LMFDB - Embedded newform 378.3.r.a.305.5

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			305.5
Character	$\chi$	$=$	378.305
Dual form			378.3.r.a.233.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421i q^{2} -2.00000 q^{4} +(1.51694 + 0.875808i) q^{5} +(-1.24611 - 6.88819i) q^{7} +2.82843i q^{8} +(1.23858 - 2.14528i) q^{10} +(-3.90930 + 2.25703i) q^{11} +(-4.80730 - 8.32649i) q^{13} +(-9.74138 + 1.76226i) q^{14} +4.00000 q^{16} +(-0.491183 - 0.283585i) q^{17} +(-10.8517 - 18.7956i) q^{19} +(-3.03389 - 1.75162i) q^{20} +(3.19193 + 5.52858i) q^{22} +(23.7816 + 13.7303i) q^{23} +(-10.9659 - 18.9935i) q^{25} +(-11.7754 + 6.79855i) q^{26} +(2.49222 + 13.7764i) q^{28} +(-48.9844 - 28.2812i) q^{29} -39.9896 q^{31} -5.65685i q^{32} +(-0.401050 + 0.694638i) q^{34} +(4.14246 - 11.5404i) q^{35} +(-7.44017 - 12.8868i) q^{37} +(-26.5810 + 15.3466i) q^{38} +(-2.47716 + 4.29057i) q^{40} +(28.0456 - 16.1921i) q^{41} +(-1.47486 + 2.55453i) q^{43} +(7.81860 - 4.51407i) q^{44} +(19.4176 - 33.6323i) q^{46} +55.1749i q^{47} +(-45.8944 + 17.1669i) q^{49} +(-26.8609 + 15.5082i) q^{50} +(9.61460 + 16.6530i) q^{52} +(-48.3659 - 27.9241i) q^{53} -7.90692 q^{55} +(19.4828 - 3.52453i) q^{56} +(-39.9956 + 69.2744i) q^{58} -12.4226i q^{59} +79.5276 q^{61} +56.5538i q^{62} -8.00000 q^{64} -16.8411i q^{65} +0.284475 q^{67} +(0.982367 + 0.567170i) q^{68} +(-16.3205 - 5.85832i) q^{70} +8.92640i q^{71} +(4.02599 - 6.97323i) q^{73} +(-18.2246 + 10.5220i) q^{74} +(21.7033 + 37.5913i) q^{76} +(20.4183 + 24.1155i) q^{77} +97.6526 q^{79} +(6.06778 + 3.50323i) q^{80} +(-22.8992 - 39.6625i) q^{82} +(19.5749 + 11.3016i) q^{83} +(-0.496732 - 0.860365i) q^{85} +(3.61265 + 2.08577i) q^{86} +(-6.38386 - 11.0572i) q^{88} +(-47.1301 + 27.2106i) q^{89} +(-51.3640 + 43.4893i) q^{91} +(-47.5633 - 27.4607i) q^{92} +78.0291 q^{94} -38.0159i q^{95} +(38.0319 - 65.8731i) q^{97} +(24.2776 + 64.9045i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.51694	+	0.875808i	0.303389	+	0.175162i	0.643964	−	0.765056i	$-0.277289\pi$
$5$	1.51694	+	0.875808i	0.303389	+	0.175162i	−0.340575	+	0.940217i	$0.610622\pi$
$6$		0			0
$7$	−1.24611	−	6.88819i	−0.178016	−	0.984028i
$7$	−1.24611	−	6.88819i	−0.178016	−	0.984028i
$8$			2.82843i			0.353553i
$9$		0			0
$10$	1.23858	−	2.14528i	0.123858	−	0.214528i
$11$	−3.90930	+	2.25703i	−0.355391	+	0.205185i	−0.667057	−	0.745007i	$-0.732446\pi$
$11$	−3.90930	+	2.25703i	−0.355391	+	0.205185i	0.311666	+	0.950192i	$0.399113\pi$
$12$		0			0
$13$	−4.80730	−	8.32649i	−0.369792	−	0.640499i	0.619741	−	0.784807i	$-0.287238\pi$
$13$	−4.80730	−	8.32649i	−0.369792	−	0.640499i	−0.989533	+	0.144308i	$0.953904\pi$
$14$	−9.74138	+	1.76226i	−0.695813	+	0.125876i
$15$		0			0
$16$	4.00000			0.250000
$17$	−0.491183	−	0.283585i	−0.0288931	−	0.0166815i	0.485484	−	0.874246i	$-0.338643\pi$
$17$	−0.491183	−	0.283585i	−0.0288931	−	0.0166815i	−0.514377	+	0.857564i	$0.671977\pi$
$18$		0			0
$19$	−10.8517	−	18.7956i	−0.571140	−	0.989244i	−0.996449	−	0.0841959i	$-0.973168\pi$
$19$	−10.8517	−	18.7956i	−0.571140	−	0.989244i	0.425309	−	0.905048i	$-0.360165\pi$
$20$	−3.03389	−	1.75162i	−0.151694	−	0.0875808i
$21$		0			0
$22$	3.19193	+	5.52858i	0.145088	+	0.251299i
$23$	23.7816	+	13.7303i	1.03398	+	0.596971i	0.918123	−	0.396294i	$-0.129704\pi$
$23$	23.7816	+	13.7303i	1.03398	+	0.596971i	0.115861	+	0.993265i	$0.463037\pi$
$24$		0			0
$25$	−10.9659	−	18.9935i	−0.438637	−	0.759741i
$26$	−11.7754	+	6.79855i	−0.452901	+	0.261483i
$27$		0			0
$28$	2.49222	+	13.7764i	0.0890078	+	0.492014i
$29$	−48.9844	−	28.2812i	−1.68912	−	0.975213i	−0.955193	−	0.295982i	$-0.904353\pi$
$29$	−48.9844	−	28.2812i	−1.68912	−	0.975213i	−0.733925	−	0.679231i	$-0.762314\pi$
$30$		0			0
$31$	−39.9896			−1.28999			−0.644993	−	0.764188i	$-0.723140\pi$
$31$	−39.9896			−1.28999			−0.644993	+	0.764188i	$0.723140\pi$
$32$		−	5.65685i		−	0.176777i
$33$		0			0
$34$	−0.401050	+	0.694638i	−0.0117956	+	0.0204305i
$35$	4.14246	−	11.5404i	0.118356	−	0.329724i
$36$		0			0
$37$	−7.44017	−	12.8868i	−0.201086	−	0.348291i	0.747793	−	0.663932i	$-0.231114\pi$
$37$	−7.44017	−	12.8868i	−0.201086	−	0.348291i	−0.948879	+	0.315641i	$0.897780\pi$
$38$	−26.5810	+	15.3466i	−0.699501	+	0.403857i
$39$		0			0
$40$	−2.47716	+	4.29057i	−0.0619290	+	0.107264i
$41$	28.0456	−	16.1921i	0.684040	−	0.394930i	−0.117336	−	0.993092i	$-0.537435\pi$
$41$	28.0456	−	16.1921i	0.684040	−	0.394930i	0.801375	+	0.598162i	$0.204102\pi$
$42$		0			0
$43$	−1.47486	+	2.55453i	−0.0342991	+	0.0594077i	−0.882665	−	0.470002i	$-0.844253\pi$
$43$	−1.47486	+	2.55453i	−0.0342991	+	0.0594077i	0.848366	+	0.529410i	$0.177587\pi$
$44$	7.81860	−	4.51407i	0.177695	−	0.102592i
$45$		0			0
$46$	19.4176	−	33.6323i	0.422122	−	0.731137i
$47$			55.1749i			1.17393i	0.809611	+	0.586967i	$0.199678\pi$
$47$			55.1749i			1.17393i	−0.809611	+	0.586967i	$0.800322\pi$
$48$		0			0
$49$	−45.8944	+	17.1669i	−0.936621	+	0.350345i
$50$	−26.8609	+	15.5082i	−0.537218	+	0.310163i
$51$		0			0
$52$	9.61460	+	16.6530i	0.184896	+	0.320249i
$53$	−48.3659	−	27.9241i	−0.912565	−	0.526870i	−0.0313093	−	0.999510i	$-0.509968\pi$
$53$	−48.3659	−	27.9241i	−0.912565	−	0.526870i	−0.881256	+	0.472640i	$0.843301\pi$
$54$		0			0
$55$	−7.90692			−0.143762
$56$	19.4828	−	3.52453i	0.347906	−	0.0629380i
$57$		0			0
$58$	−39.9956	+	69.2744i	−0.689580	+	1.19439i
$59$		−	12.4226i		−	0.210553i	−0.994443	−	0.105277i	$-0.966427\pi$
$59$		−	12.4226i		−	0.210553i	0.994443	−	0.105277i	$-0.0335728\pi$
$60$		0			0
$61$	79.5276			1.30373			0.651866	−	0.758334i	$-0.273986\pi$
$61$	79.5276			1.30373			0.651866	+	0.758334i	$0.273986\pi$
$62$			56.5538i			0.912158i
$63$		0			0
$64$	−8.00000			−0.125000
$65$		−	16.8411i		−	0.259094i
$66$		0			0
$67$	0.284475			0.00424590			0.00212295	−	0.999998i	$-0.499324\pi$
$67$	0.284475			0.00424590			0.00212295	+	0.999998i	$0.499324\pi$
$68$	0.982367	+	0.567170i	0.0144466	+	0.00834073i
$69$		0			0
$70$	−16.3205	−	5.85832i	−0.233150	−	0.0836903i
$71$			8.92640i			0.125724i	0.998022	+	0.0628619i	$0.0200228\pi$
$71$			8.92640i			0.125724i	−0.998022	+	0.0628619i	$0.979977\pi$
$72$		0			0
$73$	4.02599	−	6.97323i	0.0551506	−	0.0955237i	−0.837132	−	0.547001i	$-0.815769\pi$
$73$	4.02599	−	6.97323i	0.0551506	−	0.0955237i	0.892283	+	0.451477i	$0.149103\pi$
$74$	−18.2246	+	10.5220i	−0.246279	+	0.142189i
$75$		0			0
$76$	21.7033	+	37.5913i	0.285570	+	0.494622i
$77$	20.4183	+	24.1155i	0.265173	+	0.313188i
$78$		0			0
$79$	97.6526			1.23611			0.618055	−	0.786135i	$-0.287921\pi$
$79$	97.6526			1.23611			0.618055	+	0.786135i	$0.287921\pi$
$80$	6.06778	+	3.50323i	0.0758472	+	0.0437904i
$81$		0			0
$82$	−22.8992	−	39.6625i	−0.279258	−	0.483689i
$83$	19.5749	+	11.3016i	0.235842	+	0.136163i	0.613264	−	0.789878i	$-0.289856\pi$
$83$	19.5749	+	11.3016i	0.235842	+	0.136163i	−0.377422	+	0.926041i	$0.623189\pi$
$84$		0			0
$85$	−0.496732	−	0.860365i	−0.00584390	−	0.0101219i
$86$	3.61265	+	2.08577i	0.0420076	+	0.0242531i
$87$		0			0
$88$	−6.38386	−	11.0572i	−0.0725438	−	0.125650i
$89$	−47.1301	+	27.2106i	−0.529552	+	0.305737i	−0.740834	−	0.671688i	$-0.765570\pi$
$89$	−47.1301	+	27.2106i	−0.529552	+	0.305737i	0.211282	+	0.977425i	$0.432236\pi$
$90$		0			0
$91$	−51.3640	+	43.4893i	−0.564440	+	0.477905i
$92$	−47.5633	−	27.4607i	−0.516992	−	0.298486i
$93$		0			0
$94$	78.0291			0.830097
$95$		−	38.0159i		−	0.400167i
$96$		0			0
$97$	38.0319	−	65.8731i	0.392081	−	0.679104i	−0.600643	−	0.799517i	$-0.705089\pi$
$97$	38.0319	−	65.8731i	0.392081	−	0.679104i	0.992724	+	0.120413i	$0.0384220\pi$
$98$	24.2776	+	64.9045i	0.247731	+	0.662291i
$99$		0			0
$100$	21.9318	+	37.9871i	0.219318	+	0.379871i
$101$	168.803	−	97.4586i	1.67132	−	0.964937i	0.704419	−	0.709785i	$-0.251208\pi$
$101$	168.803	−	97.4586i	1.67132	−	0.964937i	0.966901	−	0.255152i	$-0.0821256\pi$
$102$		0			0
$103$	58.2628	−	100.914i	0.565658	−	0.979748i	−0.431330	−	0.902194i	$-0.641956\pi$
$103$	58.2628	−	100.914i	0.565658	−	0.979748i	0.996988	−	0.0775540i	$-0.0247110\pi$
$104$	23.5509	−	13.5971i	0.226451	−	0.130741i
$105$		0			0
$106$	−39.4906	+	68.3998i	−0.372553	+	0.645281i
$107$	65.8789	−	38.0352i	0.615691	−	0.355469i	−0.159498	−	0.987198i	$-0.550988\pi$
$107$	65.8789	−	38.0352i	0.615691	−	0.355469i	0.775189	+	0.631729i	$0.217654\pi$
$108$		0			0
$109$	79.6034	−	137.877i	0.730307	−	1.26493i	−0.226446	−	0.974024i	$-0.572711\pi$
$109$	79.6034	−	137.877i	0.730307	−	1.26493i	0.956752	−	0.290904i	$-0.0939561\pi$
$110$			11.1821i			0.101655i
$111$		0			0
$112$	−4.98444	−	27.5528i	−0.0445039	−	0.246007i
$113$	−88.3982	+	51.0367i	−0.782285	+	0.451652i	−0.837239	−	0.546837i	$-0.815832\pi$
$113$	−88.3982	+	51.0367i	−0.782285	+	0.451652i	0.0549546	+	0.998489i	$0.482499\pi$
$114$		0			0
$115$	24.0503	+	41.6563i	0.209133	+	0.362229i
$116$	97.9689	+	56.5623i	0.844559	+	0.487606i
$117$		0			0
$118$	−17.5683			−0.148883
$119$	−1.34132	+	3.73674i	−0.0112716	+	0.0314012i
$120$		0			0
$121$	−50.3116	+	87.1422i	−0.415798	+	0.720184i
$122$		−	112.469i		−	0.921878i
$123$		0			0
$124$	79.9791			0.644993
$125$		−	82.2066i		−	0.657652i
$126$		0			0
$127$	−221.800			−1.74646			−0.873228	−	0.487313i	$-0.837977\pi$
$127$	−221.800			−1.74646			−0.873228	+	0.487313i	$0.837977\pi$
$128$			11.3137i			0.0883883i
$129$		0			0
$130$	−23.8169			−0.183207
$131$	2.09587	+	1.21005i	0.0159990	+	0.00923703i	0.507978	−	0.861370i	$-0.330393\pi$
$131$	2.09587	+	1.21005i	0.0159990	+	0.00923703i	−0.491979	+	0.870607i	$0.663726\pi$
$132$		0			0
$133$	−115.946	+	98.1698i	−0.871772	+	0.738119i
$134$		−	0.402309i		−	0.00300230i
$135$		0			0
$136$	0.802099	−	1.38928i	0.00589779	−	0.0102153i
$137$	205.101	−	118.415i	1.49709	−	0.864344i	0.497093	−	0.867697i	$-0.334401\pi$
$137$	205.101	−	118.415i	1.49709	−	0.864344i	0.999994	+	0.00335292i	$0.00106727\pi$
$138$		0			0
$139$	112.225	+	194.379i	0.807373	+	1.39841i	0.914677	+	0.404185i	$0.132445\pi$
$139$	112.225	+	194.379i	0.807373	+	1.39841i	−0.107304	+	0.994226i	$0.534222\pi$
$140$	−8.28491	+	23.0807i	−0.0591780	+	0.164862i
$141$		0			0
$142$	12.6238			0.0889002
$143$	37.5863	+	21.7005i	0.262841	+	0.151752i
$144$		0			0
$145$	−49.5378	−	85.8019i	−0.341640	−	0.591737i
$146$	−9.86163	−	5.69362i	−0.0675454	−	0.0389974i
$147$		0			0
$148$	14.8803	+	25.7735i	0.100543	+	0.174145i
$149$	71.5236	+	41.2942i	0.480024	+	0.277142i	0.720427	−	0.693531i	$-0.243946\pi$
$149$	71.5236	+	41.2942i	0.480024	+	0.277142i	−0.240402	+	0.970673i	$0.577279\pi$
$150$		0			0
$151$	106.866	+	185.098i	0.707724	+	1.22581i	0.965700	+	0.259662i	$0.0836111\pi$
$151$	106.866	+	185.098i	0.707724	+	1.22581i	−0.257976	+	0.966151i	$0.583056\pi$
$152$	53.1621	−	30.6932i	0.349751	−	0.201929i
$153$		0			0
$154$	34.1045	−	28.8758i	0.221458	−	0.187505i
$155$	−60.6619	−	35.0232i	−0.391367	−	0.225956i
$156$		0			0
$157$	161.794			1.03054			0.515268	−	0.857029i	$-0.327693\pi$
$157$	161.794			1.03054			0.515268	+	0.857029i	$0.327693\pi$
$158$		−	138.102i		−	0.874061i
$159$		0			0
$160$	4.95432	−	8.58113i	0.0309645	−	0.0536321i
$161$	64.9427	−	180.922i	0.403371	−	1.12374i
$162$		0			0
$163$	−26.8721	−	46.5439i	−0.164860	−	0.285545i	0.771746	−	0.635931i	$-0.219384\pi$
$163$	−26.8721	−	46.5439i	−0.164860	−	0.285545i	−0.936605	+	0.350386i	$0.886050\pi$
$164$	−56.0912	+	32.3843i	−0.342020	+	0.197465i
$165$		0			0
$166$	15.9828	−	27.6831i	0.0962821	−	0.166765i
$167$	41.1006	−	23.7295i	0.246112	−	0.142093i	−0.371871	−	0.928284i	$-0.621284\pi$
$167$	41.1006	−	23.7295i	0.246112	−	0.142093i	0.617982	+	0.786192i	$0.287950\pi$
$168$		0			0
$169$	38.2798	−	66.3025i	0.226507	−	0.392322i
$170$	−1.21674	+	0.702485i	−0.00715729	+	0.00413226i
$171$		0			0
$172$	2.94972	−	5.10906i	0.0171495	−	0.0297039i
$173$			91.9101i			0.531272i	0.964073	+	0.265636i	$0.0855819\pi$
$173$			91.9101i			0.531272i	−0.964073	+	0.265636i	$0.914418\pi$
$174$		0			0
$175$	−117.166	+	99.2034i	−0.669522	+	0.566877i
$176$	−15.6372	+	9.02814i	−0.0888477	+	0.0512962i
$177$		0			0
$178$	38.4816	+	66.6521i	0.216189	+	0.374450i
$179$	−143.122	−	82.6317i	−0.799566	−	0.461629i	0.0437536	−	0.999042i	$-0.486068\pi$
$179$	−143.122	−	82.6317i	−0.799566	−	0.461629i	−0.843319	+	0.537413i	$0.819402\pi$
$180$		0			0
$181$	244.607			1.35142			0.675709	−	0.737169i	$-0.263838\pi$
$181$	244.607			1.35142			0.675709	+	0.737169i	$0.263838\pi$
$182$	61.5032	+	72.6397i	0.337930	+	0.399119i
$183$		0			0
$184$	−38.8352	+	67.2646i	−0.211061	+	0.365569i
$185$		−	26.0647i		−	0.140890i
$186$		0			0
$187$	2.56024			0.0136911
$188$		−	110.350i		−	0.586967i
$189$		0			0
$190$	−53.7626			−0.282961
$191$			146.941i			0.769324i	0.923057	+	0.384662i	$0.125682\pi$
$191$			146.941i			0.769324i	−0.923057	+	0.384662i	$0.874318\pi$
$192$		0			0
$193$	−253.782			−1.31493			−0.657466	−	0.753484i	$-0.728372\pi$
$193$	−253.782			−1.31493			−0.657466	+	0.753484i	$0.728372\pi$
$194$	−93.1586	−	53.7852i	−0.480199	−	0.277243i
$195$		0			0
$196$	91.7888	−	34.3338i	0.468310	−	0.175172i
$197$			318.129i			1.61487i	0.589958	+	0.807434i	$0.299144\pi$
$197$			318.129i			1.61487i	−0.589958	+	0.807434i	$0.700856\pi$
$198$		0			0
$199$	123.517	−	213.938i	0.620689	−	1.07506i	−0.368669	−	0.929561i	$-0.620186\pi$
$199$	123.517	−	213.938i	0.620689	−	1.07506i	0.989358	−	0.145504i	$-0.0464803\pi$
$200$	53.7218	−	31.0163i	0.268609	−	0.155082i
$201$		0			0
$202$	−137.827	−	238.724i	−0.682313	−	1.18180i
$203$	−133.766	+	372.656i	−0.658947	+	1.83574i
$204$		0			0
$205$	56.7248			0.276707
$206$	−142.714	−	82.3960i	−0.692786	−	0.399980i
$207$		0			0
$208$	−19.2292	−	33.3059i	−0.0924481	−	0.160125i
$209$	84.8448	+	48.9852i	0.405956	+	0.234379i
$210$		0			0
$211$	−107.527	−	186.242i	−0.509605	−	0.882661i	−0.999938	−	0.0111265i	$-0.996458\pi$
$211$	−107.527	−	186.242i	−0.509605	−	0.882661i	0.490333	−	0.871535i	$-0.336875\pi$
$212$	96.7319	+	55.8482i	0.456282	+	0.263435i
$213$		0			0
$214$	−53.7899	−	93.1669i	−0.251355	−	0.435359i
$215$	−4.47456	+	2.58339i	−0.0208119	+	0.0120158i
$216$		0			0
$217$	49.8314	+	275.456i	0.229638	+	1.26938i
$218$	−194.988	−	112.576i	−0.894439	−	0.516405i
$219$		0			0
$220$	15.8138			0.0718811
$221$			5.45311i			0.0246747i
$222$		0			0
$223$	−40.9462	+	70.9208i	−0.183615	+	0.318031i	−0.943109	−	0.332484i	$-0.892113\pi$
$223$	−40.9462	+	70.9208i	−0.183615	+	0.318031i	0.759494	+	0.650514i	$0.225447\pi$
$224$	−38.9655	+	7.04906i	−0.173953	+	0.0314690i
$225$		0			0
$226$	72.1768	+	125.014i	0.319366	+	0.553159i
$227$	20.4484	−	11.8059i	0.0900811	−	0.0520084i	−0.454283	−	0.890858i	$-0.650104\pi$
$227$	20.4484	−	11.8059i	0.0900811	−	0.0520084i	0.544364	+	0.838849i	$0.316771\pi$
$228$		0			0
$229$	−19.1123	+	33.1035i	−0.0834598	+	0.144557i	−0.904734	−	0.425977i	$-0.859930\pi$
$229$	−19.1123	+	33.1035i	−0.0834598	+	0.144557i	0.821274	+	0.570534i	$0.193264\pi$
$230$	58.9109	−	34.0122i	0.256134	−	0.147879i
$231$		0			0
$232$	79.9912	−	138.549i	0.344790	−	0.597193i
$233$	−118.984	+	68.6952i	−0.510659	+	0.294829i	−0.733105	−	0.680116i	$-0.761929\pi$
$233$	−118.984	+	68.6952i	−0.510659	+	0.294829i	0.222445	+	0.974945i	$0.428596\pi$
$234$		0			0
$235$	−48.3226	+	83.6973i	−0.205628	+	0.356159i
$236$			24.8453i			0.105277i
$237$		0			0
$238$	5.28455	+	1.89691i	0.0222040	+	0.00797022i
$239$	−348.038	+	200.940i	−1.45623	+	0.840753i	−0.998823	−	0.0485057i	$-0.984554\pi$
$239$	−348.038	+	200.940i	−1.45623	+	0.840753i	−0.457404	+	0.889259i	$0.651221\pi$
$240$		0			0
$241$	−219.749	−	380.616i	−0.911821	−	1.57932i	−0.811490	−	0.584366i	$-0.801343\pi$
$241$	−219.749	−	380.616i	−0.911821	−	1.57932i	−0.100330	−	0.994954i	$-0.531990\pi$
$242$	123.238	+	71.1513i	0.509247	+	0.294014i
$243$		0			0
$244$	−159.055			−0.651866
$245$	−84.6542	−	14.1535i	−0.345527	−	0.0577694i
$246$		0			0
$247$	−104.334	+	180.713i	−0.422407	+	0.731630i
$248$		−	113.108i		−	0.456079i
$249$		0			0
$250$	−116.258			−0.465031
$251$			114.101i			0.454587i	0.973826	+	0.227294i	$0.0729877\pi$
$251$			114.101i			0.454587i	−0.973826	+	0.227294i	$0.927012\pi$
$252$		0			0
$253$	−123.959			−0.489958
$254$			313.672i			1.23493i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−260.101	−	150.169i	−1.01207	−	0.584317i	−0.100270	−	0.994960i	$-0.531971\pi$
$257$	−260.101	−	150.169i	−1.01207	−	0.584317i	−0.911796	+	0.410644i	$0.865304\pi$
$258$		0			0
$259$	−79.4952	+	67.3077i	−0.306931	+	0.259875i
$260$			33.6822i			0.129547i
$261$		0			0
$262$	1.71127	−	2.96401i	0.00653157	−	0.0113130i
$263$	−365.056	+	210.765i	−1.38804	+	0.801388i	−0.993095	−	0.117315i	$-0.962571\pi$
$263$	−365.056	+	210.765i	−1.38804	+	0.801388i	−0.394949	+	0.918703i	$0.629238\pi$
$264$		0			0
$265$	−48.9123	−	84.7185i	−0.184575	−	0.319693i
$266$	138.833	+	163.972i	0.521929	+	0.616436i
$267$		0			0
$268$	−0.568950			−0.00212295
$269$	−445.841	−	257.406i	−1.65740	−	0.956901i	−0.973908	−	0.226943i	$-0.927127\pi$
$269$	−445.841	−	257.406i	−1.65740	−	0.956901i	−0.683492	−	0.729958i	$-0.739540\pi$
$270$		0			0
$271$	241.395	+	418.109i	0.890758	+	1.54284i	0.838969	+	0.544179i	$0.183159\pi$
$271$	241.395	+	418.109i	0.890758	+	1.54284i	0.0517888	+	0.998658i	$0.483508\pi$
$272$	−1.96473	−	1.13434i	−0.00722329	−	0.00417037i
$273$		0			0
$274$	−167.464	−	290.057i	−0.611184	−	1.05860i
$275$	85.7381	+	49.5009i	0.311775	+	0.180003i
$276$		0			0
$277$	−74.7657	−	129.498i	−0.269912	−	0.467501i	0.698927	−	0.715193i	$-0.253661\pi$
$277$	−74.7657	−	129.498i	−0.269912	−	0.467501i	−0.968839	+	0.247692i	$0.920328\pi$
$278$	274.894	−	158.710i	0.988826	−	0.570899i
$279$		0			0
$280$	32.6411	+	11.7166i	0.116575	+	0.0418451i
$281$	17.1238	+	9.88641i	0.0609387	+	0.0351830i	0.530160	−	0.847898i	$-0.322132\pi$
$281$	17.1238	+	9.88641i	0.0609387	+	0.0351830i	−0.469221	+	0.883081i	$0.655465\pi$
$282$		0			0
$283$	549.954			1.94330			0.971650	−	0.236425i	$-0.0759756\pi$
$283$	549.954			1.94330			0.971650	+	0.236425i	$0.0759756\pi$
$284$		−	17.8528i		−	0.0628619i
$285$		0			0
$286$	30.6891	−	53.1551i	0.107305	−	0.185857i
$287$	−146.483	−	173.006i	−0.510392	−	0.602810i
$288$		0			0
$289$	−144.339	−	250.003i	−0.499443	−	0.865061i
$290$	−121.342	+	70.0570i	−0.418421	+	0.241576i
$291$		0			0
$292$	−8.05199	+	13.9465i	−0.0275753	+	0.0477618i
$293$	113.883	−	65.7505i	0.388680	−	0.224404i	−0.292908	−	0.956141i	$-0.594623\pi$
$293$	113.883	−	65.7505i	0.388680	−	0.224404i	0.681588	+	0.731736i	$0.261290\pi$
$294$		0			0
$295$	10.8798	−	18.8444i	0.0368808	−	0.0638794i
$296$	36.4493	−	21.0440i	0.123139	−	0.0710946i
$297$		0			0
$298$	58.3988	−	101.150i	0.195969	−	0.339429i
$299$		−	264.023i		−	0.883021i
$300$		0			0
$301$	19.4339	+	6.97589i	0.0645646	+	0.0231757i
$302$	261.768	−	151.132i	0.866781	−	0.500436i
$303$		0			0
$304$	−43.4067	−	75.1826i	−0.142785	−	0.247311i
$305$	120.639	+	69.6509i	0.395538	+	0.228364i
$306$		0			0
$307$	252.488			0.822437			0.411218	−	0.911537i	$-0.365103\pi$
$307$	252.488			0.822437			0.411218	+	0.911537i	$0.365103\pi$
$308$	−40.8366	−	48.2310i	−0.132586	−	0.156594i
$309$		0			0
$310$	−49.5303	+	85.7889i	−0.159775	+	0.276738i
$311$			206.921i			0.665341i	0.943043	+	0.332671i	$0.107950\pi$
$311$			206.921i			0.665341i	−0.943043	+	0.332671i	$0.892050\pi$
$312$		0			0
$313$	−339.941			−1.08607			−0.543037	−	0.839709i	$-0.682726\pi$
$313$	−339.941			−1.08607			−0.543037	+	0.839709i	$0.682726\pi$
$314$		−	228.811i		−	0.728698i
$315$		0			0
$316$	−195.305			−0.618055
$317$		−	274.716i		−	0.866611i	−0.901247	−	0.433306i	$-0.857347\pi$
$317$		−	274.716i		−	0.866611i	0.901247	−	0.433306i	$-0.142653\pi$
$318$		0			0
$319$	255.326			0.800396
$320$	−12.1356	−	7.00646i	−0.0379236	−	0.0218952i
$321$		0			0
$322$	−255.862	−	91.8428i	−0.794604	−	0.285226i
$323$			12.3095i			0.0381098i
$324$		0			0
$325$	−105.433	+	182.615i	−0.324409	+	0.561893i
$326$	−65.8230	+	38.0029i	−0.201911	+	0.116573i
$327$		0			0
$328$	45.7983	+	79.3250i	0.139629	+	0.241844i
$329$	380.056	−	68.7540i	1.15518	−	0.208979i
$330$		0			0
$331$	−197.017			−0.595217			−0.297609	−	0.954688i	$-0.596189\pi$
$331$	−197.017			−0.595217			−0.297609	+	0.954688i	$0.596189\pi$
$332$	−39.1498	−	22.6031i	−0.117921	−	0.0680817i
$333$		0			0
$334$	−33.5585	−	58.1251i	−0.100475	−	0.174027i
$335$	0.431533	+	0.249146i	0.00128816	+	0.000743718i
$336$		0			0
$337$	−162.571	−	281.581i	−0.482405	−	0.835551i	0.517391	−	0.855749i	$-0.326903\pi$
$337$	−162.571	−	281.581i	−0.482405	−	0.835551i	−0.999796	+	0.0201987i	$0.993570\pi$
$338$	−93.7659	−	54.1358i	−0.277414	−	0.160165i
$339$		0			0
$340$	0.993464	+	1.72073i	0.00292195	+	0.00506097i
$341$	156.331	−	90.2578i	0.458449	−	0.264686i
$342$		0			0
$343$	175.438	+	294.738i	0.511482	+	0.859294i
$344$	−7.22531	−	4.17153i	−0.0210038	−	0.0121266i
$345$		0			0
$346$	129.980			0.375666
$347$			97.4654i			0.280880i	0.990089	+	0.140440i	$0.0448517\pi$
$347$			97.4654i			0.280880i	−0.990089	+	0.140440i	$0.955148\pi$
$348$		0			0
$349$	−106.817	+	185.012i	−0.306065	+	0.530121i	−0.977498	−	0.210945i	$-0.932346\pi$
$349$	−106.817	+	185.012i	−0.306065	+	0.530121i	0.671433	+	0.741066i	$0.265679\pi$
$350$	140.295	+	165.698i	0.400842	+	0.473424i
$351$		0			0
$352$	12.7677	+	22.1143i	0.0362719	+	0.0628248i
$353$	555.729	−	320.850i	1.57430	−	0.908924i	0.578670	−	0.815562i	$-0.303572\pi$
$353$	555.729	−	320.850i	1.57430	−	0.908924i	0.995632	−	0.0933624i	$-0.0297615\pi$
$354$		0			0
$355$	−7.81781	+	13.5408i	−0.0220220	+	0.0381432i
$356$	94.2603	−	54.4212i	0.264776	−	0.152869i
$357$		0			0
$358$	−116.859	+	202.405i	−0.326421	+	0.565378i
$359$	263.839	−	152.328i	0.734928	−	0.424311i	−0.0852941	−	0.996356i	$-0.527183\pi$
$359$	263.839	−	152.328i	0.734928	−	0.424311i	0.820222	+	0.572045i	$0.193850\pi$
$360$		0			0
$361$	−55.0174	+	95.2929i	−0.152403	+	0.263969i
$362$		−	345.926i		−	0.955596i
$363$		0			0
$364$	102.728	−	86.9786i	0.282220	−	0.238952i
$365$	12.2144	−	7.05200i	0.0334641	−	0.0193205i
$366$		0			0
$367$	−62.6630	−	108.536i	−0.170744	−	0.295737i	0.767936	−	0.640526i	$-0.221284\pi$
$367$	−62.6630	−	108.536i	−0.170744	−	0.295737i	−0.938680	+	0.344789i	$0.887950\pi$
$368$	95.1265	+	54.9213i	0.258496	+	0.149243i
$369$		0			0
$370$	−36.8610			−0.0996243
$371$	−132.077	+	367.950i	−0.356003	+	0.991780i
$372$		0			0
$373$	132.413	−	229.345i	0.354993	−	0.614867i	−0.632123	−	0.774868i	$-0.717816\pi$
$373$	132.413	−	229.345i	0.354993	−	0.614867i	0.987117	+	0.160001i	$0.0511498\pi$
$374$		−	3.62073i		−	0.00968110i
$375$		0			0
$376$	−156.058			−0.415049
$377$			543.824i			1.44250i
$378$		0			0
$379$	−190.773			−0.503359			−0.251679	−	0.967811i	$-0.580983\pi$
$379$	−190.773			−0.503359			−0.251679	+	0.967811i	$0.580983\pi$
$380$			76.0318i			0.200084i
$381$		0			0
$382$	207.806			0.543994
$383$	−519.145	−	299.729i	−1.35547	−	0.782582i	−0.366461	−	0.930433i	$-0.619431\pi$
$383$	−519.145	−	299.729i	−1.35547	−	0.782582i	−0.989010	+	0.147852i	$0.952764\pi$
$384$		0			0
$385$	9.85288	+	54.4644i	0.0255919	+	0.141466i
$386$			358.902i			0.929797i
$387$		0			0
$388$	−76.0637	+	131.746i	−0.196040	+	0.339552i
$389$	−87.4253	+	50.4750i	−0.224744	+	0.129756i	−0.608145	−	0.793826i	$-0.708086\pi$
$389$	−87.4253	+	50.4750i	−0.224744	+	0.129756i	0.383401	+	0.923582i	$0.374753\pi$
$390$		0			0
$391$	−7.78743	−	13.4882i	−0.0199167	−	0.0344967i
$392$	−48.5553	−	129.809i	−0.123866	−	0.331145i
$393$		0			0
$394$	449.902			1.14188
$395$	148.134	+	85.5250i	0.375022	+	0.216519i
$396$		0			0
$397$	−154.534	−	267.661i	−0.389255	−	0.674210i	0.603094	−	0.797670i	$-0.293934\pi$
$397$	−154.534	−	267.661i	−0.389255	−	0.674210i	−0.992350	+	0.123460i	$0.960601\pi$
$398$	−302.554	−	174.680i	−0.760185	−	0.438893i
$399$		0			0
$400$	−43.8637	−	75.9741i	−0.109659	−	0.189935i
$401$	522.234	+	301.512i	1.30233	+	0.751901i	0.980803	−	0.195000i	$-0.0624707\pi$
$401$	522.234	+	301.512i	1.30233	+	0.751901i	0.321527	+	0.946900i	$0.395804\pi$
$402$		0			0
$403$	192.242	+	332.973i	0.477027	+	0.826235i
$404$	−337.607	+	194.917i	−0.835660	+	0.482468i
$405$		0			0
$406$	527.015	+	189.174i	1.29807	+	0.465946i
$407$	58.1717	+	33.5855i	0.142928	+	0.0825196i
$408$		0			0
$409$	439.430			1.07440			0.537201	−	0.843454i	$-0.319482\pi$
$409$	439.430			1.07440			0.537201	+	0.843454i	$0.319482\pi$
$410$		−	80.2210i		−	0.195661i
$411$		0			0
$412$	−116.526	+	201.828i	−0.282829	+	0.489874i
$413$	−85.5695	+	15.4800i	−0.207190	+	0.0374817i
$414$		0			0
$415$	19.7960	+	34.2877i	0.0477012	+	0.0826209i
$416$	−47.1017	+	27.1942i	−0.113225	+	0.0653706i
$417$		0			0
$418$	69.2755	−	119.989i	0.165731	−	0.287054i
$419$	49.5525	−	28.6092i	0.118264	−	0.0682796i	−0.439701	−	0.898144i	$-0.644916\pi$
$419$	49.5525	−	28.6092i	0.118264	−	0.0682796i	0.557965	+	0.829864i	$0.311582\pi$
$420$		0			0
$421$	163.713	−	283.558i	0.388866	−	0.673536i	−0.603431	−	0.797415i	$-0.706200\pi$
$421$	163.713	−	283.558i	0.388866	−	0.673536i	0.992297	+	0.123879i	$0.0395336\pi$
$422$	−263.385	+	152.066i	−0.624136	+	0.360345i
$423$		0			0
$424$	78.9812	−	136.800i	0.186277	−	0.322640i
$425$			12.4391i			0.0292684i
$426$		0			0
$427$	−99.1001	−	547.802i	−0.232085	−	1.28291i
$428$	−131.758	+	76.0704i	−0.307845	+	0.177735i
$429$		0			0
$430$	3.65346	+	6.32798i	0.00849642	+	0.0147162i
$431$	−90.4104	−	52.1985i	−0.209769	−	0.121110i	0.391435	−	0.920206i	$-0.371979\pi$
$431$	−90.4104	−	52.1985i	−0.209769	−	0.121110i	−0.601204	+	0.799096i	$0.705312\pi$
$432$		0			0
$433$	426.363			0.984673			0.492337	−	0.870405i	$-0.336143\pi$
$433$	426.363			0.984673			0.492337	+	0.870405i	$0.336143\pi$
$434$	389.553	−	70.4722i	0.897589	−	0.162378i
$435$		0			0
$436$	−159.207	+	275.754i	−0.365153	+	0.632464i
$437$		−	595.988i		−	1.36382i
$438$		0			0
$439$	284.606			0.648306			0.324153	−	0.946005i	$-0.394921\pi$
$439$	284.606			0.648306			0.324153	+	0.946005i	$0.394921\pi$
$440$		−	22.3641i		−	0.0508276i
$441$		0			0
$442$	7.71186			0.0174476
$443$		−	460.919i		−	1.04045i	−0.854030	−	0.520224i	$-0.825848\pi$
$443$		−	460.919i		−	1.04045i	0.854030	−	0.520224i	$-0.174152\pi$
$444$		0			0
$445$	−95.3250			−0.214214
$446$	100.297	+	57.9066i	0.224882	+	0.129835i
$447$		0			0
$448$	9.96888	+	55.1055i	0.0222520	+	0.123003i
$449$			184.454i			0.410811i	0.978677	+	0.205406i	$0.0658514\pi$
$449$			184.454i			0.410811i	−0.978677	+	0.205406i	$0.934149\pi$
$450$		0			0
$451$	−73.0925	+	126.600i	−0.162068	+	0.280709i
$452$	176.796	−	102.073i	0.391142	−	0.225826i
$453$		0			0
$454$	−16.6961	−	28.9184i	−0.0367755	−	0.0636970i
$455$	−116.005	+	20.9858i	−0.254955	+	0.0461227i
$456$		0			0
$457$	−158.091			−0.345933			−0.172967	−	0.984928i	$-0.555335\pi$
$457$	−158.091			−0.345933			−0.172967	+	0.984928i	$0.555335\pi$
$458$	46.8154	+	27.0289i	0.102217	+	0.0590150i
$459$		0			0
$460$	−48.1005	−	83.3126i	−0.104566	−	0.181114i
$461$	301.115	+	173.849i	0.653179	+	0.377113i	0.789673	−	0.613528i	$-0.210250\pi$
$461$	301.115	+	173.849i	0.653179	+	0.377113i	−0.136494	+	0.990641i	$0.543584\pi$
$462$		0			0
$463$	170.634	+	295.547i	0.368541	+	0.638331i	0.989338	−	0.145640i	$-0.0465242\pi$
$463$	170.634	+	295.547i	0.368541	+	0.638331i	−0.620797	+	0.783971i	$0.713191\pi$
$464$	−195.938	−	113.125i	−0.422280	−	0.243803i
$465$		0			0
$466$	97.1497	+	168.268i	0.208476	+	0.361091i
$467$	222.692	−	128.571i	0.476856	−	0.275313i	−0.242249	−	0.970214i	$-0.577885\pi$
$467$	222.692	−	128.571i	0.476856	−	0.275313i	0.719105	+	0.694901i	$0.244552\pi$
$468$		0			0
$469$	−0.354487	−	1.95952i	−0.000755836	−	0.00417808i
$470$	118.366	+	68.3385i	0.251842	+	0.145401i
$471$		0			0
$472$	35.1365			0.0744417
$473$		−	13.3152i		−	0.0281506i
$474$		0			0
$475$	−237.997	+	412.223i	−0.501046	+	0.867838i
$476$	2.68264	−	7.47349i	0.00563580	−	0.0157006i
$477$		0			0
$478$	284.172	+	492.200i	0.594502	+	1.02971i
$479$	−172.286	+	99.4696i	−0.359680	+	0.207661i	−0.668940	−	0.743316i	$-0.733252\pi$
$479$	−172.286	+	99.4696i	−0.359680	+	0.207661i	0.309261	+	0.950977i	$0.399918\pi$
$480$		0			0
$481$	−71.5343	+	123.901i	−0.148720	+	0.257590i
$482$	−538.272	+	310.772i	−1.11675	+	0.644755i
$483$		0			0
$484$	100.623	−	174.284i	0.207899	−	0.360092i
$485$	115.384	−	66.6172i	0.237906	−	0.137355i
$486$		0			0
$487$	−231.666	+	401.257i	−0.475700	+	0.823937i	−0.999613	−	0.0278350i	$-0.991139\pi$
$487$	−231.666	+	401.257i	−0.475700	+	0.823937i	0.523912	+	0.851772i	$0.324472\pi$
$488$			224.938i			0.460939i
$489$		0			0
$490$	−20.0161	+	119.719i	−0.0408491	+	0.244325i
$491$	824.496	−	476.023i	1.67922	−	0.969497i	0.717056	−	0.697015i	$-0.245489\pi$
$491$	824.496	−	476.023i	1.67922	−	0.969497i	0.962161	−	0.272482i	$-0.0878444\pi$
$492$		0			0
$493$	16.0402	+	27.7825i	0.0325360	+	0.0563539i
$494$	255.566	+	147.551i	0.517340	+	0.298687i
$495$		0			0
$496$	−159.958			−0.322497
$497$	61.4867	−	11.1233i	0.123716	−	0.0223808i
$498$		0			0
$499$	−7.59991	+	13.1634i	−0.0152303	+	0.0263796i	−0.873540	−	0.486752i	$-0.838181\pi$
$499$	−7.59991	+	13.1634i	−0.0152303	+	0.0263796i	0.858310	+	0.513132i	$0.171515\pi$
$500$			164.413i			0.328826i
$501$		0			0
$502$	161.364			0.321442
$503$			247.471i			0.491989i	0.969271	+	0.245995i	$0.0791146\pi$
$503$			247.471i			0.491989i	−0.969271	+	0.245995i	$0.920885\pi$
$504$		0			0
$505$	341.420			0.676080
$506$			175.305i			0.346453i
$507$		0			0
$508$	443.600			0.873228
$509$	173.870	+	100.384i	0.341591	+	0.197217i	0.660975	−	0.750408i	$-0.270143\pi$
$509$	173.870	+	100.384i	0.341591	+	0.197217i	−0.319385	+	0.947625i	$0.603476\pi$
$510$		0			0
$511$	−53.0498	−	19.0424i	−0.103816	−	0.0372650i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−212.372	+	367.838i	−0.413174	+	0.715639i
$515$	176.763	−	102.054i	0.343228	−	0.198163i
$516$		0			0
$517$	−124.532	−	215.695i	−0.240874	−	0.417206i
$518$	95.1874	+	112.423i	0.183760	+	0.217033i
$519$		0			0
$520$	47.6338			0.0916034
$521$	248.569	+	143.512i	0.477101	+	0.275454i	0.719207	−	0.694795i	$-0.244505\pi$
$521$	248.569	+	143.512i	0.477101	+	0.275454i	−0.242107	+	0.970250i	$0.577838\pi$
$522$		0			0
$523$	−280.624	−	486.054i	−0.536565	−	0.929358i	−0.999086	−	0.0427498i	$-0.986388\pi$
$523$	−280.624	−	486.054i	−0.536565	−	0.929358i	0.462520	−	0.886609i	$-0.346945\pi$
$524$	−4.19174	−	2.42010i	−0.00799951	−	0.00461852i
$525$		0			0
$526$	298.067	+	516.267i	0.566667	+	0.981495i
$527$	19.6422	+	11.3404i	0.0372718	+	0.0215189i
$528$		0			0
$529$	112.544	+	194.932i	0.212749	+	0.368492i
$530$	−119.810	+	69.1724i	−0.226057	+	0.130514i
$531$		0			0
$532$	231.891	−	196.340i	0.435886	−	0.369059i
$533$	−269.647	−	155.681i	−0.505905	−	0.292084i
$534$		0			0
$535$	133.246			0.249058
$536$			0.804617i			0.00150115i
$537$		0			0
$538$	−364.027	+	630.514i	−0.676631	+	1.17196i
$539$	140.669	−	170.696i	0.260981	−	0.316690i
$540$		0			0
$541$	−58.2830	−	100.949i	−0.107732	−	0.186597i	0.807119	−	0.590389i	$-0.201026\pi$
$541$	−58.2830	−	100.949i	−0.107732	−	0.186597i	−0.914851	+	0.403791i	$0.867692\pi$
$542$	591.295	−	341.385i	1.09095	−	0.629861i
$543$		0			0
$544$	−1.60420	+	2.77855i	−0.00294889	+	0.00510763i
$545$	241.508	−	139.435i	0.443134	−	0.255843i
$546$		0			0
$547$	22.9108	−	39.6827i	0.0418845	−	0.0725461i	−0.844323	−	0.535834i	$-0.819997\pi$
$547$	22.9108	−	39.6827i	0.0418845	−	0.0725461i	0.886208	+	0.463288i	$0.153331\pi$
$548$	−410.202	+	236.830i	−0.748544	+	0.432172i
$549$		0			0
$550$	70.0049	−	121.252i	0.127282	−	0.220458i
$551$			1227.59i			2.22793i
$552$		0			0
$553$	−121.686	−	672.650i	−0.220047	−	1.21637i
$554$	−183.138	+	105.735i	−0.330573	+	0.190857i
$555$		0			0
$556$	−224.450	−	388.758i	−0.403686	−	0.699205i
$557$	−772.053	−	445.745i	−1.38609	−	0.800260i	−0.393219	−	0.919445i	$-0.628639\pi$
$557$	−772.053	−	445.745i	−1.38609	−	0.800260i	−0.992872	+	0.119185i	$0.961972\pi$
$558$		0			0
$559$	28.3604			0.0507341
$560$	16.5698	−	46.1614i	0.0295890	−	0.0824311i
$561$		0			0
$562$	13.9815	−	24.2167i	0.0248781	−	0.0430901i
$563$			335.625i			0.596137i	0.954544	+	0.298069i	$0.0963424\pi$
$563$			335.625i			0.596137i	−0.954544	+	0.298069i	$0.903658\pi$
$564$		0			0
$565$	−178.793			−0.316449
$566$		−	777.752i		−	1.37412i
$567$		0			0
$568$	−25.2477			−0.0444501
$569$		−	945.483i		−	1.66166i	−0.556529	−	0.830828i	$-0.687867\pi$
$569$		−	945.483i		−	1.66166i	0.556529	−	0.830828i	$-0.312133\pi$
$570$		0			0
$571$	−516.310			−0.904221			−0.452111	−	0.891962i	$-0.649329\pi$
$571$	−516.310			−0.904221			−0.452111	+	0.891962i	$0.649329\pi$
$572$	−75.1727	−	43.4010i	−0.131421	−	0.0758758i
$573$		0			0
$574$	−244.668	+	207.158i	−0.426251	+	0.360902i
$575$		−	602.263i		−	1.04741i
$576$		0			0
$577$	−222.167	+	384.804i	−0.385038	+	0.666905i	−0.991774	−	0.127998i	$-0.959145\pi$
$577$	−222.167	+	384.804i	−0.385038	+	0.666905i	0.606737	+	0.794903i	$0.292478\pi$
$578$	−353.557	+	204.126i	−0.611691	+	0.353160i
$579$		0			0
$580$	99.0755	+	171.604i	0.170820	+	0.295869i
$581$	53.4549	−	148.919i	0.0920050	−	0.256314i
$582$		0			0
$583$	252.103			0.432423
$584$	19.7233	+	11.3872i	0.0337727	+	0.0194987i
$585$		0			0
$586$	−92.9853	−	161.055i	−0.158678	−	0.274838i
$587$	−333.063	−	192.294i	−0.567398	−	0.327588i	0.188711	−	0.982033i	$-0.439569\pi$
$587$	−333.063	−	192.294i	−0.567398	−	0.327588i	−0.756110	+	0.654445i	$0.772902\pi$
$588$		0			0
$589$	433.954	+	751.630i	0.736763	+	1.27611i
$590$	−26.6501	−	15.3864i	−0.0451696	−	0.0260787i
$591$		0			0
$592$	−29.7607	−	51.5470i	−0.0502714	−	0.0870727i
$593$	234.426	−	135.346i	0.395321	−	0.228239i	−0.289142	−	0.957286i	$-0.593370\pi$
$593$	234.426	−	135.346i	0.395321	−	0.228239i	0.684463	+	0.729047i	$0.260037\pi$
$594$		0			0
$595$	−5.30738	+	4.49369i	−0.00891996	+	0.00755243i
$596$	−143.047	−	82.5884i	−0.240012	−	0.138571i
$597$		0			0
$598$	−373.385			−0.624390
$599$		−	290.145i		−	0.484383i	−0.970228	−	0.242191i	$-0.922134\pi$
$599$		−	290.145i		−	0.484383i	0.970228	−	0.242191i	$-0.0778662\pi$
$600$		0			0
$601$	332.538	−	575.974i	0.553309	−	0.958359i	−0.444724	−	0.895667i	$-0.646698\pi$
$601$	332.538	−	575.974i	0.553309	−	0.958359i	0.998033	−	0.0626911i	$-0.0199683\pi$
$602$	9.86540	−	27.4838i	0.0163877	−	0.0456541i
$603$		0			0
$604$	−213.733	−	370.196i	−0.353862	−	0.612907i
$605$	−152.640	+	88.1266i	−0.252297	+	0.145664i
$606$		0			0
$607$	137.803	−	238.683i	0.227024	−	0.393217i	−0.729901	−	0.683553i	$-0.760434\pi$
$607$	137.803	−	238.683i	0.227024	−	0.393217i	0.956925	+	0.290336i	$0.0937672\pi$
$608$	−106.324	+	61.3863i	−0.174875	+	0.100964i
$609$		0			0
$610$	98.5013	−	170.609i	0.161478	−	0.279687i
$611$	459.413	−	265.242i	0.751904	−	0.434112i
$612$		0			0
$613$	31.3289	−	54.2633i	0.0511075	−	0.0885209i	−0.839340	−	0.543607i	$-0.817058\pi$
$613$	31.3289	−	54.2633i	0.0511075	−	0.0885209i	0.890447	+	0.455086i	$0.150392\pi$
$614$		−	357.072i		−	0.581551i
$615$		0			0
$616$	−68.2089	+	57.7517i	−0.110729	+	0.0937527i
$617$	−446.057	+	257.531i	−0.722945	+	0.417392i	−0.815836	−	0.578284i	$-0.803723\pi$
$617$	−446.057	+	257.531i	−0.722945	+	0.417392i	0.0928908	+	0.995676i	$0.470389\pi$
$618$		0			0
$619$	−539.269	−	934.042i	−0.871194	−	1.50895i	−0.860762	−	0.509007i	$-0.830013\pi$
$619$	−539.269	−	934.042i	−0.871194	−	1.50895i	−0.0104316	−	0.999946i	$-0.503321\pi$
$620$	121.324	+	70.0464i	0.195684	+	0.112978i
$621$		0			0
$622$	292.631			0.470467
$623$	246.161	+	290.734i	0.395122	+	0.466668i
$624$		0			0
$625$	−202.151	+	350.136i	−0.323441	+	0.560217i
$626$			480.749i			0.767970i
$627$		0			0
$628$	−323.588			−0.515268
$629$			8.43968i			0.0134176i
$630$		0			0
$631$	65.5284			0.103848			0.0519242	−	0.998651i	$-0.483465\pi$
$631$	65.5284			0.103848			0.0519242	+	0.998651i	$0.483465\pi$
$632$			276.203i			0.437031i
$633$		0			0
$634$	−388.507			−0.612787
$635$	−336.458	−	194.254i	−0.529855	−	0.305912i
$636$		0			0
$637$	363.568	+	299.613i	0.570750	+	0.470350i
$638$		−	361.086i		−	0.565966i
$639$		0			0
$640$	−9.90864	+	17.1623i	−0.0154822	+	0.0268160i
$641$	−685.053	+	395.516i	−1.06873	+	0.617029i	−0.927833	−	0.372996i	$-0.878331\pi$
$641$	−685.053	+	395.516i	−1.06873	+	0.617029i	−0.140893	+	0.990025i	$0.544997\pi$
$642$		0			0
$643$	−414.293	−	717.577i	−0.644313	−	1.11598i	−0.984460	−	0.175610i	$-0.943810\pi$
$643$	−414.293	−	717.577i	−0.644313	−	1.11598i	0.340147	−	0.940372i	$-0.389523\pi$
$644$	−129.885	+	361.844i	−0.201685	+	0.561870i
$645$		0			0
$646$	17.4082			0.0269477
$647$	−54.8043	−	31.6413i	−0.0847053	−	0.0489046i	0.457049	−	0.889441i	$-0.348906\pi$
$647$	−54.8043	−	31.6413i	−0.0847053	−	0.0489046i	−0.541754	+	0.840537i	$0.682240\pi$
$648$		0			0
$649$	28.0383	+	48.5638i	0.0432023	+	0.0748286i
$650$	258.257	+	149.105i	0.397318	+	0.229392i
$651$		0			0
$652$	53.7443	+	93.0878i	0.0824298	+	0.142773i
$653$	−564.419	−	325.867i	−0.864347	−	0.499031i	0.00111857	−	0.999999i	$-0.499644\pi$
$653$	−564.419	−	325.867i	−0.864347	−	0.499031i	−0.865466	+	0.500968i	$0.832977\pi$
$654$		0			0
$655$	2.11955	+	3.67116i	0.00323595	+	0.00560482i
$656$	112.182	−	64.7686i	0.171010	−	0.0987326i
$657$		0			0
$658$	−97.2328	−	537.480i	−0.147770	−	0.816839i
$659$	58.2921	+	33.6550i	0.0884554	+	0.0510698i	0.543575	−	0.839360i	$-0.317070\pi$
$659$	58.2921	+	33.6550i	0.0884554	+	0.0510698i	−0.455120	+	0.890430i	$0.650404\pi$
$660$		0			0
$661$	−486.564			−0.736102			−0.368051	−	0.929806i	$-0.619975\pi$
$661$	−486.564			−0.736102			−0.368051	+	0.929806i	$0.619975\pi$
$662$			278.624i			0.420882i
$663$		0			0
$664$	−31.9656	+	55.3661i	−0.0481410	+	0.0833827i
$665$	−261.861	+	47.3720i	−0.393776	+	0.0712361i
$666$		0			0
$667$	−776.620	−	1345.15i	−1.16435	−	2.01671i
$668$	−82.2012	+	47.4589i	−0.123056	+	0.0710463i
$669$		0			0
$670$	0.352345	−	0.610280i	0.000525888	−	0.000910865i
$671$	−310.897	+	179.497i	−0.463334	+	0.267506i
$672$		0			0
$673$	135.979	−	235.523i	0.202050	−	0.349960i	−0.747139	−	0.664668i	$-0.768573\pi$
$673$	135.979	−	235.523i	0.202050	−	0.349960i	0.949189	+	0.314707i	$0.101906\pi$
$674$	−398.215	+	229.910i	−0.590824	+	0.341112i
$675$		0			0
$676$	−76.5595	+	132.605i	−0.113254	+	0.196161i
$677$			593.459i			0.876601i	0.898829	+	0.438300i	$0.144419\pi$
$677$			593.459i			0.876601i	−0.898829	+	0.438300i	$0.855581\pi$
$678$		0			0
$679$	−501.139	−	179.886i	−0.738054	−	0.264927i
$680$	2.43348	−	1.40497i	0.00357865	−	0.00206613i
$681$		0			0
$682$	−127.644	−	221.086i	−0.187161	−	0.324173i
$683$	763.359	+	440.725i	1.11766	+	0.645279i	0.940801	−	0.338958i	$-0.110075\pi$
$683$	763.359	+	440.725i	1.11766	+	0.645279i	0.176854	+	0.984237i	$0.443408\pi$
$684$		0			0
$685$	414.836			0.605600
$686$	416.822	−	248.107i	0.607613	−	0.361672i
$687$		0			0
$688$	−5.89944	+	10.2181i	−0.00857477	+	0.0148519i
$689$			536.958i			0.779329i
$690$		0			0
$691$	876.408			1.26832			0.634159	−	0.773203i	$-0.281346\pi$
$691$	876.408			1.26832			0.634159	+	0.773203i	$0.281346\pi$
$692$		−	183.820i		−	0.265636i
$693$		0			0
$694$	137.837			0.198612
$695$			393.150i			0.565683i
$696$		0			0
$697$	−18.3674			−0.0263521
$698$	261.647	+	151.062i	0.374852	+	0.216421i
$699$		0			0
$700$	234.333	−	198.407i	0.334761	−	0.283438i
$701$			286.681i			0.408961i	0.978871	+	0.204480i	$0.0655504\pi$
$701$			286.681i			0.408961i	−0.978871	+	0.204480i	$0.934450\pi$
$702$		0			0
$703$	−161.477	+	279.686i	−0.229696	+	0.397846i
$704$	31.2744	−	18.0563i	0.0444238	−	0.0256481i
$705$		0			0
$706$	−453.751	−	785.919i	−0.642706	−	1.11320i
$707$	−881.661	−	1041.31i	−1.24705	−	1.47285i
$708$		0			0
$709$	657.204			0.926945			0.463473	−	0.886111i	$-0.346603\pi$
$709$	657.204			0.926945			0.463473	+	0.886111i	$0.346603\pi$
$710$	19.1496	+	11.0561i	0.0269713	+	0.0155719i
$711$		0			0
$712$	−76.9632	−	133.304i	−0.108094	−	0.187225i
$713$	−951.017	−	549.070i	−1.33383	−	0.770084i
$714$		0			0
$715$	38.0109	+	65.8368i	0.0531621	+	0.0920795i
$716$	286.244	+	165.263i	0.399783	+	0.230815i
$717$		0			0
$718$	−215.424	−	373.125i	−0.300033	−	0.519673i
$719$	−404.412	+	233.488i	−0.562465	+	0.324739i	−0.754134	−	0.656720i	$-0.771943\pi$
$719$	−404.412	+	233.488i	−0.562465	+	0.324739i	0.191669	+	0.981460i	$0.438610\pi$
$720$		0			0
$721$	−767.717	−	275.575i	−1.06480	−	0.382212i
$722$	134.765	+	77.8064i	0.186655	+	0.107765i
$723$		0			0
$724$	−489.213			−0.675709
$725$			1240.52i			1.71106i
$726$		0			0
$727$	−21.8124	+	37.7802i	−0.0300033	+	0.0519673i	−0.880637	−	0.473791i	$-0.842885\pi$
$727$	−21.8124	+	37.7802i	−0.0300033	+	0.0519673i	0.850634	+	0.525759i	$0.176218\pi$
$728$	−123.006	−	145.279i	−0.168965	−	0.199560i
$729$		0			0
$730$	−9.97303	−	17.2738i	−0.0136617	−	0.0236627i
$731$	1.44885	−	0.836496i	0.00198202	−	0.00114432i
$732$		0			0
$733$	−559.033	+	968.274i	−0.762665	+	1.32097i	0.178808	+	0.983884i	$0.442776\pi$
$733$	−559.033	+	968.274i	−0.762665	+	1.32097i	−0.941472	+	0.337090i	$0.890557\pi$
$734$	−153.492	+	88.6189i	−0.209118	+	0.120734i
$735$		0			0
$736$	77.6705	−	134.529i	0.105531	−	0.182784i
$737$	−1.11210	+	0.642070i	−0.00150895	+	0.000871194i
$738$		0			0
$739$	414.623	−	718.148i	0.561060	−	0.971784i	−0.436345	−	0.899780i	$-0.643727\pi$
$739$	414.623	−	718.148i	0.561060	−	0.971784i	0.997404	−	0.0720041i	$-0.0229395\pi$
$740$			52.1293i			0.0704450i
$741$		0			0
$742$	520.360	+	186.785i	0.701294	+	0.251732i
$743$	1010.16	−	583.214i	1.35957	−	0.784945i	0.370000	−	0.929032i	$-0.379358\pi$
$743$	1010.16	−	583.214i	1.35957	−	0.784945i	0.989565	+	0.144086i	$0.0460242\pi$
$744$		0			0
$745$	72.3316	+	125.282i	0.0970893	+	0.168164i
$746$	−324.343	−	187.260i	−0.434776	−	0.251018i
$747$		0			0
$748$	−5.12049			−0.00684557
$749$	−344.086	−	406.391i	−0.459394	−	0.542578i
$750$		0			0
$751$	−608.863	+	1054.58i	−0.810737	+	1.40424i	0.101612	+	0.994824i	$0.467600\pi$
$751$	−608.863	+	1054.58i	−0.810737	+	1.40424i	−0.912349	+	0.409413i	$0.865733\pi$
$752$			220.700i			0.293484i
$753$		0			0
$754$	769.084			1.02000
$755$			374.377i			0.495864i
$756$		0			0
$757$	212.121			0.280213			0.140106	−	0.990136i	$-0.455256\pi$
$757$	212.121			0.280213			0.140106	+	0.990136i	$0.455256\pi$
$758$			269.794i			0.355928i
$759$		0			0
$760$	107.525			0.141481
$761$	884.489	+	510.660i	1.16227	+	0.671038i	0.951848	−	0.306572i	$-0.0991819\pi$
$761$	884.489	+	510.660i	1.16227	+	0.671038i	0.210425	+	0.977610i	$0.432515\pi$
$762$		0			0
$763$	−1048.92	−	376.514i	−1.37473	−	0.493465i
$764$		−	293.882i		−	0.384662i
$765$		0			0
$766$	−423.880	+	734.182i	−0.553369	+	0.958463i
$767$	−103.437	+	59.7193i	−0.134859	+	0.0778609i
$768$		0			0
$769$	−19.1405	−	33.1524i	−0.0248902	−	0.0431110i	0.853312	−	0.521401i	$-0.174590\pi$
$769$	−19.1405	−	33.1524i	−0.0248902	−	0.0431110i	−0.878202	+	0.478290i	$0.841257\pi$
$770$	77.0242	−	13.9341i	0.100031	−	0.0180962i
$771$		0			0
$772$	507.564			0.657466
$773$	−329.696	−	190.350i	−0.426515	−	0.246249i	0.271346	−	0.962482i	$-0.412531\pi$
$773$	−329.696	−	190.350i	−0.426515	−	0.246249i	−0.697861	+	0.716233i	$0.745865\pi$
$774$		0			0
$775$	438.522	+	759.543i	0.565835	+	0.980056i
$776$	186.317	+	107.570i	0.240100	+	0.138622i
$777$		0			0
$778$	71.3824	+	123.638i	0.0917512	+	0.158918i
$779$	−608.684	−	351.424i	−0.781365	−	0.451121i
$780$		0			0
$781$	−20.1472	−	34.8960i	−0.0257967	−	0.0446811i
$782$	−19.0752	+	11.0131i	−0.0243929	+	0.0140832i
$783$		0			0
$784$	−183.578	+	68.6675i	−0.234155	+	0.0875862i
$785$	245.432	+	141.700i	0.312653	+	0.180510i
$786$		0			0
$787$	855.666			1.08725			0.543625	−	0.839328i	$-0.317051\pi$
$787$	855.666			1.08725			0.543625	+	0.839328i	$0.317051\pi$
$788$		−	636.258i		−	0.807434i
$789$		0			0
$790$	120.951	−	209.493i	0.153102	−	0.265180i
$791$	461.705	+	545.306i	0.583697	+	0.689389i
$792$		0			0
$793$	−382.313	−	662.186i	−0.482110	−	0.835039i
$794$	−378.530	+	218.544i	−0.476738	+	0.275245i
$795$		0			0
$796$	−247.034	+	427.876i	−0.310344	+	0.537532i
$797$	27.2948	−	15.7587i	0.0342469	−	0.0197725i	−0.482779	−	0.875742i	$-0.660372\pi$
$797$	27.2948	−	15.7587i	0.0342469	−	0.0197725i	0.517026	+	0.855970i	$0.327039\pi$
$798$		0			0
$799$	15.6468	−	27.1010i	0.0195829	−	0.0339187i
$800$	−107.444	+	62.0326i	−0.134305	+	0.0775408i
$801$		0			0
$802$	426.403	−	738.551i	0.531674	−	0.920886i
$803$			36.3472i			0.0452643i
$804$		0			0
$805$	256.967	−	217.571i	0.319214	−	0.270275i
$806$	470.894	−	271.871i	0.584236	−	0.337309i
$807$		0			0
$808$	275.655	+	477.448i	0.341157	+	0.590901i
$809$	−366.440	−	211.564i	−0.452955	−	0.261514i	0.256123	−	0.966644i	$-0.417555\pi$
$809$	−366.440	−	211.564i	−0.452955	−	0.261514i	−0.709077	+	0.705131i	$0.750888\pi$
$810$		0			0
$811$	695.569			0.857668			0.428834	−	0.903383i	$-0.358925\pi$
$811$	695.569			0.857668			0.428834	+	0.903383i	$0.358925\pi$
$812$	267.532	−	745.311i	0.329473	−	0.917871i
$813$		0			0
$814$	47.4970	−	82.2672i	0.0583501	−	0.101065i
$815$		−	94.1393i		−	0.115508i
$816$		0			0
$817$	64.0188			0.0783583
$818$		−	621.448i		−	0.759717i
$819$		0			0
$820$	−113.450			−0.138353
$821$		−	91.3532i		−	0.111271i	−0.998451	−	0.0556353i	$-0.982282\pi$
$821$		−	91.3532i		−	0.111271i	0.998451	−	0.0556353i	$-0.0177184\pi$
$822$		0			0
$823$	−657.997			−0.799511			−0.399755	−	0.916622i	$-0.630905\pi$
$823$	−657.997			−0.799511			−0.399755	+	0.916622i	$0.630905\pi$
$824$	285.428	+	164.792i	0.346393	+	0.199990i
$825$		0			0
$826$	21.8920	+	121.014i	0.0265036	+	0.146505i
$827$		−	1364.30i		−	1.64969i	−0.565355	−	0.824847i	$-0.691261\pi$
$827$		−	1364.30i		−	1.64969i	0.565355	−	0.824847i	$-0.308739\pi$
$828$		0			0
$829$	−388.984	+	673.740i	−0.469221	+	0.812715i	−0.999381	−	0.0351831i	$-0.988799\pi$
$829$	−388.984	+	673.740i	−0.469221	+	0.812715i	0.530160	+	0.847898i	$0.322132\pi$
$830$	48.4901	−	27.9958i	0.0584218	−	0.0337298i
$831$		0			0
$832$	38.4584	+	66.6119i	0.0462240	+	0.0800624i
$833$	27.4108	+	4.58287i	0.0329062	+	0.00550165i
$834$		0			0
$835$	83.1298			0.0995566
$836$	−169.690	−	97.9704i	−0.202978	−	0.117189i
$837$		0			0
$838$	−40.4595	−	70.0778i	−0.0482810	−	0.0836251i
$839$	1355.78	+	782.761i	1.61595	+	0.932969i	0.987953	+	0.154752i	$0.0494580\pi$
$839$	1355.78	+	782.761i	1.61595	+	0.932969i	0.627996	+	0.778216i	$0.283875\pi$
$840$		0			0
$841$	1179.15	+	2042.35i	1.40208	+	2.42847i
$842$	−401.012	−	231.525i	−0.476262	−	0.274970i
$843$		0			0
$844$	215.053	+	372.483i	0.254802	+	0.441331i
$845$	116.136	−	67.0514i	0.137440	−	0.0793508i
$846$		0			0
$847$	662.946	+	237.967i	0.782699	+	0.280953i
$848$	−193.464	−	111.696i	−0.228141	−	0.131717i
$849$		0			0
$850$	17.5915			0.0206959
$851$		−	408.624i		−	0.480170i
$852$		0			0
$853$	−484.334	+	838.891i	−0.567801	+	0.983460i	0.428982	+	0.903313i	$0.358872\pi$
$853$	−484.334	+	838.891i	−0.567801	+	0.983460i	−0.996783	+	0.0801471i	$0.974461\pi$
$854$	−774.709	+	140.149i	−0.907153	+	0.164109i
$855$		0			0
$856$	107.580	+	186.334i	0.125677	+	0.217680i
$857$	−1149.35	+	663.578i	−1.34113	+	0.774304i	−0.986974	−	0.160881i	$-0.948566\pi$
$857$	−1149.35	+	663.578i	−1.34113	+	0.774304i	−0.354160	+	0.935185i	$0.615233\pi$
$858$		0			0
$859$	−181.100	+	313.675i	−0.210827	+	0.365163i	−0.951974	−	0.306180i	$-0.900949\pi$
$859$	−181.100	+	313.675i	−0.210827	+	0.365163i	0.741147	+	0.671343i	$0.234282\pi$
$860$	8.94912	−	5.16678i	0.0104060	−	0.00600788i
$861$		0			0
$862$	−73.8198	+	127.860i	−0.0856378	+	0.148329i
$863$	−938.041	+	541.578i	−1.08695	+	0.627553i	−0.932764	−	0.360488i	$-0.882610\pi$
$863$	−938.041	+	541.578i	−1.08695	+	0.627553i	−0.154190	+	0.988041i	$0.549277\pi$
$864$		0			0
$865$	−80.4956	+	139.422i	−0.0930584	+	0.161182i
$866$		−	602.969i		−	0.696269i
$867$		0			0
$868$	−99.6628	−	550.912i	−0.114819	−	0.634691i
$869$	−381.753	+	220.405i	−0.439302	+	0.253631i
$870$		0			0
$871$	−1.36756	−	2.36868i	−0.00157010	−	0.00271949i
$872$	389.975	+	225.152i	0.447220	+	0.258202i
$873$		0			0
$874$	−842.854			−0.964364
$875$	−566.255	+	102.438i	−0.647148	+	0.117072i
$876$		0			0
$877$	570.778	−	988.617i	0.650830	−	1.12727i	−0.332091	−	0.943247i	$-0.607754\pi$
$877$	570.778	−	988.617i	0.650830	−	1.12727i	0.982922	−	0.184024i	$-0.0589125\pi$
$878$		−	402.494i		−	0.458421i
$879$		0			0
$880$	−31.6277			−0.0359405
$881$			536.022i			0.608424i	0.952604	+	0.304212i	$0.0983931\pi$
$881$			536.022i			0.608424i	−0.952604	+	0.304212i	$0.901607\pi$
$882$		0			0
$883$	−413.964			−0.468816			−0.234408	−	0.972138i	$-0.575315\pi$
$883$	−413.964			−0.468816			−0.234408	+	0.972138i	$0.575315\pi$
$884$		−	10.9062i		−	0.0123374i
$885$		0			0
$886$	−651.837			−0.735708
$887$	−99.9924	−	57.7307i	−0.112731	−	0.0650853i	0.442574	−	0.896732i	$-0.354065\pi$
$887$	−99.9924	−	57.7307i	−0.112731	−	0.0650853i	−0.555305	+	0.831647i	$0.687399\pi$
$888$		0			0
$889$	276.387	+	1527.80i	0.310896	+	1.71856i
$890$			134.810i			0.151472i
$891$		0			0
$892$	81.8923	−	141.842i	0.0918076	−	0.159015i
$893$	1037.05	−	598.740i	1.16131	−	0.670482i
$894$		0			0
$895$	−144.739	−	250.695i	−0.161719	−	0.280106i
$896$	77.9310	−	14.0981i	0.0869766	−	0.0157345i
$897$		0			0
$898$	260.858			0.290487
$899$	1958.87	+	1130.95i	2.17894	+	1.25801i
$900$		0			0
$901$	15.8377	+	27.4317i	0.0175779	+	0.0304458i
$902$	179.039	+	103.368i	0.198491	+	0.114599i
$903$		0			0
$904$	−144.354	−	250.028i	−0.159683	−	0.276579i
$905$	371.054	+	214.228i	0.410005	+	0.236716i
$906$		0			0
$907$	91.2855	+	158.111i	0.100646	+	0.174323i	0.911951	−	0.410300i	$-0.134576\pi$
$907$	91.2855	+	158.111i	0.100646	+	0.174323i	−0.811305	+	0.584623i	$0.801243\pi$
$908$	−40.8968	+	23.6118i	−0.0450406	+	0.0260042i
$909$		0			0
$910$	29.6784	+	164.055i	0.0326137	+	0.180281i
$911$	781.868	+	451.411i	0.858252	+	0.495512i	0.863427	−	0.504475i	$-0.168314\pi$
$911$	781.868	+	451.411i	0.858252	+	0.495512i	−0.00517457	+	0.999987i	$0.501647\pi$
$912$		0			0
$913$	−102.032			−0.111755
$914$			223.575i			0.244612i
$915$		0			0
$916$	38.2246	−	66.2070i	0.0417299	−	0.0722783i
$917$	5.72338	−	15.9446i	0.00624142	−	0.0173878i
$918$		0			0
$919$	−590.898	−	1023.47i	−0.642979	−	1.11367i	−0.984764	−	0.173895i	$-0.944365\pi$
$919$	−590.898	−	1023.47i	−0.642979	−	1.11367i	0.341785	−	0.939778i	$-0.388969\pi$
$920$	−117.822	+	68.0244i	−0.128067	+	0.0739396i
$921$		0			0
$922$	245.860	−	425.841i	0.266659	−	0.461867i
$923$	74.3255	−	42.9119i	0.0805260	−	0.0464917i
$924$		0			0
$925$	−163.177	+	282.630i	−0.176407	+	0.305546i
$926$	417.967	−	241.313i	0.451368	−	0.260598i
$927$		0			0
$928$	−159.982	+	277.098i	−0.172395	+	0.298597i
$929$		−	877.848i		−	0.944939i	−0.881347	−	0.472469i	$-0.843363\pi$
$929$		−	877.848i		−	0.944939i	0.881347	−	0.472469i	$-0.156637\pi$
$930$		0			0
$931$	820.694	+	676.326i	0.881518	+	0.726451i
$932$	237.967	−	137.390i	0.255330	−	0.147415i
$933$		0			0
$934$	−181.827	−	314.934i	−0.194676	−	0.337188i
$935$	3.88375	+	2.24228i	0.00415374	+	0.00239816i
$936$		0			0
$937$	−618.122			−0.659682			−0.329841	−	0.944037i	$-0.606995\pi$
$937$	−618.122			−0.659682			−0.329841	+	0.944037i	$0.606995\pi$
$938$	−2.77118	+	0.501321i	−0.00295435	+	0.000534457i
$939$		0			0
$940$	96.6453	−	167.395i	0.102814	−	0.178079i
$941$			959.816i			1.02000i	0.860176	+	0.509998i	$0.170354\pi$
$941$			959.816i			1.02000i	−0.860176	+	0.509998i	$0.829646\pi$
$942$		0			0
$943$	889.294			0.943048
$944$		−	49.6905i		−	0.0526383i
$945$		0			0
$946$	−18.8306			−0.0199055
$947$		−	746.630i		−	0.788416i	−0.919021	−	0.394208i	$-0.871019\pi$
$947$		−	746.630i		−	0.788416i	0.919021	−	0.394208i	$-0.128981\pi$
$948$		0			0
$949$	−77.4166			−0.0815771
$950$	582.971	+	336.579i	0.613654	+	0.354293i
$951$		0			0
$952$	−10.5691	−	3.79382i	−0.0111020	−	0.00398511i
$953$			1477.27i			1.55013i	0.631881	+	0.775065i	$0.282283\pi$
$953$			1477.27i			1.55013i	−0.631881	+	0.775065i	$0.717717\pi$
$954$		0			0
$955$	−128.692	+	222.901i	−0.134756	+	0.233404i
$956$	696.077	−	401.880i	0.728114	−	0.420377i
$957$		0			0
$958$	140.671	+	243.650i	0.146839	+	0.254332i
$959$	−1071.24	−	1265.22i	−1.11704	−	1.31931i
$960$		0			0
$961$	638.166			0.664064
$962$	175.222	+	101.165i	0.182144	+	0.105161i
$963$		0			0
$964$	439.498	+	761.232i	0.455910	+	0.789660i
$965$	−384.973	−	222.264i	−0.398936	−	0.230326i
$966$		0			0
$967$	81.0172	+	140.326i	0.0837820	+	0.145115i	0.904872	−	0.425685i	$-0.139967\pi$
$967$	81.0172	+	140.326i	0.0837820	+	0.145115i	−0.821090	+	0.570799i	$0.806633\pi$
$968$	−246.475	−	142.303i	−0.254623	−	0.147007i
$969$		0			0
$970$	−94.2109	−	163.178i	−0.0971247	−	0.168225i
$971$	1063.88	−	614.232i	1.09565	−	0.632577i	0.160579	−	0.987023i	$-0.448664\pi$
$971$	1063.88	−	614.232i	1.09565	−	0.632577i	0.935076	+	0.354446i	$0.115331\pi$
$972$		0			0
$973$	1199.08	−	1015.24i	1.23235	−	1.04342i
$974$	567.464	+	327.625i	0.582612	+	0.336371i
$975$		0			0
$976$	318.111			0.325933
$977$		−	1042.27i		−	1.06681i	−0.845860	−	0.533405i	$-0.820912\pi$
$977$		−	1042.27i		−	1.06681i	0.845860	−	0.533405i	$-0.179088\pi$
$978$		0			0
$979$	122.831	−	212.749i	0.125465	−	0.217312i
$980$	169.308	+	28.3070i	0.172764	+	0.0288847i
$981$		0			0
$982$	−673.198	−	1166.01i	−0.685538	−	1.18739i
$983$	−679.154	+	392.110i	−0.690899	+	0.398891i	−0.803949	−	0.594698i	$-0.797271\pi$
$983$	−679.154	+	392.110i	−0.690899	+	0.398891i	0.113050	+	0.993589i	$0.463938\pi$
$984$		0			0
$985$	−278.620	+	482.584i	−0.282863	+	0.489933i
$986$	39.2904	−	22.6843i	0.0398482	−	0.0230064i
$987$		0			0
$988$	208.669	−	361.425i	0.211203	−	0.365815i
$989$	−70.1492	+	40.5006i	−0.0709294	+	0.0409511i
$990$		0			0
$991$	−81.5488	+	141.247i	−0.0822894	+	0.142529i	−0.904233	−	0.427040i	$-0.859557\pi$
$991$	−81.5488	+	141.247i	−0.0822894	+	0.142529i	0.821944	+	0.569569i	$0.192890\pi$
$992$			226.215i			0.228039i
$993$		0			0
$994$	−15.7307	−	86.9554i	−0.0158256	−	0.0874803i
$995$	374.737	−	216.354i	0.376620	−	0.217442i
$996$		0			0
$997$	113.216	+	196.096i	0.113557	+	0.196686i	0.917202	−	0.398423i	$-0.130442\pi$
$997$	113.216	+	196.096i	0.113557	+	0.196686i	−0.803645	+	0.595109i	$0.797109\pi$
$998$	18.6159	+	10.7479i	0.0186532	+	0.0107694i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.r.a.305.5		32
3.2	odd	2		126.3.r.a.11.9	yes	32
7.2	even	3		378.3.i.a.359.4		32
9.4	even	3		126.3.i.a.95.12	yes	32
9.5	odd	6		378.3.i.a.179.5		32
21.2	odd	6		126.3.i.a.65.12	✓	32
63.23	odd	6	inner	378.3.r.a.233.13		32
63.58	even	3		126.3.r.a.23.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.12	✓	32	21.2	odd	6
126.3.i.a.95.12	yes	32	9.4	even	3
126.3.r.a.11.9	yes	32	3.2	odd	2
126.3.r.a.23.1	yes	32	63.58	even	3
378.3.i.a.179.5		32	9.5	odd	6
378.3.i.a.359.4		32	7.2	even	3
378.3.r.a.233.13		32	63.23	odd	6	inner
378.3.r.a.305.5		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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -2.00000 q^{4} +(1.51694 + 0.875808i) q^{5} +(-1.24611 - 6.88819i) q^{7} +2.82843i q^{8} +(1.23858 - 2.14528i) q^{10} +(-3.90930 + 2.25703i) q^{11} +(-4.80730 - 8.32649i) q^{13} +(-9.74138 + 1.76226i) q^{14} +4.00000 q^{16} +(-0.491183 - 0.283585i) q^{17} +(-10.8517 - 18.7956i) q^{19} +(-3.03389 - 1.75162i) q^{20} +(3.19193 + 5.52858i) q^{22} +(23.7816 + 13.7303i) q^{23} +(-10.9659 - 18.9935i) q^{25} +(-11.7754 + 6.79855i) q^{26} +(2.49222 + 13.7764i) q^{28} +(-48.9844 - 28.2812i) q^{29} -39.9896 q^{31} -5.65685i q^{32} +(-0.401050 + 0.694638i) q^{34} +(4.14246 - 11.5404i) q^{35} +(-7.44017 - 12.8868i) q^{37} +(-26.5810 + 15.3466i) q^{38} +(-2.47716 + 4.29057i) q^{40} +(28.0456 - 16.1921i) q^{41} +(-1.47486 + 2.55453i) q^{43} +(7.81860 - 4.51407i) q^{44} +(19.4176 - 33.6323i) q^{46} +55.1749i q^{47} +(-45.8944 + 17.1669i) q^{49} +(-26.8609 + 15.5082i) q^{50} +(9.61460 + 16.6530i) q^{52} +(-48.3659 - 27.9241i) q^{53} -7.90692 q^{55} +(19.4828 - 3.52453i) q^{56} +(-39.9956 + 69.2744i) q^{58} -12.4226i q^{59} +79.5276 q^{61} +56.5538i q^{62} -8.00000 q^{64} -16.8411i q^{65} +0.284475 q^{67} +(0.982367 + 0.567170i) q^{68} +(-16.3205 - 5.85832i) q^{70} +8.92640i q^{71} +(4.02599 - 6.97323i) q^{73} +(-18.2246 + 10.5220i) q^{74} +(21.7033 + 37.5913i) q^{76} +(20.4183 + 24.1155i) q^{77} +97.6526 q^{79} +(6.06778 + 3.50323i) q^{80} +(-22.8992 - 39.6625i) q^{82} +(19.5749 + 11.3016i) q^{83} +(-0.496732 - 0.860365i) q^{85} +(3.61265 + 2.08577i) q^{86} +(-6.38386 - 11.0572i) q^{88} +(-47.1301 + 27.2106i) q^{89} +(-51.3640 + 43.4893i) q^{91} +(-47.5633 - 27.4607i) q^{92} +78.0291 q^{94} -38.0159i q^{95} +(38.0319 - 65.8731i) q^{97} +(24.2776 + 64.9045i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} + 2 q^{7} + 36 q^{11} + 10 q^{13} - 36 q^{14} + 128 q^{16} + 54 q^{17} + 28 q^{19} + 126 q^{23} + 80 q^{25} + 72 q^{26} - 4 q^{28} - 36 q^{29} + 16 q^{31} + 90 q^{35} + 22 q^{37} - 72 q^{41}+ \cdots - 288 q^{98}+O(q^{100}) \) 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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