194 - 16.6657i) q^{58} -72.3172i q^{59} -7.98282 q^{61} +34.0867i q^{62} -8.00000 q^{64} +127.365i q^{65} -83.6147 q^{67} +(24.9000 + 14.3760i) q^{68} +(-48.6257 + 69.4509i) q^{70} -61.0012i q^{71} +(-9.83762 + 17.0393i) q^{73} +(43.1560 - 24.9162i) q^{74} +(-19.3291 - 33.4789i) q^{76} +(-44.7442 + 20.8668i) q^{77} -10.1882 q^{79} +(29.6673 + 17.1284i) q^{80} +(6.36399 + 11.0228i) q^{82} +(-15.8646 - 9.15941i) q^{83} +(-61.5598 - 106.625i) q^{85} +(-79.4934 - 45.8955i) q^{86} +(9.97439 + 17.2762i) q^{88} +(-40.0208 + 23.1060i) q^{89} +(-43.9995 - 94.3469i) q^{91} +(-68.1923 - 39.3708i) q^{92} -47.2071 q^{94} +165.538i q^{95} +(-49.1454 + 85.1224i) q^{97} +(12.0275 - 68.2447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} + 2 q^{7} + 36 q^{11} + 10 q^{13} - 36 q^{14} + 128 q^{16} + 54 q^{17} + 28 q^{19} + 126 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} - 36 q^{29} + 16 q^{31} + 90 q^{35} + 22 q^{37} - 72 q^{41}+ \cdots - 288 q^{98}+O(q^{100}) $ 32 * q - 64 * q^4 + 2 * q^7 + 36 * q^11 + 10 * q^13 - 36 * q^14 + 128 * q^16 + 54 * q^17 + 28 * q^19 + 126 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 - 36 * q^29 + 16 * q^31 + 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 - 72 * q^44 - 12 * q^46 + 2 * q^49 + 288 * q^50 - 20 * q^52 + 72 * q^53 - 24 * q^55 + 72 * q^56 - 24 * q^58 + 124 * q^61 - 256 * q^64 - 140 * q^67 - 108 * q^68 + 72 * q^70 + 196 * q^73 - 216 * q^74 - 56 * q^76 - 486 * q^77 + 76 * q^79 + 60 * q^85 + 144 * q^86 + 486 * q^89 - 122 * q^91 - 252 * q^92 - 336 * q^94 - 38 * q^97 - 288 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−2.00000			−0.500000
$5$	7.41683	+	4.28211i	1.48337	+	0.856422i	0.999821	−	0.0188976i	$-0.00601566\pi$
$5$	7.41683	+	4.28211i	1.48337	+	0.856422i	0.483545	+	0.875320i	$0.339349\pi$
$6$		0			0
$7$	−6.97339	−	0.609798i	−0.996198	−	0.0871140i
$7$	−6.97339	−	0.609798i	−0.996198	−	0.0871140i
$8$			2.82843i			0.353553i
$9$		0			0
$10$	6.05582	−	10.4890i	0.605582	−	1.04890i
$11$	6.10804	−	3.52648i	0.555277	−	0.320589i	−0.195971	−	0.980610i	$-0.562786\pi$
$11$	6.10804	−	3.52648i	0.555277	−	0.320589i	0.751248	+	0.660021i	$0.229452\pi$
$12$		0			0
$13$	7.43588	+	12.8793i	0.571991	+	0.990717i	0.996361	+	0.0852287i	$0.0271621\pi$
$13$	7.43588	+	12.8793i	0.571991	+	0.990717i	−0.424371	+	0.905489i	$0.639505\pi$
$14$	−0.862384	+	9.86186i	−0.0615989	+	0.704419i
$15$		0			0
$16$	4.00000			0.250000
$17$	−12.4500	−	7.18802i	−0.732354	−	0.422825i	0.0869287	−	0.996215i	$-0.472295\pi$
$17$	−12.4500	−	7.18802i	−0.732354	−	0.422825i	−0.819283	+	0.573390i	$0.805628\pi$
$18$		0			0
$19$	9.66453	+	16.7395i	0.508659	+	0.881024i	0.999950	+	0.0100280i	$0.00319207\pi$
$19$	9.66453	+	16.7395i	0.508659	+	0.881024i	−0.491290	+	0.870996i	$0.663475\pi$
$20$	−14.8337	−	8.56422i	−0.741683	−	0.428211i
$21$		0			0
$22$	−4.98720	−	8.63808i	−0.226691	−	0.392640i
$23$	34.0962	+	19.6854i	1.48244	+	0.855888i	0.999801	−	0.0199309i	$-0.00634462\pi$
$23$	34.0962	+	19.6854i	1.48244	+	0.855888i	0.482640	+	0.875819i	$0.339678\pi$
$24$		0			0
$25$	24.1729	+	41.8687i	0.966917	+	1.67475i
$26$	18.2141	−	10.5159i	0.700543	−	0.404459i
$27$		0			0
$28$	13.9468	+	1.21960i	0.498099	+	0.0435570i
$29$	11.7844	+	6.80374i	0.406360	+	0.234612i	0.689224	−	0.724548i	$-0.257951\pi$
$29$	11.7844	+	6.80374i	0.406360	+	0.234612i	−0.282865	+	0.959160i	$0.591285\pi$
$30$		0			0
$31$	−24.1029			−0.777513			−0.388757	−	0.921341i	$-0.627095\pi$
$31$	−24.1029			−0.777513			−0.388757	+	0.921341i	$0.627095\pi$
$32$		−	5.65685i		−	0.176777i
$33$		0			0
$34$	−10.1654	+	17.6070i	−0.298982	+	0.517853i
$35$	−49.1092	−	34.3836i	−1.40312	−	0.982388i
$36$		0			0
$37$	17.6184	+	30.5159i	0.476172	+	0.824755i	0.999627	−	0.0272985i	$-0.00869046\pi$
$37$	17.6184	+	30.5159i	0.476172	+	0.824755i	−0.523455	+	0.852053i	$0.675357\pi$
$38$	23.6732	−	13.6677i	0.622978	−	0.359676i
$39$		0			0
$40$	−12.1116	+	20.9780i	−0.302791	+	0.524449i
$41$	−7.79426	+	4.50002i	−0.190104	+	0.109757i	−0.592031	−	0.805915i	$-0.701674\pi$
$41$	−7.79426	+	4.50002i	−0.190104	+	0.109757i	0.401927	+	0.915672i	$0.368340\pi$
$42$		0			0
$43$	32.4531	−	56.2103i	0.754722	−	1.30722i	−0.190790	−	0.981631i	$-0.561105\pi$
$43$	32.4531	−	56.2103i	0.754722	−	1.30722i	0.945512	−	0.325586i	$-0.105562\pi$
$44$	−12.2161	+	7.05296i	−0.277638	+	0.160295i
$45$		0			0
$46$	27.8394	−	48.2192i	0.605204	−	1.04824i
$47$		−	33.3805i		−	0.710223i	−0.934824	−	0.355111i	$-0.884443\pi$
$47$		−	33.3805i		−	0.710223i	0.934824	−	0.355111i	$-0.115557\pi$
$48$		0			0
$49$	48.2563	+	8.50471i	0.984822	+	0.173566i
$50$	59.2113	−	34.1857i	1.18423	−	0.683714i
$51$		0			0
$52$	−14.8718	−	25.7586i	−0.285995	−	0.495359i
$53$	52.4399	+	30.2762i	0.989433	+	0.571249i	0.905105	−	0.425189i	$-0.139792\pi$
$53$	52.4399	+	30.2762i	0.989433	+	0.571249i	0.0843280	+	0.996438i	$0.473126\pi$
$54$		0			0
$55$	60.4031			1.09824
$56$	1.72477	−	19.7237i	0.0307994	−	0.352209i
$57$		0			0
$58$	9.62194	−	16.6657i	0.165896	−	0.287340i
$59$		−	72.3172i		−	1.22572i	−0.790193	−	0.612858i	$-0.790020\pi$
$59$		−	72.3172i		−	1.22572i	0.790193	−	0.612858i	$-0.209980\pi$
$60$		0			0
$61$	−7.98282			−0.130866			−0.0654329	−	0.997857i	$-0.520843\pi$
$61$	−7.98282			−0.130866			−0.0654329	+	0.997857i	$0.520843\pi$
$62$			34.0867i			0.549785i
$63$		0			0
$64$	−8.00000			−0.125000
$65$			127.365i			1.95946i
$66$		0			0
$67$	−83.6147			−1.24798			−0.623990	−	0.781432i	$-0.714489\pi$
$67$	−83.6147			−1.24798			−0.623990	+	0.781432i	$0.714489\pi$
$68$	24.9000	+	14.3760i	0.366177	+	0.211412i
$69$		0			0
$70$	−48.6257	+	69.4509i	−0.694653	+	0.992156i
$71$		−	61.0012i		−	0.859172i	−0.903026	−	0.429586i	$-0.858660\pi$
$71$		−	61.0012i		−	0.859172i	0.903026	−	0.429586i	$-0.141340\pi$
$72$		0			0
$73$	−9.83762	+	17.0393i	−0.134762	+	0.233415i	−0.925506	−	0.378732i	$-0.876360\pi$
$73$	−9.83762	+	17.0393i	−0.134762	+	0.233415i	0.790745	+	0.612146i	$0.209694\pi$
$74$	43.1560	−	24.9162i	0.583190	−	0.336705i
$75$		0			0
$76$	−19.3291	−	33.4789i	−0.254330	−	0.440512i
$77$	−44.7442	+	20.8668i	−0.581093	+	0.270998i
$78$		0			0
$79$	−10.1882			−0.128965			−0.0644824	−	0.997919i	$-0.520540\pi$
$79$	−10.1882			−0.128965			−0.0644824	+	0.997919i	$0.520540\pi$
$80$	29.6673	+	17.1284i	0.370842	+	0.214105i
$81$		0			0
$82$	6.36399	+	11.0228i	0.0776096	+	0.134424i
$83$	−15.8646	−	9.15941i	−0.191139	−	0.110354i	0.401376	−	0.915913i	$-0.368532\pi$
$83$	−15.8646	−	9.15941i	−0.191139	−	0.110354i	−0.592516	+	0.805559i	$0.701865\pi$
$84$		0			0
$85$	−61.5598	−	106.625i	−0.724233	−	1.25441i
$86$	−79.4934	−	45.8955i	−0.924342	−	0.533669i
$87$		0			0
$88$	9.97439	+	17.2762i	0.113345	+	0.196320i
$89$	−40.0208	+	23.1060i	−0.449672	+	0.259618i	−0.707692	−	0.706522i	$-0.750263\pi$
$89$	−40.0208	+	23.1060i	−0.449672	+	0.259618i	0.258020	+	0.966140i	$0.416930\pi$
$90$		0			0
$91$	−43.9995	−	94.3469i	−0.483511	−	1.03678i
$92$	−68.1923	−	39.3708i	−0.741221	−	0.427944i
$93$		0			0
$94$	−47.2071			−0.502203
$95$			165.538i			1.74251i
$96$		0			0
$97$	−49.1454	+	85.1224i	−0.506654	+	0.877550i	0.493316	+	0.869850i	$0.335784\pi$
$97$	−49.1454	+	85.1224i	−0.506654	+	0.877550i	−0.999970	+	0.00770043i	$0.997549\pi$
$98$	12.0275	−	68.2447i	0.122729	−	0.696375i
$99$		0			0
$100$	−48.3459	−	83.7375i	−0.483459	−	0.837375i
$101$	−95.9495	+	55.3965i	−0.949995	+	0.548480i	−0.893079	−	0.449899i	$-0.851460\pi$
$101$	−95.9495	+	55.3965i	−0.949995	+	0.548480i	−0.0569157	+	0.998379i	$0.518127\pi$
$102$		0			0
$103$	−43.8080	+	75.8776i	−0.425320	+	0.736676i	−0.996450	−	0.0841834i	$-0.973172\pi$
$103$	−43.8080	+	75.8776i	−0.425320	+	0.736676i	0.571130	+	0.820860i	$0.306505\pi$
$104$	−36.4282	+	21.0318i	−0.350271	+	0.202229i
$105$		0			0
$106$	42.8170	−	74.1613i	0.403934	−	0.699635i
$107$	22.3256	−	12.8897i	0.208651	−	0.120465i	−0.392033	−	0.919951i	$-0.628228\pi$
$107$	22.3256	−	12.8897i	0.208651	−	0.120465i	0.600684	+	0.799486i	$0.294895\pi$
$108$		0			0
$109$	52.7615	−	91.3856i	0.484050	−	0.838400i	−0.515782	−	0.856720i	$-0.672498\pi$
$109$	52.7615	−	91.3856i	0.484050	−	0.838400i	0.999832	+	0.0183201i	$0.00583180\pi$
$110$		−	85.4229i		−	0.776572i
$111$		0			0
$112$	−27.8936	−	2.43919i	−0.249050	−	0.0217785i
$113$	−12.7398	+	7.35535i	−0.112742	+	0.0650916i	−0.555311	−	0.831643i	$-0.687401\pi$
$113$	−12.7398	+	7.35535i	−0.112742	+	0.0650916i	0.442569	+	0.896735i	$0.354067\pi$
$114$		0			0
$115$	168.590	+	292.007i	1.46600	+	2.53919i
$116$	−23.5689	−	13.6075i	−0.203180	−	0.117306i
$117$		0			0
$118$	−102.272			−0.866712
$119$	82.4356	+	57.7169i	0.692736	+	0.485016i
$120$		0			0
$121$	−35.6279	+	61.7093i	−0.294445	+	0.509994i
$122$			11.2894i			0.0925361i
$123$		0			0
$124$	48.2058			0.388757
$125$			199.939i			1.59951i
$126$		0			0
$127$	−14.2742			−0.112395			−0.0561976	−	0.998420i	$-0.517898\pi$
$127$	−14.2742			−0.112395			−0.0561976	+	0.998420i	$0.517898\pi$
$128$			11.3137i			0.0883883i
$129$		0			0
$130$	180.121			1.38555
$131$	−149.602	−	86.3726i	−1.14200	−	0.659333i	−0.195073	−	0.980789i	$-0.562495\pi$
$131$	−149.602	−	86.3726i	−1.14200	−	0.659333i	−0.946925	+	0.321456i	$0.895828\pi$
$132$		0			0
$133$	−57.1868	−	122.624i	−0.429976	−	0.921986i
$134$			118.249i			0.882455i
$135$		0			0
$136$	20.3308	−	35.2140i	0.149491	−	0.258926i
$137$	140.373	−	81.0447i	1.02462	−	0.591567i	0.109184	−	0.994022i	$-0.465176\pi$
$137$	140.373	−	81.0447i	1.02462	−	0.591567i	0.915440	+	0.402455i	$0.131843\pi$
$138$		0			0
$139$	−78.4637	−	135.903i	−0.564487	−	0.977720i	−0.997097	−	0.0761389i	$-0.975741\pi$
$139$	−78.4637	−	135.903i	−0.564487	−	0.977720i	0.432610	−	0.901581i	$-0.357593\pi$
$140$	98.2185	+	68.7672i	0.701560	+	0.491194i
$141$		0			0
$142$	−86.2687			−0.607526
$143$	90.8374	+	52.4450i	0.635226	+	0.366748i
$144$		0			0
$145$	58.2687	+	100.924i	0.401853	+	0.696030i
$146$	24.0972	+	13.9125i	0.165049	+	0.0952911i
$147$		0			0
$148$	−35.2368	−	61.0319i	−0.238086	−	0.412377i
$149$	−214.914	−	124.081i	−1.44237	−	0.832755i	−0.444367	−	0.895845i	$-0.646571\pi$
$149$	−214.914	−	124.081i	−1.44237	−	0.832755i	−0.998008	+	0.0630898i	$0.979905\pi$
$150$		0			0
$151$	47.2013	+	81.7551i	0.312592	+	0.541424i	0.978923	−	0.204232i	$-0.0654696\pi$
$151$	47.2013	+	81.7551i	0.312592	+	0.541424i	−0.666331	+	0.745656i	$0.732136\pi$
$152$	−47.3463	+	27.3354i	−0.311489	+	0.179838i
$153$		0			0
$154$	29.5102	+	63.2779i	0.191625	+	0.410895i
$155$	−178.767	−	103.211i	−1.15334	−	0.665879i
$156$		0			0
$157$	205.055			1.30608			0.653042	−	0.757322i	$-0.273493\pi$
$157$	205.055			1.30608			0.653042	+	0.757322i	$0.273493\pi$
$158$			14.4083i			0.0911919i
$159$		0			0
$160$	24.2233	−	41.9559i	0.151395	−	0.262225i
$161$	−225.762	−	158.066i	−1.40225	−	0.981775i
$162$		0			0
$163$	−130.276	−	225.645i	−0.799241	−	1.38433i	−0.920111	−	0.391657i	$-0.871902\pi$
$163$	−130.276	−	225.645i	−0.799241	−	1.38433i	0.120870	−	0.992668i	$-0.461431\pi$
$164$	15.5885	−	9.00004i	0.0950520	−	0.0548783i
$165$		0			0
$166$	−12.9534	+	22.4359i	−0.0780323	+	0.135156i
$167$	110.267	−	63.6624i	0.660279	−	0.381212i	−0.132105	−	0.991236i	$-0.542173\pi$
$167$	110.267	−	63.6624i	0.660279	−	0.381212i	0.792383	+	0.610024i	$0.208840\pi$
$168$		0			0
$169$	−26.0847	+	45.1800i	−0.154347	+	0.267337i
$170$	−150.790	+	87.0587i	−0.887001	+	0.512110i
$171$		0			0
$172$	−64.9061	+	112.421i	−0.377361	+	0.653609i
$173$		−	6.54440i		−	0.0378289i	−0.999821	−	0.0189145i	$-0.993979\pi$
$173$		−	6.54440i		−	0.0378289i	0.999821	−	0.0189145i	$-0.00602102\pi$
$174$		0			0
$175$	−143.036	−	306.708i	−0.817347	−	1.75261i
$176$	24.4322	−	14.1059i	0.138819	−	0.0801473i
$177$		0			0
$178$	32.6768	+	56.5979i	0.183578	+	0.317966i
$179$	−3.77964	−	2.18217i	−0.0211153	−	0.0121909i	0.489405	−	0.872057i	$-0.337214\pi$
$179$	−3.77964	−	2.18217i	−0.0211153	−	0.0121909i	−0.510520	+	0.859866i	$0.670547\pi$
$180$		0			0
$181$	71.3386			0.394136			0.197068	−	0.980390i	$-0.436858\pi$
$181$	71.3386			0.394136			0.197068	+	0.980390i	$0.436858\pi$
$182$	−133.427	+	62.2247i	−0.733114	+	0.341894i
$183$		0			0
$184$	−55.6788	+	96.4385i	−0.302602	+	0.524122i
$185$			301.775i			1.63122i
$186$		0			0
$187$	−101.394			−0.542212
$188$			66.7609i			0.355111i
$189$		0			0
$190$	234.106			1.23214
$191$			118.465i			0.620236i	0.950698	+	0.310118i	$0.100369\pi$
$191$			118.465i			0.620236i	−0.950698	+	0.310118i	$0.899631\pi$
$192$		0			0
$193$	−192.291			−0.996326			−0.498163	−	0.867083i	$-0.665992\pi$
$193$	−192.291			−0.996326			−0.498163	+	0.867083i	$0.665992\pi$
$194$	120.381	+	69.5021i	0.620522	+	0.358258i
$195$		0			0
$196$	−96.5126	−	17.0094i	−0.492411	−	0.0867828i
$197$		−	278.566i		−	1.41404i	−0.707193	−	0.707021i	$-0.750039\pi$
$197$		−	278.566i		−	1.41404i	0.707193	−	0.707021i	$-0.249961\pi$
$198$		0			0
$199$	−121.675	+	210.747i	−0.611431	+	1.05903i	0.379568	+	0.925164i	$0.376073\pi$
$199$	−121.675	+	210.747i	−0.611431	+	1.05903i	−0.990999	+	0.133866i	$0.957261\pi$
$200$	−118.423	+	68.3714i	−0.592113	+	0.341857i
$201$		0			0
$202$	78.3424	+	135.693i	0.387834	+	0.671748i
$203$	−78.0285	−	54.6312i	−0.384377	−	0.269119i
$204$		0			0
$205$	−77.0783			−0.375992
$206$	107.307	+	61.9538i	0.520909	+	0.300747i
$207$		0			0
$208$	29.7435	+	51.5173i	0.142998	+	0.247679i
$209$	118.063	+	68.1635i	0.564893	+	0.326141i
$210$		0			0
$211$	65.3669	+	113.219i	0.309796	+	0.536582i	0.978318	−	0.207110i	$-0.0664060\pi$
$211$	65.3669	+	113.219i	0.309796	+	0.536582i	−0.668522	+	0.743693i	$0.733073\pi$
$212$	−104.880	−	60.5524i	−0.494716	−	0.285625i
$213$		0			0
$214$	−18.2288	−	31.5732i	−0.0851814	−	0.147538i
$215$	481.398	−	277.935i	2.23906	−	1.29272i
$216$		0			0
$217$	168.079	+	14.6979i	0.774557	+	0.0677322i
$218$	−129.239	−	74.6160i	−0.592838	−	0.342275i
$219$		0			0
$220$	−120.806			−0.549119
$221$		−	213.797i		−	0.967408i
$222$		0			0
$223$	−25.5565	+	44.2652i	−0.114603	+	0.198498i	−0.917621	−	0.397456i	$-0.869893\pi$
$223$	−25.5565	+	44.2652i	−0.114603	+	0.198498i	0.803018	+	0.595955i	$0.203226\pi$
$224$	−3.44954	+	39.4474i	−0.0153997	+	0.176105i
$225$		0			0
$226$	10.4020	+	18.0169i	0.0460267	+	0.0797206i
$227$	300.441	−	173.459i	1.32353	−	0.764139i	0.339237	−	0.940701i	$-0.389831\pi$
$227$	300.441	−	173.459i	1.32353	−	0.764139i	0.984289	+	0.176562i	$0.0564977\pi$
$228$		0			0
$229$	83.6131	−	144.822i	0.365123	−	0.632411i	−0.623673	−	0.781685i	$-0.714360\pi$
$229$	83.6131	−	144.822i	0.365123	−	0.632411i	0.988796	+	0.149274i	$0.0476937\pi$
$230$	412.960	−	238.423i	1.79548	−	1.03662i
$231$		0			0
$232$	−19.2439	+	33.3314i	−0.0829478	+	0.143670i
$233$	171.970	−	99.2867i	0.738067	−	0.426123i	−0.0832991	−	0.996525i	$-0.526546\pi$
$233$	171.970	−	99.2867i	0.738067	−	0.426123i	0.821366	+	0.570401i	$0.193212\pi$
$234$		0			0
$235$	142.939	−	247.577i	0.608250	−	1.05352i
$236$			144.634i			0.612858i
$237$		0			0
$238$	81.6240	−	116.582i	0.342958	−	0.489838i
$239$	248.637	−	143.551i	1.04032	−	0.600631i	0.120398	−	0.992726i	$-0.461583\pi$
$239$	248.637	−	143.551i	1.04032	−	0.600631i	0.919925	+	0.392095i	$0.128249\pi$
$240$		0			0
$241$	−189.297	−	327.872i	−0.785464	−	1.36046i	−0.928721	−	0.370778i	$-0.879091\pi$
$241$	−189.297	−	327.872i	−0.785464	−	1.36046i	0.143257	−	0.989685i	$-0.454242\pi$
$242$	87.2701	+	50.3854i	0.360620	+	0.208204i
$243$		0			0
$244$	15.9656			0.0654329
$245$	321.491	+	269.717i	1.31221	+	1.10088i
$246$		0			0
$247$	−143.729	+	248.945i	−0.581897	+	1.00788i
$248$		−	68.1733i		−	0.274892i
$249$		0			0
$250$	282.756			1.13103
$251$			98.4672i			0.392300i	0.980574	+	0.196150i	$0.0628439\pi$
$251$			98.4672i			0.392300i	−0.980574	+	0.196150i	$0.937156\pi$
$252$		0			0
$253$	277.681			1.09755
$254$			20.1868i			0.0794755i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−186.439	−	107.641i	−0.725443	−	0.418835i	0.0913097	−	0.995823i	$-0.470895\pi$
$257$	−186.439	−	107.641i	−0.725443	−	0.418835i	−0.816753	+	0.576988i	$0.804228\pi$
$258$		0			0
$259$	−104.251	−	223.543i	−0.402515	−	0.863101i
$260$		−	254.730i		−	0.979731i
$261$		0			0
$262$	−122.149	+	211.569i	−0.466219	+	0.807515i
$263$	−10.8390	+	6.25790i	−0.0412130	+	0.0237943i	−0.520465	−	0.853883i	$-0.674241\pi$
$263$	−10.8390	+	6.25790i	−0.0412130	+	0.0237943i	0.479252	+	0.877677i	$0.340908\pi$
$264$		0			0
$265$	259.292	+	449.107i	0.978461	+	1.69474i
$266$	−173.417	+	80.8744i	−0.651942	+	0.304039i
$267$		0			0
$268$	167.229			0.623990
$269$	150.771	+	87.0476i	0.560487	+	0.323597i	0.753341	−	0.657630i	$-0.228441\pi$
$269$	150.771	+	87.0476i	0.560487	+	0.323597i	−0.192854	+	0.981227i	$0.561774\pi$
$270$		0			0
$271$	−17.5923	−	30.4707i	−0.0649161	−	0.112438i	0.831741	−	0.555164i	$-0.187345\pi$
$271$	−17.5923	−	30.4707i	−0.0649161	−	0.112438i	−0.896657	+	0.442726i	$0.854011\pi$
$272$	−49.8001	−	28.7521i	−0.183089	−	0.105706i
$273$		0			0
$274$	−114.614	−	198.518i	−0.418301	−	0.724519i
$275$	295.299	+	170.491i	1.07381	+	0.619966i
$276$		0			0
$277$	26.2551	+	45.4752i	0.0947839	+	0.164171i	0.909518	−	0.415664i	$-0.136451\pi$
$277$	26.2551	+	45.4752i	0.0947839	+	0.164171i	−0.814735	+	0.579834i	$0.803117\pi$
$278$	−192.196	+	110.964i	−0.691352	+	0.399152i
$279$		0			0
$280$	97.2515	−	138.902i	0.347327	−	0.496078i
$281$	−327.425	−	189.039i	−1.16521	−	0.672737i	−0.212666	−	0.977125i	$-0.568215\pi$
$281$	−327.425	−	189.039i	−1.16521	−	0.672737i	−0.952548	+	0.304388i	$0.901548\pi$
$282$		0			0
$283$	551.762			1.94969			0.974844	−	0.222888i	$-0.0715483\pi$
$283$	551.762			1.94969			0.974844	+	0.222888i	$0.0715483\pi$
$284$			122.002i			0.429586i
$285$		0			0
$286$	74.1684	−	128.463i	0.259330	−	0.449173i
$287$	57.0965	−	26.6275i	0.198943	−	0.0927786i
$288$		0			0
$289$	−41.1647	−	71.2993i	−0.142438	−	0.246710i
$290$	142.729	−	82.4044i	0.492168	−	0.284153i
$291$		0			0
$292$	19.6752	−	34.0785i	0.0673810	−	0.116707i
$293$	−344.440	+	198.863i	−1.17556	+	0.678712i	−0.954984	−	0.296657i	$-0.904128\pi$
$293$	−344.440	+	198.863i	−1.17556	+	0.678712i	−0.220579	+	0.975369i	$0.570795\pi$
$294$		0			0
$295$	309.670	−	536.365i	1.04973	−	1.81819i
$296$	−86.3121	+	49.8323i	−0.291595	+	0.168352i
$297$		0			0
$298$	−175.476	+	303.934i	−0.588847	+	1.01991i
$299$			585.514i			1.95824i
$300$		0			0
$301$	−260.585	+	372.187i	−0.865730	+	1.23650i
$302$	115.619	−	66.7528i	0.382845	−	0.221036i
$303$		0			0
$304$	38.6581	+	66.9578i	0.127165	+	0.220256i
$305$	−59.2072	−	34.1833i	−0.194122	−	0.112076i
$306$		0			0
$307$	−295.323			−0.961964			−0.480982	−	0.876731i	$-0.659720\pi$
$307$	−295.323			−0.961964			−0.480982	+	0.876731i	$0.659720\pi$
$308$	89.4884	−	41.7337i	0.290547	−	0.135499i
$309$		0			0
$310$	−145.963	+	252.815i	−0.470848	+	0.815532i
$311$		−	278.718i		−	0.896200i	−0.893983	−	0.448100i	$-0.852101\pi$
$311$		−	278.718i		−	0.896200i	0.893983	−	0.448100i	$-0.147899\pi$
$312$		0			0
$313$	199.467			0.637276			0.318638	−	0.947876i	$-0.396775\pi$
$313$	199.467			0.637276			0.318638	+	0.947876i	$0.396775\pi$
$314$		−	289.992i		−	0.923541i
$315$		0			0
$316$	20.3764			0.0644824
$317$		−	18.7055i		−	0.0590080i	−0.999565	−	0.0295040i	$-0.990607\pi$
$317$		−	18.7055i		−	0.0590080i	0.999565	−	0.0295040i	$-0.00939278\pi$
$318$		0			0
$319$	95.9730			0.300856
$320$	−59.3347	−	34.2569i	−0.185421	−	0.107053i
$321$		0			0
$322$	−223.539	+	319.275i	−0.694220	+	0.991538i
$323$		−	277.875i		−	0.860295i
$324$		0			0
$325$	−359.494	+	622.662i	−1.10614	+	1.91588i
$326$	−319.110	+	184.238i	−0.978866	+	0.565149i
$327$		0			0
$328$	−12.7280	−	22.0455i	−0.0388048	−	0.0672119i
$329$	−20.3553	+	232.775i	−0.0618703	+	0.707523i
$330$		0			0
$331$	211.382			0.638616			0.319308	−	0.947651i	$-0.396550\pi$
$331$	211.382			0.638616			0.319308	+	0.947651i	$0.396550\pi$
$332$	31.7291	+	18.3188i	0.0955697	+	0.0551772i
$333$		0			0
$334$	−90.0322	−	155.940i	−0.269558	−	0.466887i
$335$	−620.156	−	358.047i	−1.85121	−	1.06880i
$336$		0			0
$337$	271.681	+	470.566i	0.806175	+	1.39634i	0.915495	+	0.402330i	$0.131800\pi$
$337$	271.681	+	470.566i	0.806175	+	1.39634i	−0.109319	+	0.994007i	$0.534867\pi$
$338$	63.8941	+	36.8893i	0.189036	+	0.109140i
$339$		0			0
$340$	123.120	+	213.249i	0.362116	+	0.627204i
$341$	−147.222	+	84.9984i	−0.431735	+	0.249262i
$342$		0			0
$343$	−331.324	−	88.7332i	−0.965958	−	0.258698i
$344$	158.987	+	91.7911i	0.462171	+	0.266835i
$345$		0			0
$346$	−9.25519			−0.0267491
$347$		−	148.921i		−	0.429167i	−0.976706	−	0.214584i	$-0.931161\pi$
$347$		−	148.921i		−	0.429167i	0.976706	−	0.214584i	$-0.0688394\pi$
$348$		0			0
$349$	−229.407	+	397.344i	−0.657325	+	1.13852i	0.323980	+	0.946064i	$0.394979\pi$
$349$	−229.407	+	397.344i	−0.657325	+	1.13852i	−0.981305	+	0.192457i	$0.938354\pi$
$350$	−433.750	+	202.283i	−1.23929	+	0.577952i
$351$		0			0
$352$	−19.9488	−	34.5523i	−0.0566727	−	0.0981600i
$353$	419.426	−	242.156i	1.18817	−	0.685993i	0.230283	−	0.973124i	$-0.426035\pi$
$353$	419.426	−	242.156i	1.18817	−	0.685993i	0.957891	+	0.287130i	$0.0927013\pi$
$354$		0			0
$355$	261.214	−	452.436i	0.735813	−	1.27447i
$356$	80.0415	−	46.2120i	0.224836	−	0.129809i
$357$		0			0
$358$	−3.08606	+	5.34521i	−0.00862028	+	0.0149308i
$359$	−321.625	+	185.690i	−0.895892	+	0.517244i	−0.875865	−	0.482556i	$-0.839709\pi$
$359$	−321.625	+	185.690i	−0.895892	+	0.517244i	−0.0200269	+	0.999799i	$0.506375\pi$
$360$		0			0
$361$	−6.30620	+	10.9227i	−0.0174687	+	0.0302567i
$362$		−	100.888i		−	0.278696i
$363$		0			0
$364$	87.9990	+	188.694i	0.241756	+	0.518390i
$365$	−145.928	+	84.2516i	−0.399803	+	0.230826i
$366$		0			0
$367$	−122.345	−	211.909i	−0.333366	−	0.577407i	0.649803	−	0.760102i	$-0.274851\pi$
$367$	−122.345	−	211.909i	−0.333366	−	0.577407i	−0.983170	+	0.182695i	$0.941518\pi$
$368$	136.385	+	78.7417i	0.370610	+	0.213972i
$369$		0			0
$370$	426.775			1.15345
$371$	−347.222	−	243.106i	−0.935907	−	0.655271i
$372$		0			0
$373$	324.653	−	562.316i	0.870385	−	1.50755i	0.00878512	−	0.999961i	$-0.497204\pi$
$373$	324.653	−	562.316i	0.870385	−	1.50755i	0.861599	−	0.507589i	$-0.169463\pi$
$374$			143.392i			0.383402i
$375$		0			0
$376$	94.4142			0.251102
$377$			202.367i			0.536783i
$378$		0			0
$379$	−118.934			−0.313809			−0.156905	−	0.987614i	$-0.550152\pi$
$379$	−118.934			−0.313809			−0.156905	+	0.987614i	$0.550152\pi$
$380$		−	331.077i		−	0.871254i
$381$		0			0
$382$	167.535			0.438573
$383$	309.658	+	178.781i	0.808506	+	0.466791i	0.846437	−	0.532489i	$-0.178743\pi$
$383$	309.658	+	178.781i	0.808506	+	0.466791i	−0.0379309	+	0.999280i	$0.512077\pi$
$384$		0			0
$385$	−421.214	−	36.8337i	−1.09406	−	0.0956719i
$386$			271.940i			0.704509i
$387$		0			0
$388$	98.2909	−	170.245i	0.253327	−	0.438775i
$389$	303.765	−	175.379i	0.780887	−	0.450845i	−0.0558576	−	0.998439i	$-0.517789\pi$
$389$	303.765	−	175.379i	0.780887	−	0.450845i	0.836745	+	0.547593i	$0.184456\pi$
$390$		0			0
$391$	−282.999	−	490.168i	−0.723781	−	1.25363i
$392$	−24.0550	+	136.489i	−0.0613647	+	0.348187i
$393$		0			0
$394$	−393.952			−0.999878
$395$	−75.5643	−	43.6271i	−0.191302	−	0.110448i
$396$		0			0
$397$	126.600	+	219.278i	0.318893	+	0.552338i	0.980257	−	0.197726i	$-0.0633557\pi$
$397$	126.600	+	219.278i	0.318893	+	0.552338i	−0.661365	+	0.750065i	$0.730022\pi$
$398$	298.041	+	172.074i	0.748847	+	0.432347i
$399$		0			0
$400$	96.6917	+	167.475i	0.241729	+	0.418687i
$401$	415.228	+	239.732i	1.03548	+	0.597835i	0.918550	−	0.395305i	$-0.129361\pi$
$401$	415.228	+	239.732i	1.03548	+	0.597835i	0.116931	+	0.993140i	$0.462694\pi$
$402$		0			0
$403$	−179.226	−	310.429i	−0.444730	−	0.770296i
$404$	191.899	−	110.793i	0.474998	−	0.274240i
$405$		0			0
$406$	−77.2603	+	110.349i	−0.190296	+	0.271795i
$407$	215.228	+	124.262i	0.528815	+	0.305311i
$408$		0			0
$409$	10.5978			0.0259115			0.0129558	−	0.999916i	$-0.495876\pi$
$409$	10.5978			0.0259115			0.0129558	+	0.999916i	$0.495876\pi$
$410$			109.005i			0.265866i
$411$		0			0
$412$	87.6160	−	151.755i	0.212660	−	0.368338i
$413$	−44.0989	+	504.296i	−0.106777	+	1.22106i
$414$		0			0
$415$	−78.4432	−	135.868i	−0.189020	−	0.327392i
$416$	72.8565	−	42.0637i	0.175136	−	0.101115i
$417$		0			0
$418$	96.3978	−	166.966i	0.230617	−	0.399440i
$419$	−611.154	+	352.850i	−1.45860	+	0.842124i	−0.998943	−	0.0459710i	$-0.985362\pi$
$419$	−611.154	+	352.850i	−1.45860	+	0.842124i	−0.459659	+	0.888095i	$0.652028\pi$
$420$		0			0
$421$	212.170	−	367.490i	0.503968	−	0.872897i	−0.496022	−	0.868310i	$-0.665206\pi$
$421$	212.170	−	367.490i	0.503968	−	0.872897i	0.999989	−	0.00458746i	$-0.00146024\pi$
$422$	160.116	−	92.4428i	0.379421	−	0.219059i
$423$		0			0
$424$	−85.6341	+	148.323i	−0.201967	+	0.349817i
$425$		−	695.022i		−	1.63535i
$426$		0			0
$427$	55.6673	+	4.86790i	0.130368	+	0.0114002i
$428$	−44.6513	+	25.7794i	−0.104325	+	0.0602323i
$429$		0			0
$430$	−393.060	−	680.799i	−0.914092	−	1.58325i
$431$	−360.974	−	208.408i	−0.837526	−	0.483546i	0.0188965	−	0.999821i	$-0.493985\pi$
$431$	−360.974	−	208.408i	−0.837526	−	0.483546i	−0.856423	+	0.516276i	$0.827318\pi$
$432$		0			0
$433$	−457.197			−1.05588			−0.527941	−	0.849281i	$-0.677036\pi$
$433$	−457.197			−1.05588			−0.527941	+	0.849281i	$0.677036\pi$
$434$	20.7860	−	237.699i	0.0478939	−	0.547695i
$435$		0			0
$436$	−105.523	+	182.771i	−0.242025	+	0.419200i
$437$			761.001i			1.74142i
$438$		0			0
$439$	−122.763			−0.279642			−0.139821	−	0.990177i	$-0.544653\pi$
$439$	−122.763			−0.279642			−0.139821	+	0.990177i	$0.544653\pi$
$440$			170.846i			0.388286i
$441$		0			0
$442$	−302.355			−0.684061
$443$			313.476i			0.707621i	0.935317	+	0.353811i	$0.115114\pi$
$443$			313.476i			0.707621i	−0.935317	+	0.353811i	$0.884886\pi$
$444$		0			0
$445$	−395.770			−0.889370
$446$	62.6004	+	36.1423i	0.140360	+	0.0810367i
$447$		0			0
$448$	55.7871	+	4.87838i	0.124525	+	0.0108892i
$449$			216.459i			0.482092i	0.970514	+	0.241046i	$0.0774904\pi$
$449$			216.459i			0.482092i	−0.970514	+	0.241046i	$0.922510\pi$
$450$		0			0
$451$	−31.7385	+	54.9726i	−0.0703735	+	0.121891i
$452$	25.4797	−	14.7107i	0.0563710	−	0.0325458i
$453$		0			0
$454$	−245.309	−	424.887i	−0.540328	−	0.935875i
$455$	77.6669	−	888.166i	0.170697	−	1.95201i
$456$		0			0
$457$	564.973			1.23627			0.618133	−	0.786074i	$-0.287889\pi$
$457$	564.973			1.23627			0.618133	+	0.786074i	$0.287889\pi$
$458$	−204.810	−	118.247i	−0.447182	−	0.258181i
$459$		0			0
$460$	−337.181	−	584.014i	−0.733001	−	1.26960i
$461$	504.476	+	291.259i	1.09431	+	0.631799i	0.934720	−	0.355385i	$-0.115650\pi$
$461$	504.476	+	291.259i	1.09431	+	0.631799i	0.159588	+	0.987184i	$0.448983\pi$
$462$		0			0
$463$	128.093	+	221.863i	0.276658	+	0.479186i	0.970552	−	0.240891i	$-0.0774397\pi$
$463$	128.093	+	221.863i	0.276658	+	0.479186i	−0.693894	+	0.720077i	$0.744106\pi$
$464$	47.1377	+	27.2150i	0.101590	+	0.0586529i
$465$		0			0
$466$	−140.413	−	243.202i	−0.301315	−	0.521892i
$467$	300.844	−	173.693i	0.644206	−	0.371933i	−0.142027	−	0.989863i	$-0.545362\pi$
$467$	300.844	−	173.693i	0.644206	−	0.371933i	0.786233	+	0.617930i	$0.212029\pi$
$468$		0			0
$469$	583.078	+	50.9880i	1.24324	+	0.108716i
$470$	−350.127	−	202.146i	−0.744952	−	0.430098i
$471$		0			0
$472$	204.544			0.433356
$473$		−	457.780i		−	0.967823i
$474$		0			0
$475$	−467.240	+	809.283i	−0.983663	+	1.70375i
$476$	−164.871	−	115.434i	−0.346368	−	0.242508i
$477$		0			0
$478$	−203.011	−	351.626i	−0.424710	−	0.735620i
$479$	−58.7577	+	33.9238i	−0.122667	+	0.0708220i	−0.560078	−	0.828440i	$-0.689229\pi$
$479$	−58.7577	+	33.9238i	−0.122667	+	0.0708220i	0.437411	+	0.899262i	$0.355896\pi$
$480$		0			0
$481$	−262.016	+	453.826i	−0.544733	+	0.943505i
$482$	−463.681	+	267.706i	−0.961993	+	0.555407i
$483$		0			0
$484$	71.2557	−	123.419i	0.147223	−	0.254997i
$485$	−729.007	+	420.892i	−1.50311	+	0.867819i
$486$		0			0
$487$	−231.777	+	401.449i	−0.475927	+	0.824330i	−0.999620	−	0.0275774i	$-0.991221\pi$
$487$	−231.777	+	401.449i	−0.475927	+	0.824330i	0.523693	+	0.851907i	$0.324554\pi$
$488$		−	22.5788i		−	0.0462681i
$489$		0			0
$490$	381.437	−	454.656i	0.778443	−	0.927870i
$491$	−93.7518	+	54.1276i	−0.190941	+	0.110240i	−0.592423	−	0.805627i	$-0.701828\pi$
$491$	−93.7518	+	54.1276i	−0.190941	+	0.110240i	0.401482	+	0.915867i	$0.368495\pi$
$492$		0			0
$493$	−97.8109	−	169.413i	−0.198399	−	0.343638i
$494$	352.062	+	203.263i	0.712675	+	0.411463i
$495$		0			0
$496$	−96.4116			−0.194378
$497$	−37.1984	+	425.385i	−0.0748458	+	0.855905i
$498$		0			0
$499$	3.76956	−	6.52906i	0.00755422	−	0.0130843i	−0.862224	−	0.506528i	$-0.830929\pi$
$499$	3.76956	−	6.52906i	0.00755422	−	0.0130843i	0.869778	+	0.493444i	$0.164262\pi$
$500$		−	399.878i		−	0.799756i
$501$		0			0
$502$	139.254			0.277398
$503$		−	402.034i		−	0.799272i	−0.916674	−	0.399636i	$-0.869137\pi$
$503$		−	402.034i		−	0.799272i	0.916674	−	0.399636i	$-0.130863\pi$
$504$		0			0
$505$	−948.855			−1.87892
$506$		−	392.700i		−	0.776088i
$507$		0			0
$508$	28.5484			0.0561976
$509$	−637.847	−	368.261i	−1.25314	−	0.723499i	−0.281406	−	0.959589i	$-0.590801\pi$
$509$	−637.847	−	368.261i	−1.25314	−	0.723499i	−0.971731	+	0.236090i	$0.924134\pi$
$510$		0			0
$511$	78.9921	−	112.822i	0.154583	−	0.220788i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−152.227	+	263.664i	−0.296161	+	0.512966i
$515$	−649.833	+	375.181i	−1.26181	+	0.728507i
$516$		0			0
$517$	−117.716	−	203.889i	−0.227690	−	0.394370i
$518$	−316.138	+	147.434i	−0.610304	+	0.284621i
$519$		0			0
$520$	−360.243			−0.692775
$521$	−455.192	−	262.805i	−0.873690	−	0.504425i	−0.00511719	−	0.999987i	$-0.501629\pi$
$521$	−455.192	−	262.805i	−0.873690	−	0.504425i	−0.868573	+	0.495562i	$0.834962\pi$
$522$		0			0
$523$	46.2741	+	80.1490i	0.0884781	+	0.153249i	0.906868	−	0.421415i	$-0.138466\pi$
$523$	46.2741	+	80.1490i	0.0884781	+	0.153249i	−0.818390	+	0.574663i	$0.805133\pi$
$524$	299.203	+	172.745i	0.570999	+	0.329666i
$525$		0			0
$526$	8.85001	+	15.3287i	0.0168251	+	0.0291420i
$527$	300.082	+	173.252i	0.569415	+	0.328752i
$528$		0			0
$529$	510.532	+	884.267i	0.965088	+	1.67158i
$530$	635.133	−	366.694i	1.19836	−	0.691876i
$531$		0			0
$532$	114.374	+	245.248i	0.214988	+	0.460993i
$533$	−115.914	−	66.9232i	−0.217475	−	0.125560i
$534$		0			0
$535$	220.781			0.412674
$536$		−	236.498i		−	0.441228i
$537$		0			0
$538$	123.104	−	213.222i	0.228818	−	0.396324i
$539$	324.743	−	118.228i	0.602492	−	0.219346i
$540$		0			0
$541$	−66.8426	−	115.775i	−0.123554	−	0.214001i	0.797613	−	0.603170i	$-0.206096\pi$
$541$	−66.8426	−	115.775i	−0.123554	−	0.214001i	−0.921167	+	0.389168i	$0.872762\pi$
$542$	−43.0921	+	24.8792i	−0.0795056	+	0.0459026i
$543$		0			0
$544$	−40.6616	+	70.4279i	−0.0747456	+	0.129463i
$545$	782.646	−	451.861i	1.43605	−	0.829103i
$546$		0			0
$547$	28.0279	−	48.5457i	0.0512393	−	0.0887490i	−0.839268	−	0.543718i	$-0.817016\pi$
$547$	28.0279	−	48.5457i	0.0512393	−	0.0887490i	0.890507	+	0.454969i	$0.150350\pi$
$548$	−280.747	+	162.089i	−0.512312	+	0.295783i
$549$		0			0
$550$	241.110	−	417.615i	0.438382	−	0.759300i
$551$			263.020i			0.477350i
$552$		0			0
$553$	71.0464	+	6.21276i	0.128475	+	0.0112346i
$554$	64.3117	−	37.1304i	0.116086	−	0.0670223i
$555$		0			0
$556$	156.927	+	271.806i	0.282243	+	0.488860i
$557$	−173.289	−	100.048i	−0.311111	−	0.179620i	0.336313	−	0.941750i	$-0.390820\pi$
$557$	−173.289	−	100.048i	−0.311111	−	0.179620i	−0.647423	+	0.762130i	$0.724153\pi$
$558$		0			0
$559$	965.268			1.72678
$560$	−196.437	−	137.534i	−0.350780	−	0.245597i
$561$		0			0
$562$	−267.342	+	463.049i	−0.475697	+	0.823931i
$563$			603.474i			1.07189i	0.844253	+	0.535945i	$0.180044\pi$
$563$			603.474i			1.07189i	−0.844253	+	0.535945i	$0.819956\pi$
$564$		0			0
$565$	−125.986			−0.222984
$566$		−	780.309i		−	1.37864i
$567$		0			0
$568$	172.537			0.303763
$569$		−	4.01413i		−	0.00705472i	−0.999994	−	0.00352736i	$-0.998877\pi$
$569$		−	4.01413i		−	0.00705472i	0.999994	−	0.00352736i	$-0.00112280\pi$
$570$		0			0
$571$	−606.712			−1.06254			−0.531271	−	0.847202i	$-0.678285\pi$
$571$	−606.712			−1.06254			−0.531271	+	0.847202i	$0.678285\pi$
$572$	−181.675	−	104.890i	−0.317613	−	0.183374i
$573$		0			0
$574$	−37.6569	−	80.7467i	−0.0656044	−	0.140674i
$575$			1903.42i			3.31029i
$576$		0			0
$577$	290.727	−	503.553i	0.503859	−	0.872709i	−0.496131	−	0.868248i	$-0.665247\pi$
$577$	290.727	−	503.553i	0.503859	−	0.872709i	0.999990	−	0.00446157i	$-0.00142017\pi$
$578$	−100.832	+	58.2156i	−0.174451	+	0.100719i
$579$		0			0
$580$	−116.537	−	201.849i	−0.200927	−	0.348015i
$581$	105.044	+	73.5463i	0.180799	+	0.126586i
$582$		0			0
$583$	427.074			0.732545
$584$	−48.1943	−	27.8250i	−0.0825245	−	0.0476455i
$585$		0			0
$586$	281.234	+	487.112i	0.479922	+	0.831249i
$587$	−119.284	−	68.8684i	−0.203209	−	0.117323i	0.394943	−	0.918706i	$-0.370764\pi$
$587$	−119.284	−	68.8684i	−0.203209	−	0.117323i	−0.598151	+	0.801383i	$0.704098\pi$
$588$		0			0
$589$	−232.943	−	403.469i	−0.395489	−	0.685008i
$590$	−758.534	−	437.940i	−1.28565	−	0.742271i
$591$		0			0
$592$	70.4735	+	122.064i	0.119043	+	0.206189i
$593$	491.375	−	283.696i	0.828626	−	0.478407i	−0.0247561	−	0.999694i	$-0.507881\pi$
$593$	491.375	−	283.696i	0.828626	−	0.478407i	0.853382	+	0.521286i	$0.174548\pi$
$594$		0			0
$595$	364.261	+	781.075i	0.612203	+	1.31273i
$596$	429.828	+	248.161i	0.721187	+	0.416378i
$597$		0			0
$598$	828.042			1.38469
$599$		−	812.389i		−	1.35624i	−0.734950	−	0.678121i	$-0.762794\pi$
$599$		−	812.389i		−	1.35624i	0.734950	−	0.678121i	$-0.237206\pi$
$600$		0			0
$601$	370.313	−	641.402i	0.616162	−	1.06722i	−0.374017	−	0.927422i	$-0.622020\pi$
$601$	370.313	−	641.402i	0.616162	−	1.06722i	0.990179	−	0.139802i	$-0.0446467\pi$
$602$	526.352	+	368.522i	0.874338	+	0.612163i
$603$		0			0
$604$	−94.4026	−	163.510i	−0.156296	−	0.270712i
$605$	−528.492	+	305.125i	−0.873540	+	0.504339i
$606$		0			0
$607$	−93.4601	+	161.878i	−0.153971	+	0.266685i	−0.932684	−	0.360695i	$-0.882539\pi$
$607$	−93.4601	+	161.878i	−0.153971	+	0.266685i	0.778713	+	0.627380i	$0.215873\pi$
$608$	94.6926	−	54.6708i	0.155744	−	0.0899191i
$609$		0			0
$610$	−48.3425	+	83.7316i	−0.0792500	+	0.137265i
$611$	429.918	−	248.213i	0.703630	−	0.406241i
$612$		0			0
$613$	435.744	−	754.731i	0.710839	−	1.23121i	−0.253704	−	0.967282i	$-0.581649\pi$
$613$	435.744	−	754.731i	0.710839	−	1.23121i	0.964543	−	0.263927i	$-0.0850178\pi$
$614$			417.650i			0.680211i
$615$		0			0
$616$	−59.0204	−	126.556i	−0.0958123	−	0.205448i
$617$	−441.505	+	254.903i	−0.715567	+	0.413133i	−0.813119	−	0.582098i	$-0.802232\pi$
$617$	−441.505	+	254.903i	−0.715567	+	0.413133i	0.0975522	+	0.995230i	$0.468899\pi$
$618$		0			0
$619$	532.400	+	922.144i	0.860097	+	1.48973i	0.871835	+	0.489801i	$0.162930\pi$
$619$	532.400	+	922.144i	0.860097	+	1.48973i	−0.0117376	+	0.999931i	$0.503736\pi$
$620$	357.534	+	206.423i	0.576668	+	0.332940i
$621$		0			0
$622$	−394.167			−0.633709
$623$	293.170	−	136.723i	0.470578	−	0.219458i
$624$		0			0
$625$	−251.838	+	436.196i	−0.402940	+	0.697913i
$626$		−	282.090i		−	0.450622i
$627$		0			0
$628$	−410.110			−0.653042
$629$		−	506.565i		−	0.805350i
$630$		0			0
$631$	479.402			0.759750			0.379875	−	0.925038i	$-0.375967\pi$
$631$	479.402			0.759750			0.379875	+	0.925038i	$0.375967\pi$
$632$		−	28.8167i		−	0.0455960i
$633$		0			0
$634$	−26.4536			−0.0417250
$635$	−105.869	−	61.1237i	−0.166723	−	0.0962578i
$636$		0			0
$637$	249.293	+	684.749i	0.391355	+	1.07496i
$638$		−	135.726i		−	0.212737i
$639$		0			0
$640$	−48.4465	+	83.9119i	−0.0756977	+	0.131112i
$641$	−181.333	+	104.693i	−0.282891	+	0.163327i	−0.634732	−	0.772733i	$-0.718889\pi$
$641$	−181.333	+	104.693i	−0.282891	+	0.163327i	0.351840	+	0.936060i	$0.385556\pi$
$642$		0			0
$643$	−184.919	−	320.289i	−0.287588	−	0.498117i	0.685645	−	0.727936i	$-0.259520\pi$
$643$	−184.919	−	320.289i	−0.287588	−	0.498117i	−0.973234	+	0.229818i	$0.926187\pi$
$644$	451.523	+	316.132i	0.701123	+	0.490888i
$645$		0			0
$646$	−392.975			−0.608321
$647$	227.896	+	131.576i	0.352235	+	0.203363i	0.665669	−	0.746247i	$-0.268146\pi$
$647$	227.896	+	131.576i	0.352235	+	0.203363i	−0.313434	+	0.949610i	$0.601479\pi$
$648$		0			0
$649$	−255.025	−	441.717i	−0.392951	−	0.680611i
$650$	880.577	+	508.401i	1.35473	+	0.782156i
$651$		0			0
$652$	260.553	+	451.290i	0.399620	+	0.692163i
$653$	702.567	+	405.628i	1.07591	+	0.621175i	0.929789	−	0.368092i	$-0.119989\pi$
$653$	702.567	+	405.628i	1.07591	+	0.621175i	0.146118	+	0.989267i	$0.453322\pi$
$654$		0			0
$655$	−739.714	−	1281.22i	−1.12933	−	1.95606i
$656$	−31.1771	+	18.0001i	−0.0475260	+	0.0274391i
$657$		0			0
$658$	329.194	+	28.7868i	0.500294	+	0.0437489i
$659$	−31.0199	−	17.9093i	−0.0470711	−	0.0271765i	0.476280	−	0.879294i	$-0.341985\pi$
$659$	−31.0199	−	17.9093i	−0.0470711	−	0.0271765i	−0.523351	+	0.852117i	$0.675318\pi$
$660$		0			0
$661$	389.167			0.588756			0.294378	−	0.955689i	$-0.404888\pi$
$661$	389.167			0.588756			0.294378	+	0.955689i	$0.404888\pi$
$662$		−	298.939i		−	0.451570i
$663$		0			0
$664$	25.9067	−	44.8718i	0.0390162	−	0.0675780i
$665$	100.945	−	1154.36i	0.151797	−	1.73588i
$666$		0			0
$667$	267.869	+	463.963i	0.401603	+	0.695596i
$668$	−220.533	+	127.325i	−0.330139	+	0.190606i
$669$		0			0
$670$	−506.355	+	877.033i	−0.755754	+	1.30900i
$671$	−48.7594	+	28.1512i	−0.0726668	+	0.0419542i
$672$		0			0
$673$	−399.256	+	691.532i	−0.593248	+	1.02754i	0.400543	+	0.916278i	$0.368821\pi$
$673$	−399.256	+	691.532i	−0.593248	+	1.02754i	−0.993792	+	0.111258i	$0.964512\pi$
$674$	665.480	−	384.215i	0.987359	−	0.570052i
$675$		0			0
$676$	52.1693	−	90.3600i	0.0771736	−	0.133669i
$677$			512.442i			0.756930i	0.925616	+	0.378465i	$0.123548\pi$
$677$			512.442i			0.756930i	−0.925616	+	0.378465i	$0.876452\pi$
$678$		0			0
$679$	394.618	−	563.623i	0.581175	−	0.830078i
$680$	301.580	−	174.117i	0.443500	−	0.256055i
$681$		0			0
$682$	120.206	+	208.203i	0.176255	+	0.305283i
$683$	1041.76	+	601.463i	1.52528	+	0.880619i	0.999551	+	0.0299649i	$0.00953956\pi$
$683$	1041.76	+	601.463i	1.52528	+	0.880619i	0.525726	+	0.850654i	$0.323794\pi$
$684$		0			0
$685$	1388.17			2.02652
$686$	−125.488	+	468.563i	−0.182927	+	0.683036i
$687$		0			0
$688$	129.812	−	224.841i	0.188681	−	0.326804i
$689$			900.521i			1.30700i
$690$		0			0
$691$	−541.984			−0.784347			−0.392174	−	0.919891i	$-0.628277\pi$
$691$	−541.984			−0.784347			−0.392174	+	0.919891i	$0.628277\pi$
$692$			13.0888i			0.0189145i
$693$		0			0
$694$	−210.606			−0.303467
$695$		−	1343.96i		−	1.93376i
$696$		0			0
$697$	129.385			0.185631
$698$	561.929	+	324.430i	0.805056	+	0.464799i
$699$		0			0
$700$	286.072	+	613.415i	0.408674	+	0.876307i
$701$		−	1106.17i		−	1.57800i	−0.614396	−	0.788998i	$-0.710600\pi$
$701$		−	1106.17i		−	1.57800i	0.614396	−	0.788998i	$-0.289400\pi$
$702$		0			0
$703$	−340.547	+	589.844i	−0.484419	+	0.839039i
$704$	−48.8643	+	28.2118i	−0.0694096	+	0.0400736i
$705$		0			0
$706$	−342.460	−	593.158i	−0.485070	−	0.840167i
$707$	702.874	−	327.791i	0.994164	−	0.463637i
$708$		0			0
$709$	1359.73			1.91781			0.958907	−	0.283721i	$-0.0915690\pi$
$709$	1359.73			1.91781			0.958907	+	0.283721i	$0.0915690\pi$
$710$	−639.840	−	369.412i	−0.901184	−	0.520299i
$711$		0			0
$712$	−65.3537	−	113.196i	−0.0917888	−	0.158983i
$713$	−821.816	−	474.476i	−1.15262	−	0.665464i
$714$		0			0
$715$	449.150	+	777.951i	0.628182	+	1.08804i
$716$	7.55927	+	4.36435i	0.0105576	+	0.00609546i
$717$		0			0
$718$	262.606	+	454.847i	0.365746	+	0.633491i
$719$	−669.276	+	386.407i	−0.930843	+	0.537422i	−0.887078	−	0.461620i	$-0.847269\pi$
$719$	−669.276	+	386.407i	−0.930843	+	0.537422i	−0.0437647	+	0.999042i	$0.513935\pi$
$720$		0			0
$721$	351.760	−	502.410i	0.487878	−	0.696824i
$722$	15.4470	+	8.91832i	0.0213947	+	0.0123522i
$723$		0			0
$724$	−142.677			−0.197068
$725$			657.865i			0.907401i
$726$		0			0
$727$	−332.257	+	575.485i	−0.457024	+	0.791589i	−0.998802	−	0.0489326i	$-0.984418\pi$
$727$	−332.257	+	575.485i	−0.457024	+	0.791589i	0.541778	+	0.840522i	$0.317751\pi$
$728$	266.853	−	124.449i	0.366557	−	0.170947i
$729$		0			0
$730$	119.150	+	206.373i	0.163219	+	0.282703i
$731$	−808.082	+	466.547i	−1.10545	+	0.638231i
$732$		0			0
$733$	−491.449	+	851.214i	−0.670462	+	1.16127i	0.307311	+	0.951609i	$0.400571\pi$
$733$	−491.449	+	851.214i	−0.670462	+	1.16127i	−0.977773	+	0.209666i	$0.932762\pi$
$734$	−299.684	+	173.023i	−0.408289	+	0.235726i
$735$		0			0
$736$	111.358	−	192.877i	0.151301	−	0.262061i
$737$	−510.722	+	294.865i	−0.692974	+	0.400089i
$738$		0			0
$739$	−451.664	+	782.306i	−0.611183	+	1.05860i	0.379858	+	0.925045i	$0.375973\pi$
$739$	−451.664	+	782.306i	−0.611183	+	1.05860i	−0.991041	+	0.133556i	$0.957360\pi$
$740$		−	603.551i		−	0.815609i
$741$		0			0
$742$	−343.803	+	491.046i	−0.463347	+	0.661787i
$743$	662.703	−	382.612i	0.891928	−	0.514955i	0.0173557	−	0.999849i	$-0.494475\pi$
$743$	662.703	−	382.612i	0.891928	−	0.514955i	0.874573	+	0.484894i	$0.161142\pi$
$744$		0			0
$745$	−1062.65	−	1840.57i	−1.42638	−	2.47056i
$746$	−795.235	−	459.129i	−1.06600	−	0.615455i
$747$		0			0
$748$	202.787			0.271106
$749$	−163.545	+	76.2709i	−0.218352	+	0.101830i
$750$		0			0
$751$	−224.037	+	388.044i	−0.298319	+	0.516703i	−0.975751	−	0.218881i	$-0.929759\pi$
$751$	−224.037	+	388.044i	−0.298319	+	0.516703i	0.677433	+	0.735585i	$0.263093\pi$
$752$		−	133.522i		−	0.177556i
$753$		0			0
$754$	286.191			0.379563
$755$			808.485i			1.07084i
$756$		0			0
$757$	−1350.52			−1.78404			−0.892020	−	0.451995i	$-0.850712\pi$
$757$	−1350.52			−1.78404			−0.892020	+	0.451995i	$0.850712\pi$
$758$			168.198i			0.221897i
$759$		0			0
$760$	−468.213			−0.616070
$761$	−184.282	−	106.395i	−0.242158	−	0.139810i	0.374010	−	0.927425i	$-0.377983\pi$
$761$	−184.282	−	106.395i	−0.242158	−	0.139810i	−0.616168	+	0.787615i	$0.711316\pi$
$762$		0			0
$763$	−423.653	+	605.093i	−0.555247	+	0.793045i
$764$		−	236.930i		−	0.310118i
$765$		0			0
$766$	252.834	−	437.922i	0.330071	−	0.571700i
$767$	931.397	−	537.742i	1.21434	−	0.701098i
$768$		0			0
$769$	349.195	+	604.823i	0.454090	+	0.786506i	0.998635	−	0.0522249i	$-0.0166313\pi$
$769$	349.195	+	604.823i	0.454090	+	0.786506i	−0.544546	+	0.838731i	$0.683298\pi$
$770$	−52.0907	+	595.687i	−0.0676502	+	0.773619i
$771$		0			0
$772$	384.582			0.498163
$773$	−156.237	−	90.2037i	−0.202118	−	0.116693i	0.395525	−	0.918455i	$-0.370563\pi$
$773$	−156.237	−	90.2037i	−0.202118	−	0.116693i	−0.597643	+	0.801762i	$0.703896\pi$
$774$		0			0
$775$	−582.638	−	1009.16i	−0.751791	−	1.30214i
$776$	−240.762	−	139.004i	−0.310261	−	0.179129i
$777$		0			0
$778$	−248.023	−	429.589i	−0.318796	−	0.552170i
$779$	−150.656	−	86.9811i	−0.193396	−	0.111657i
$780$		0			0
$781$	−215.119	−	372.598i	−0.275441	−	0.477078i
$782$	−693.202	+	400.220i	−0.886448	+	0.511791i
$783$		0			0
$784$	193.025	+	34.0189i	0.246206	+	0.0433914i
$785$	1520.86	+	878.069i	1.93740	+	1.11856i
$786$		0			0
$787$	160.454			0.203880			0.101940	−	0.994791i	$-0.467495\pi$
$787$	160.454			0.203880			0.101940	+	0.994791i	$0.467495\pi$
$788$			557.132i			0.707021i
$789$		0			0
$790$	−61.6980	+	106.864i	−0.0780988	+	0.135271i
$791$	93.3252	−	43.5230i	0.117984	−	0.0550228i
$792$		0			0
$793$	−59.3593	−	102.813i	−0.0748541	−	0.129651i
$794$	310.106	−	179.040i	0.390562	−	0.225491i
$795$		0			0
$796$	243.350	−	421.494i	0.305716	−	0.529515i
$797$	969.679	−	559.844i	1.21666	−	0.702439i	0.252459	−	0.967608i	$-0.418761\pi$
$797$	969.679	−	559.844i	1.21666	−	0.702439i	0.964202	+	0.265168i	$0.0854275\pi$
$798$		0			0
$799$	−239.940	+	415.588i	−0.300300	+	0.520135i
$800$	236.845	−	136.743i	0.296057	−	0.170928i
$801$		0			0
$802$	339.032	−	587.221i	0.422733	−	0.732196i
$803$			138.769i			0.172813i
$804$		0			0
$805$	−997.580	−	2139.08i	−1.23923	−	2.65725i
$806$	−439.013	+	253.464i	−0.544681	+	0.314472i
$807$		0			0
$808$	−156.685	−	271.386i	−0.193917	−	0.335874i
$809$	−262.167	−	151.362i	−0.324063	−	0.187098i	0.329139	−	0.944282i	$-0.393242\pi$
$809$	−262.167	−	151.362i	−0.324063	−	0.187098i	−0.653202	+	0.757183i	$0.726575\pi$
$810$		0			0
$811$	1037.56			1.27936			0.639680	−	0.768641i	$-0.279067\pi$
$811$	1037.56			1.27936			0.639680	+	0.768641i	$0.279067\pi$
$812$	156.057	+	109.262i	0.192188	+	0.134560i
$813$		0			0
$814$	175.733	−	304.378i	0.215888	−	0.373929i
$815$		−	2231.43i		−	2.73795i
$816$		0			0
$817$	1254.57			1.53559
$818$		−	14.9876i		−	0.0183222i
$819$		0			0
$820$	154.157			0.187996
$821$		−	603.941i		−	0.735617i	−0.929902	−	0.367808i	$-0.880108\pi$
$821$		−	603.941i		−	0.735617i	0.929902	−	0.367808i	$-0.119892\pi$
$822$		0			0
$823$	−28.4475			−0.0345657			−0.0172828	−	0.999851i	$-0.505502\pi$
$823$	−28.4475			−0.0345657			−0.0172828	+	0.999851i	$0.505502\pi$
$824$	−214.614	−	123.908i	−0.260454	−	0.150373i
$825$		0			0
$826$	713.183	+	62.3652i	0.863417	+	0.0755027i
$827$			798.699i			0.965778i	0.875681	+	0.482889i	$0.160413\pi$
$827$			798.699i			0.965778i	−0.875681	+	0.482889i	$0.839587\pi$
$828$		0			0
$829$	216.869	−	375.628i	0.261603	−	0.453110i	−0.705065	−	0.709143i	$-0.749082\pi$
$829$	216.869	−	375.628i	0.261603	−	0.453110i	0.966668	+	0.256033i	$0.0824154\pi$
$830$	−192.146	+	110.935i	−0.231501	+	0.133657i
$831$		0			0
$832$	−59.4871	−	103.035i	−0.0714989	−	0.123840i
$833$	−539.660	−	452.751i	−0.647851	−	0.543519i
$834$		0			0
$835$	1090.44			1.30591
$836$	−236.125	−	136.327i	−0.282447	−	0.163071i
$837$		0			0
$838$	499.005	+	864.303i	0.595472	+	1.03139i
$839$	−338.993	−	195.718i	−0.404044	−	0.233275i	0.284183	−	0.958770i	$-0.408278\pi$
$839$	−338.993	−	195.718i	−0.404044	−	0.233275i	−0.688227	+	0.725495i	$0.741611\pi$
$840$		0			0
$841$	−327.918	−	567.971i	−0.389915	−	0.675352i
$842$	−519.709	−	300.054i	−0.617232	−	0.356359i
$843$		0			0
$844$	−130.734	−	226.438i	−0.154898	−	0.268291i
$845$	−386.931	+	223.395i	−0.457907	+	0.264373i
$846$		0			0
$847$	286.077	−	408.597i	0.337753	−	0.482405i
$848$	209.760	+	121.105i	0.247358	+	0.142812i
$849$		0			0
$850$	−982.910			−1.15636
$851$			1387.30i			1.63020i
$852$		0			0
$853$	−517.801	+	896.857i	−0.607035	+	1.05141i	0.384692	+	0.923045i	$0.374308\pi$
$853$	−517.801	+	896.857i	−0.607035	+	1.05141i	−0.991726	+	0.128370i	$0.959026\pi$
$854$	6.88426	−	78.7254i	0.00806119	−	0.0921843i
$855$		0			0
$856$	36.4576	+	63.1464i	0.0425907	+	0.0737692i
$857$	735.819	−	424.825i	0.858599	−	0.495712i	−0.00494405	−	0.999988i	$-0.501574\pi$
$857$	735.819	−	424.825i	0.858599	−	0.495712i	0.863543	+	0.504276i	$0.168240\pi$
$858$		0			0
$859$	−610.792	+	1057.92i	−0.711050	+	1.23157i	0.253414	+	0.967358i	$0.418447\pi$
$859$	−610.792	+	1057.92i	−0.711050	+	1.23157i	−0.964464	+	0.264216i	$0.914887\pi$
$860$	−962.795	+	555.870i	−1.11953	+	0.646361i
$861$		0			0
$862$	−294.734	+	510.494i	−0.341919	+	0.592220i
$863$	232.708	−	134.354i	0.269650	−	0.155682i	−0.359079	−	0.933307i	$-0.616909\pi$
$863$	232.708	−	134.354i	0.269650	−	0.155682i	0.628728	+	0.777625i	$0.283576\pi$
$864$		0			0
$865$	28.0239	−	48.5387i	0.0323975	−	0.0561142i
$866$			646.574i			0.746621i
$867$		0			0
$868$	−336.158	−	29.3958i	−0.387279	−	0.0338661i
$869$	−62.2301	+	35.9286i	−0.0716112	+	0.0413447i
$870$		0			0
$871$	−621.749	−	1076.90i	−0.713833	−	1.23640i
$872$	258.477	+	149.232i	0.296419	+	0.171138i
$873$		0			0
$874$	1076.22			1.23137
$875$	121.922	−	1394.25i	0.139340	−	1.59343i
$876$		0			0
$877$	502.028	−	869.538i	0.572438	−	0.991491i	−0.423877	−	0.905720i	$-0.639331\pi$
$877$	502.028	−	869.538i	0.572438	−	0.991491i	0.996315	−	0.0857714i	$-0.0273355\pi$
$878$			173.613i			0.197737i
$879$		0			0
$880$	241.612			0.274560
$881$			370.961i			0.421068i	0.977587	+	0.210534i	$0.0675203\pi$
$881$			370.961i			0.421068i	−0.977587	+	0.210534i	$0.932480\pi$
$882$		0			0
$883$	694.091			0.786060			0.393030	−	0.919526i	$-0.371427\pi$
$883$	694.091			0.786060			0.393030	+	0.919526i	$0.371427\pi$
$884$			427.594i			0.483704i
$885$		0			0
$886$	443.322			0.500364
$887$	−252.024	−	145.506i	−0.284131	−	0.164043i	0.351161	−	0.936315i	$-0.385787\pi$
$887$	−252.024	−	145.506i	−0.284131	−	0.164043i	−0.635292	+	0.772272i	$0.719120\pi$
$888$		0			0
$889$	99.5396	+	8.70438i	0.111968	+	0.00979120i
$890$			559.703i			0.628880i
$891$		0			0
$892$	51.1130	−	88.5303i	0.0573016	−	0.0992492i
$893$	558.771	−	322.607i	0.625723	−	0.361261i
$894$		0			0
$895$	−18.6886	−	32.3696i	−0.0208811	−	0.0361672i
$896$	6.89907	−	78.8949i	0.00769986	−	0.0880523i
$897$		0			0
$898$	306.120			0.340890
$899$	−284.039	−	163.990i	−0.315950	−	0.182414i
$900$		0			0
$901$	−435.252	−	753.879i	−0.483077	−	0.836713i
$902$	77.7430	+	44.8850i	0.0861896	+	0.0497616i
$903$		0			0
$904$	−20.8041	−	36.0337i	−0.0230134	−	0.0398603i
$905$	529.107	+	305.480i	0.584648	+	0.337547i
$906$		0			0
$907$	727.823	+	1260.63i	0.802451	+	1.38989i	0.917999	+	0.396583i	$0.129804\pi$
$907$	727.823	+	1260.63i	0.802451	+	1.38989i	−0.115548	+	0.993302i	$0.536862\pi$
$908$	−600.881	+	346.919i	−0.661763	+	0.382069i
$909$		0			0
$910$	−1256.06	−	109.838i	−1.38028	−	0.120701i
$911$	−310.858	−	179.474i	−0.341228	−	0.197008i	0.319587	−	0.947557i	$-0.396456\pi$
$911$	−310.858	−	179.474i	−0.341228	−	0.197008i	−0.660815	+	0.750549i	$0.729789\pi$
$912$		0			0
$913$	−129.202			−0.141514
$914$		−	798.993i		−	0.874172i
$915$		0			0
$916$	−167.226	+	289.644i	−0.182561	+	0.316206i
$917$	990.561	+	693.537i	1.08022	+	0.756310i
$918$		0			0
$919$	−739.927	−	1281.59i	−0.805144	−	1.39455i	−0.916194	−	0.400735i	$-0.868755\pi$
$919$	−739.927	−	1281.59i	−0.805144	−	1.39455i	0.111050	−	0.993815i	$-0.464579\pi$
$920$	−825.920	+	476.845i	−0.897739	+	0.518310i
$921$		0			0
$922$	411.903	−	713.437i	0.446749	−	0.773793i
$923$	785.654	−	453.598i	0.851196	−	0.491438i
$924$		0			0
$925$	−851.776	+	1475.32i	−0.920839	+	1.59494i
$926$	313.762	−	181.150i	0.338835	−	0.195627i
$927$		0			0
$928$	38.4878	−	66.6628i	0.0414739	−	0.0718349i
$929$		−	494.398i		−	0.532183i	−0.963948	−	0.266092i	$-0.914268\pi$
$929$		−	494.398i		−	0.532183i	0.963948	−	0.266092i	$-0.0857324\pi$
$930$		0			0
$931$	324.010	+	889.978i	0.348024	+	0.955938i
$932$	−343.939	+	198.573i	−0.369033	+	0.213062i
$933$		0			0
$934$	−245.638	−	425.458i	−0.262996	−	0.455523i
$935$	−752.020	−	434.179i	−0.804299	−	0.464362i
$936$		0			0
$937$	−1460.33			−1.55852			−0.779258	−	0.626704i	$-0.784404\pi$
$937$	−1460.33			−1.55852			−0.779258	+	0.626704i	$0.784404\pi$
$938$	72.1080	−	824.596i	0.0768742	−	0.879100i
$939$		0			0
$940$	−285.878	+	495.155i	−0.304125	+	0.526760i
$941$		−	1320.00i		−	1.40276i	−0.712786	−	0.701381i	$-0.752567\pi$
$941$		−	1320.00i		−	1.40276i	0.712786	−	0.701381i	$-0.247433\pi$
$942$		0			0
$943$	−354.339			−0.375757
$944$		−	289.269i		−	0.306429i
$945$		0			0
$946$	−647.399			−0.684354
$947$			529.269i			0.558890i	0.960162	+	0.279445i	$0.0901505\pi$
$947$			529.269i			0.558890i	−0.960162	+	0.279445i	$0.909849\pi$
$948$		0			0
$949$	−292.606			−0.308330
$950$	1144.50	+	660.777i	1.20474	+	0.695555i
$951$		0			0
$952$	−163.248	+	233.163i	−0.171479	+	0.244919i
$953$			193.203i			0.202731i	0.994849	+	0.101366i	$0.0323212\pi$
$953$			193.203i			0.202731i	−0.994849	+	0.101366i	$0.967679\pi$
$954$		0			0
$955$	−507.281	+	878.636i	−0.531184	+	0.920038i
$956$	−497.275	+	287.102i	−0.520162	+	0.300315i
$957$		0			0
$958$	47.9754	+	83.0959i	0.0500787	+	0.0867389i
$959$	−1028.30	+	479.557i	−1.07226	+	0.500059i
$960$		0			0
$961$	−380.050			−0.395473
$962$	641.806	+	370.547i	0.667159	+	0.385184i
$963$		0			0
$964$	378.594	+	655.743i	0.392732	+	0.680232i
$965$	−1426.19	−	823.411i	−1.47792	−	0.853275i
$966$		0			0
$967$	−802.035	−	1389.17i	−0.829405	−	1.43657i	−0.898505	−	0.438962i	$-0.855346\pi$
$967$	−802.035	−	1389.17i	−0.829405	−	1.43657i	0.0691002	−	0.997610i	$-0.477987\pi$
$968$	−174.540	−	100.771i	−0.180310	−	0.104102i
$969$		0			0
$970$	595.232	+	1030.97i	0.613641	+	1.06286i
$971$	−1197.47	+	691.361i	−1.23324	+	0.712010i	−0.967703	−	0.252092i	$-0.918881\pi$
$971$	−1197.47	+	691.361i	−1.23324	+	0.712010i	−0.265534	+	0.964102i	$0.585548\pi$
$972$		0			0
$973$	464.284	+	995.552i	0.477168	+	1.02318i
$974$	567.734	+	327.781i	0.582889	+	0.336531i
$975$		0			0
$976$	−31.9313			−0.0327165
$977$			1293.34i			1.32379i	0.749597	+	0.661894i	$0.230247\pi$
$977$			1293.34i			1.32379i	−0.749597	+	0.661894i	$0.769753\pi$
$978$		0			0
$979$	−162.966	+	282.265i	−0.166461	+	0.288320i
$980$	−642.981	−	539.434i	−0.656103	−	0.550442i
$981$		0			0
$982$	76.5481	+	132.585i	0.0779512	+	0.135015i
$983$	−1217.90	+	703.156i	−1.23896	+	0.715317i	−0.968883	−	0.247520i	$-0.920384\pi$
$983$	−1217.90	+	703.156i	−1.23896	+	0.715317i	−0.270082	+	0.962837i	$0.587051\pi$
$984$		0			0
$985$	1192.85	−	2066.08i	1.21102	−	2.09754i
$986$	−239.587	+	138.325i	−0.242989	+	0.140290i
$987$		0			0
$988$	287.457	−	497.890i	0.290949	−	0.503938i
$989$	2213.05	−	1277.70i	2.23766	−	1.29192i
$990$		0			0
$991$	929.154	−	1609.34i	0.937593	−	1.62396i	0.167649	−	0.985847i	$-0.446383\pi$
$991$	929.154	−	1609.34i	0.937593	−	1.62396i	0.769944	−	0.638111i	$-0.220284\pi$
$992$			136.347i			0.137446i
$993$		0			0
$994$	601.585	+	52.6065i	0.605216	+	0.0529240i
$995$	−1804.88	+	1042.05i	−1.81395	+	1.04729i
$996$		0			0
$997$	−321.374	−	556.637i	−0.322341	−	0.558312i	0.658629	−	0.752468i	$-0.271137\pi$
$997$	−321.374	−	556.637i	−0.322341	−	0.558312i	−0.980971	+	0.194156i	$0.937803\pi$
$998$	−9.23349	−	5.33096i	−0.00925200	−	0.00534164i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.r.a.305.8		32
3.2	odd	2		126.3.r.a.11.13	yes	32
7.2	even	3		378.3.i.a.359.1		32
9.4	even	3		126.3.i.a.95.9	yes	32
9.5	odd	6		378.3.i.a.179.8		32
21.2	odd	6		126.3.i.a.65.9	✓	32
63.23	odd	6	inner	378.3.r.a.233.16		32
63.58	even	3		126.3.r.a.23.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.9	✓	32	21.2	odd	6
126.3.i.a.95.9	yes	32	9.4	even	3
126.3.r.a.11.13	yes	32	3.2	odd	2
126.3.r.a.23.5	yes	32	63.58	even	3
378.3.i.a.179.8		32	9.5	odd	6
378.3.i.a.359.1		32	7.2	even	3
378.3.r.a.233.16		32	63.23	odd	6	inner
378.3.r.a.305.8		32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(7.41683 + 4.28211i) q^{5} +(-6.97339 - 0.609798i) q^{7} +2.82843i q^{8} +(6.05582 - 10.4890i) q^{10} +(6.10804 - 3.52648i) q^{11} +(7.43588 + 12.8793i) q^{13} +(-0.862384 + 9.86186i) q^{14} +4.00000 q^{16} +(-12.4500 - 7.18802i) q^{17} +(9.66453 + 16.7395i) q^{19} +(-14.8337 - 8.56422i) q^{20} +(-4.98720 - 8.63808i) q^{22} +(34.0962 + 19.6854i) q^{23} +(24.1729 + 41.8687i) q^{25} +(18.2141 - 10.5159i) q^{26} +(13.9468 + 1.21960i) q^{28} +(11.7844 + 6.80374i) q^{29} -24.1029 q^{31} -5.65685i q^{32} +(-10.1654 + 17.6070i) q^{34} +(-49.1092 - 34.3836i) q^{35} +(17.6184 + 30.5159i) q^{37} +(23.6732 - 13.6677i) q^{38} +(-12.1116 + 20.9780i) q^{40} +(-7.79426 + 4.50002i) q^{41} +(32.4531 - 56.2103i) q^{43} +(-12.2161 + 7.05296i) q^{44} +(27.8394 - 48.2192i) q^{46} -33.3805i q^{47} +(48.2563 + 8.50471i) q^{49} +(59.2113 - 34.1857i) q^{50} +(-14.8718 - 25.7586i) q^{52} +(52.4399 + 30.2762i) q^{53} +60.4031 q^{55} +(1.72477 - 19.7237i) q^{56} +(9.62194 - 16.6657i) q^{58} -72.3172i q^{59} -7.98282 q^{61} +34.0867i q^{62} -8.00000 q^{64} +127.365i q^{65} -83.6147 q^{67} +(24.9000 + 14.3760i) q^{68} +(-48.6257 + 69.4509i) q^{70} -61.0012i q^{71} +(-9.83762 + 17.0393i) q^{73} +(43.1560 - 24.9162i) q^{74} +(-19.3291 - 33.4789i) q^{76} +(-44.7442 + 20.8668i) q^{77} -10.1882 q^{79} +(29.6673 + 17.1284i) q^{80} +(6.36399 + 11.0228i) q^{82} +(-15.8646 - 9.15941i) q^{83} +(-61.5598 - 106.625i) q^{85} +(-79.4934 - 45.8955i) q^{86} +(9.97439 + 17.2762i) q^{88} +(-40.0208 + 23.1060i) q^{89} +(-43.9995 - 94.3469i) q^{91} +(-68.1923 - 39.3708i) q^{92} -47.2071 q^{94} +165.538i q^{95} +(-49.1454 + 85.1224i) q^{97} +(12.0275 - 68.2447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 2 q^{7} + 36 q^{11} + 10 q^{13} - 36 q^{14} + 128 q^{16} + 54 q^{17} + 28 q^{19} + 126 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} - 36 q^{29} + 16 q^{31} + 90 q^{35} + 22 q^{37} - 72 q^{41}+ \cdots - 288 q^{98}+O(q^{100}) \) 32 * q - 64 * q^4 + 2 * q^7 + 36 * q^11 + 10 * q^13 - 36 * q^14 + 128 * q^16 + 54 * q^17 + 28 * q^19 + 126 * q^23 + 80 * q^25 + 72 * q^26 - 4 * q^28 - 36 * q^29 + 16 * q^31 + 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 - 72 * q^44 - 12 * q^46 + 2 * q^49 + 288 * q^50 - 20 * q^52 + 72 * q^53 - 24 * q^55 + 72 * q^56 - 24 * q^58 + 124 * q^61 - 256 * q^64 - 140 * q^67 - 108 * q^68 + 72 * q^70 + 196 * q^73 - 216 * q^74 - 56 * q^76 - 486 * q^77 + 76 * q^79 + 60 * q^85 + 144 * q^86 + 486 * q^89 - 122 * q^91 - 252 * q^92 - 336 * q^94 - 38 * q^97 - 288 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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