LMFDB - Embedded newform 378.3.i.a.359.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(179,378)] 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, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.179"); S:= CuspForms(chi, 3); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$10.2997539928$
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			359.4
Character	$\chi$	$=$	378.359
Dual form			378.3.i.a.179.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} -1.75162i q^{5} +(6.58841 - 2.36493i) q^{7} +2.82843i q^{8} +(1.23858 + 2.14528i) q^{10} -4.51407i q^{11} +(-4.80730 - 8.32649i) q^{13} +(-6.39685 + 7.55515i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(0.491183 - 0.283585i) q^{17} +(-10.8517 + 18.7956i) q^{19} +(-3.03389 - 1.75162i) q^{20} +(3.19193 + 5.52858i) q^{22} -27.4607i q^{23} +21.9318 q^{25} +(11.7754 + 6.79855i) q^{26} +(2.49222 - 13.7764i) q^{28} +(-48.9844 - 28.2812i) q^{29} +(19.9948 - 34.6320i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-0.401050 + 0.694638i) q^{34} +(-4.14246 - 11.5404i) q^{35} +(-7.44017 + 12.8868i) q^{37} -30.6932i q^{38} +4.95432 q^{40} +(28.0456 - 16.1921i) q^{41} +(-1.47486 + 2.55453i) q^{43} +(-7.81860 - 4.51407i) q^{44} +(19.4176 + 33.6323i) q^{46} +(47.7829 - 27.5875i) q^{47} +(37.8142 - 31.1623i) q^{49} +(-26.8609 + 15.5082i) q^{50} -19.2292 q^{52} +(48.3659 - 27.9241i) q^{53} -7.90692 q^{55} +(6.68904 + 18.6348i) q^{56} +79.9912 q^{58} +(10.7583 + 6.21132i) q^{59} +(-39.7638 - 68.8730i) q^{61} +56.5538i q^{62} -8.00000 q^{64} +(-14.5848 + 8.42054i) q^{65} +(-0.142238 + 0.246363i) q^{67} -1.13434i q^{68} +(13.2337 + 11.2048i) q^{70} +8.92640i q^{71} +(4.02599 + 6.97323i) q^{73} -21.0440i q^{74} +(21.7033 + 37.5913i) q^{76} +(-10.6755 - 29.7405i) q^{77} +(-48.8263 - 84.5697i) q^{79} +(-6.06778 + 3.50323i) q^{80} +(-22.8992 + 39.6625i) q^{82} +(19.5749 + 11.3016i) q^{83} +(-0.496732 - 0.860365i) q^{85} -4.17153i q^{86} +12.7677 q^{88} +(47.1301 + 27.2106i) q^{89} +(-51.3640 - 43.4893i) q^{91} +(-47.5633 - 27.4607i) q^{92} +(-39.0146 + 67.5752i) q^{94} +(32.9227 + 19.0080i) q^{95} +(38.0319 - 65.8731i) q^{97} +(-24.2776 + 64.9045i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 2 q^{7} + 10 q^{13} - 36 q^{14} - 64 q^{16} - 54 q^{17} + 28 q^{19} - 160 q^{25} - 72 q^{26} - 4 q^{28} - 36 q^{29} - 8 q^{31} - 90 q^{35} + 22 q^{37} - 72 q^{41} + 16 q^{43} + 72 q^{44}+ \cdots + 288 q^{98}+O(q^{100}) $ 32 * q + 32 * q^4 + 2 * q^7 + 10 * q^13 - 36 * q^14 - 64 * q^16 - 54 * q^17 + 28 * q^19 - 160 * q^25 - 72 * q^26 - 4 * q^28 - 36 * q^29 - 8 * q^31 - 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 + 72 * q^44 - 12 * q^46 + 108 * q^47 + 74 * q^49 + 288 * q^50 + 40 * q^52 - 72 * q^53 - 24 * q^55 + 48 * q^58 + 90 * q^59 - 62 * q^61 - 256 * q^64 - 378 * q^65 + 70 * q^67 - 108 * q^70 + 196 * q^73 - 56 * q^76 - 630 * q^77 - 38 * q^79 + 60 * q^85 - 486 * q^89 - 122 * q^91 - 252 * q^92 + 168 * q^94 + 72 * q^95 - 38 * q^97 + 288 * q^98

Character values

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

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

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 $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		−	1.75162i		−	0.350323i	−0.984540	−	0.175162i	$-0.943955\pi$
$5$		−	1.75162i		−	0.350323i	0.984540	−	0.175162i	$-0.0560448\pi$
$6$		0			0
$7$	6.58841	−	2.36493i	0.941201	−	0.337848i
$7$	6.58841	−	2.36493i	0.941201	−	0.337848i
$8$			2.82843i			0.353553i
$9$		0			0
$10$	1.23858	+	2.14528i	0.123858	+	0.214528i
$11$		−	4.51407i		−	0.410370i	−0.978723	−	0.205185i	$-0.934220\pi$
$11$		−	4.51407i		−	0.410370i	0.978723	−	0.205185i	$-0.0657796\pi$
$12$		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	$0.953904\pi$
$14$	−6.39685	+	7.55515i	−0.456918	+	0.539653i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	0.491183	−	0.283585i	0.0288931	−	0.0166815i	−0.485484	−	0.874246i	$-0.661357\pi$
$17$	0.491183	−	0.283585i	0.0288931	−	0.0166815i	0.514377	+	0.857564i	$0.328023\pi$
$18$		0			0
$19$	−10.8517	+	18.7956i	−0.571140	+	0.989244i	0.425309	+	0.905048i	$0.360165\pi$
$19$	−10.8517	+	18.7956i	−0.571140	+	0.989244i	−0.996449	+	0.0841959i	$0.973168\pi$
$20$	−3.03389	−	1.75162i	−0.151694	−	0.0875808i
$21$		0			0
$22$	3.19193	+	5.52858i	0.145088	+	0.251299i
$23$		−	27.4607i		−	1.19394i	−0.802263	−	0.596971i	$-0.796371\pi$
$23$		−	27.4607i		−	1.19394i	0.802263	−	0.596971i	$-0.203629\pi$
$24$		0			0
$25$	21.9318			0.877274
$26$	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
$31$	19.9948	−	34.6320i	0.644993	−	1.11716i	−0.339310	−	0.940675i	$-0.610194\pi$
$31$	19.9948	−	34.6320i	0.644993	−	1.11716i	0.984303	−	0.176486i	$-0.0564731\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$		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	−0.948879	−	0.315641i	$-0.897780\pi$
$37$	−7.44017	+	12.8868i	−0.201086	+	0.348291i	0.747793	+	0.663932i	$0.231114\pi$
$38$		−	30.6932i		−	0.807715i
$39$		0			0
$40$	4.95432			0.123858
$41$	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
$47$	47.7829	−	27.5875i	1.01666	−	0.586967i	0.103523	−	0.994627i	$-0.466988\pi$
$47$	47.7829	−	27.5875i	1.01666	−	0.586967i	0.913134	+	0.407660i	$0.133655\pi$
$48$		0			0
$49$	37.8142	−	31.1623i	0.771718	−	0.635965i
$50$	−26.8609	+	15.5082i	−0.537218	+	0.310163i
$51$		0			0
$52$	−19.2292			−0.369792
$53$	48.3659	−	27.9241i	0.912565	−	0.526870i	0.0313093	−	0.999510i	$-0.490032\pi$
$53$	48.3659	−	27.9241i	0.912565	−	0.526870i	0.881256	+	0.472640i	$0.156699\pi$
$54$		0			0
$55$	−7.90692			−0.143762
$56$	6.68904	+	18.6348i	0.119447	+	0.332765i
$57$		0			0
$58$	79.9912			1.37916
$59$	10.7583	+	6.21132i	0.182344	+	0.105277i	0.588394	−	0.808575i	$-0.299761\pi$
$59$	10.7583	+	6.21132i	0.182344	+	0.105277i	−0.406049	+	0.913851i	$0.633094\pi$
$60$		0			0
$61$	−39.7638	−	68.8730i	−0.651866	−	1.12906i	−0.982670	−	0.185365i	$-0.940653\pi$
$61$	−39.7638	−	68.8730i	−0.651866	−	1.12906i	0.330804	−	0.943700i	$-0.392680\pi$
$62$			56.5538i			0.912158i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−14.5848	+	8.42054i	−0.224382	+	0.129547i
$66$		0			0
$67$	−0.142238	+	0.246363i	−0.00212295	+	0.00367706i	−0.867085	−	0.498160i	$-0.834009\pi$
$67$	−0.142238	+	0.246363i	−0.00212295	+	0.00367706i	0.864962	+	0.501837i	$0.167342\pi$
$68$		−	1.13434i		−	0.0166815i
$69$		0			0
$70$	13.2337	+	11.2048i	0.189053	+	0.160069i
$71$			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	0.892283	−	0.451477i	$-0.149103\pi$
$73$	4.02599	+	6.97323i	0.0551506	+	0.0955237i	−0.837132	+	0.547001i	$0.815769\pi$
$74$		−	21.0440i		−	0.284378i
$75$		0			0
$76$	21.7033	+	37.5913i	0.285570	+	0.494622i
$77$	−10.6755	−	29.7405i	−0.138643	−	0.386241i
$78$		0			0
$79$	−48.8263	−	84.5697i	−0.618055	−	1.07050i	−0.989840	−	0.142184i	$-0.954588\pi$
$79$	−48.8263	−	84.5697i	−0.618055	−	1.07050i	0.371786	−	0.928319i	$-0.378746\pi$
$80$	−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
$86$		−	4.17153i		−	0.0485062i
$87$		0			0
$88$	12.7677			0.145088
$89$	47.1301	+	27.2106i	0.529552	+	0.305737i	0.740834	−	0.671688i	$-0.234430\pi$
$89$	47.1301	+	27.2106i	0.529552	+	0.305737i	−0.211282	+	0.977425i	$0.567764\pi$
$90$		0			0
$91$	−51.3640	−	43.4893i	−0.564440	−	0.477905i
$92$	−47.5633	−	27.4607i	−0.516992	−	0.298486i
$93$		0			0
$94$	−39.0146	+	67.5752i	−0.415049	+	0.718885i
$95$	32.9227	+	19.0080i	0.346555	+	0.200084i
$96$		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
$101$			194.917i			1.92987i	0.262482	+	0.964937i	$0.415459\pi$
$101$			194.917i			1.92987i	−0.262482	+	0.964937i	$0.584541\pi$
$102$		0			0
$103$	−116.526			−1.13132			−0.565658	−	0.824640i	$-0.691378\pi$
$103$	−116.526			−1.13132			−0.565658	+	0.824640i	$0.691378\pi$
$104$	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	$-0.449012\pi$
$107$	−65.8789	−	38.0352i	−0.615691	−	0.355469i	−0.775189	+	0.631729i	$0.782346\pi$
$108$		0			0
$109$	79.6034	+	137.877i	0.730307	+	1.26493i	0.956752	+	0.290904i	$0.0939561\pi$
$109$	79.6034	+	137.877i	0.730307	+	1.26493i	−0.226446	+	0.974024i	$0.572711\pi$
$110$	9.68395	−	5.59103i	0.0880359	−	0.0508276i
$111$		0			0
$112$	−21.3692	−	18.0930i	−0.190796	−	0.161545i
$113$	−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
$115$	−48.1005			−0.418266
$116$	−97.9689	+	56.5623i	−0.844559	+	0.487606i
$117$		0			0
$118$	−17.5683			−0.148883
$119$	2.56546	−	3.02999i	0.0215585	−	0.0254621i
$120$		0			0
$121$	100.623			0.831597
$122$	97.4011	+	56.2345i	0.798369	+	0.460939i
$123$		0			0
$124$	−39.9896	−	69.2640i	−0.322497	−	0.558580i
$125$		−	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	$0.837977\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$		0			0
$130$	11.9084	−	20.6260i	0.0916034	−	0.158662i
$131$		−	2.42010i		−	0.0184741i	−0.999957	−	0.00923703i	$-0.997060\pi$
$131$		−	2.42010i		−	0.0184741i	0.999957	−	0.00923703i	$-0.00294028\pi$
$132$		0			0
$133$	−27.0447	+	149.497i	−0.203344	+	1.12404i
$134$		−	0.402309i		−	0.00300230i
$135$		0			0
$136$	0.802099	+	1.38928i	0.00589779	+	0.0102153i
$137$			236.830i			1.72869i	0.502901	+	0.864344i	$0.332266\pi$
$137$			236.830i			1.72869i	−0.502901	+	0.864344i	$0.667734\pi$
$138$		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	$0.534222\pi$
$140$	−24.1309	−	4.36541i	−0.172364	−	0.0311815i
$141$		0			0
$142$	−6.31192	−	10.9326i	−0.0444501	−	0.0769899i
$143$	−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
$149$		−	82.5884i		−	0.554284i	−0.960829	−	0.277142i	$-0.910613\pi$
$149$		−	82.5884i		−	0.554284i	0.960829	−	0.277142i	$-0.0893873\pi$
$150$		0			0
$151$	−213.733			−1.41545			−0.707724	−	0.706489i	$-0.750278\pi$
$151$	−213.733			−1.41545			−0.707724	+	0.706489i	$0.750278\pi$
$152$	−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
$157$	−80.8970	+	140.118i	−0.515268	+	0.892470i	0.484575	+	0.874749i	$0.338974\pi$
$157$	−80.8970	+	140.118i	−0.515268	+	0.892470i	−0.999843	+	0.0177201i	$0.994359\pi$
$158$	119.600	+	69.0508i	0.756959	+	0.437031i
$159$		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	−0.936605	−	0.350386i	$-0.886050\pi$
$163$	−26.8721	+	46.5439i	−0.164860	+	0.285545i	0.771746	+	0.635931i	$0.219384\pi$
$164$		−	64.7686i		−	0.394930i
$165$		0			0
$166$	−31.9656			−0.192564
$167$	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
$173$	79.5964	−	45.9550i	0.460095	−	0.265636i	−0.251989	−	0.967730i	$-0.581085\pi$
$173$	79.5964	−	45.9550i	0.460095	−	0.265636i	0.712084	+	0.702094i	$0.247751\pi$
$174$		0			0
$175$	144.496	−	51.8674i	0.825691	−	0.296385i
$176$	−15.6372	+	9.02814i	−0.0888477	+	0.0512962i
$177$		0			0
$178$	−76.9632			−0.432378
$179$	143.122	−	82.6317i	0.799566	−	0.461629i	−0.0437536	−	0.999042i	$-0.513932\pi$
$179$	143.122	−	82.6317i	0.799566	−	0.461629i	0.843319	+	0.537413i	$0.180598\pi$
$180$		0			0
$181$	244.607			1.35142			0.675709	−	0.737169i	$-0.263838\pi$
$181$	244.607			1.35142			0.675709	+	0.737169i	$0.263838\pi$
$182$	93.6594	+	16.9435i	0.514612	+	0.0930960i
$183$		0			0
$184$	77.6705			0.422122
$185$	22.5727	+	13.0323i	0.122014	+	0.0704450i
$186$		0			0
$187$	−1.28012	−	2.21724i	−0.00684557	−	0.0118569i
$188$		−	110.350i		−	0.586967i
$189$		0			0
$190$	−53.7626			−0.282961
$191$	127.255	−	73.4705i	0.666254	−	0.384662i	−0.128402	−	0.991722i	$-0.540985\pi$
$191$	127.255	−	73.4705i	0.666254	−	0.384662i	0.794656	+	0.607060i	$0.207651\pi$
$192$		0			0
$193$	126.891	−	219.782i	0.657466	−	1.13876i	−0.323803	−	0.946124i	$-0.604962\pi$
$193$	126.891	−	219.782i	0.657466	−	1.13876i	0.981269	−	0.192640i	$-0.0617050\pi$
$194$			107.570i			0.554486i
$195$		0			0
$196$	−16.1605	−	96.6584i	−0.0824515	−	0.493155i
$197$			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	0.989358	+	0.145504i	$0.0464803\pi$
$199$	123.517	+	213.938i	0.620689	+	1.07506i	−0.368669	+	0.929561i	$0.620186\pi$
$200$			62.0326i			0.310163i
$201$		0			0
$202$	−137.827	−	238.724i	−0.682313	−	1.18180i
$203$	−389.612	−	70.4829i	−1.91927	−	0.347206i
$204$		0			0
$205$	−28.3624	−	49.1252i	−0.138353	−	0.239635i
$206$	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	$-0.336875\pi$
$212$		−	111.696i		−	0.526870i
$213$		0			0
$214$	107.580			0.502710
$215$	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
$220$	−7.90692	+	13.6952i	−0.0359405	+	0.0622508i
$221$	−4.72253	−	2.72655i	−0.0213689	−	0.0123374i
$222$		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
$227$			23.6118i			0.104017i	0.998647	+	0.0520084i	$0.0165622\pi$
$227$			23.6118i			0.104017i	−0.998647	+	0.0520084i	$0.983438\pi$
$228$		0			0
$229$	38.2246			0.166920			0.0834598	−	0.996511i	$-0.473403\pi$
$229$	38.2246			0.166920			0.0834598	+	0.996511i	$0.473403\pi$
$230$	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	$-0.238071\pi$
$233$	118.984	+	68.6952i	0.510659	+	0.294829i	−0.222445	+	0.974945i	$0.571404\pi$
$234$		0			0
$235$	−48.3226	−	83.6973i	−0.205628	−	0.356159i
$236$	21.5166	−	12.4226i	0.0911721	−	0.0526383i
$237$		0			0
$238$	−0.999503	+	5.52501i	−0.00419959	+	0.0232143i
$239$	−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
$241$	439.498			1.82364			0.911821	−	0.410588i	$-0.134677\pi$
$241$	439.498			1.82364			0.911821	+	0.410588i	$0.134677\pi$
$242$	−123.238	+	71.1513i	−0.509247	+	0.294014i
$243$		0			0
$244$	−159.055			−0.651866
$245$	−54.5844	−	66.2359i	−0.222793	−	0.270351i
$246$		0			0
$247$	208.669			0.844813
$248$	97.9540	+	56.5538i	0.394976	+	0.228039i
$249$		0			0
$250$	58.1288	+	100.682i	0.232515	+	0.402728i
$251$			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
$254$	271.648	−	156.836i	1.06948	−	0.617465i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$			300.339i			1.16863i	0.811526	+	0.584317i	$0.198637\pi$
$257$			300.339i			1.16863i	−0.811526	+	0.584317i	$0.801363\pi$
$258$		0			0
$259$	−18.5425	+	102.499i	−0.0715928	+	0.395748i
$260$			33.6822i			0.129547i
$261$		0			0
$262$	1.71127	+	2.96401i	0.00653157	+	0.0113130i
$263$		−	421.530i		−	1.60278i	−0.598145	−	0.801388i	$-0.704096\pi$
$263$		−	421.530i		−	1.60278i	0.598145	−	0.801388i	$-0.295904\pi$
$264$		0			0
$265$	−48.9123	−	84.7185i	−0.184575	−	0.319693i
$266$	−72.5873	−	202.219i	−0.272885	−	0.760222i
$267$		0			0
$268$	0.284475	+	0.492725i	0.00106147	+	0.00183853i
$269$	445.841	−	257.406i	1.65740	−	0.956901i	0.683492	−	0.729958i	$-0.260460\pi$
$269$	445.841	−	257.406i	1.65740	−	0.956901i	0.973908	−	0.226943i	$-0.0728730\pi$
$270$		0			0
$271$	241.395	−	418.109i	0.890758	−	1.54284i	0.0517888	−	0.998658i	$-0.483508\pi$
$271$	241.395	−	418.109i	0.890758	−	1.54284i	0.838969	−	0.544179i	$-0.183159\pi$
$272$	−1.96473	−	1.13434i	−0.00722329	−	0.00417037i
$273$		0			0
$274$	−167.464	−	290.057i	−0.611184	−	1.05860i
$275$		−	99.0019i		−	0.360007i
$276$		0			0
$277$	149.531			0.539824			0.269912	−	0.962885i	$-0.413005\pi$
$277$	149.531			0.539824			0.269912	+	0.962885i	$0.413005\pi$
$278$	−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
$283$	−274.977	+	476.274i	−0.971650	+	1.68295i	−0.281075	+	0.959686i	$0.590691\pi$
$283$	−274.977	+	476.274i	−0.971650	+	1.68295i	−0.690575	+	0.723261i	$0.742642\pi$
$284$	15.4610	+	8.92640i	0.0544400	+	0.0314310i
$285$		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
$290$		−	140.114i		−	0.483151i
$291$		0			0
$292$	16.1040			0.0551506
$293$	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
$299$	−228.651	+	132.012i	−0.764719	+	0.441510i
$300$		0			0
$301$	−3.67567	+	20.3182i	−0.0122115	+	0.0675025i
$302$	261.768	−	151.132i	0.866781	−	0.500436i
$303$		0			0
$304$	86.8133			0.285570
$305$	−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	$0.365103\pi$
$308$	−62.1876	−	11.2500i	−0.201908	−	0.0365261i
$309$		0			0
$310$	99.0605			0.319550
$311$	−179.199	−	103.461i	−0.576202	−	0.332671i	0.183420	−	0.983035i	$-0.441283\pi$
$311$	−179.199	−	103.461i	−0.576202	−	0.332671i	−0.759623	+	0.650364i	$0.774616\pi$
$312$		0			0
$313$	169.971	+	294.398i	0.543037	+	0.940568i	0.998728	+	0.0504294i	$0.0160590\pi$
$313$	169.971	+	294.398i	0.543037	+	0.940568i	−0.455691	+	0.890138i	$0.650608\pi$
$314$		−	228.811i		−	0.728698i
$315$		0			0
$316$	−195.305			−0.618055
$317$	−237.911	+	137.358i	−0.750507	+	0.433306i	−0.825877	−	0.563850i	$-0.809320\pi$
$317$	−237.911	+	137.358i	−0.750507	+	0.433306i	0.0753699	+	0.997156i	$0.475986\pi$
$318$		0			0
$319$	−127.663	+	221.119i	−0.400198	+	0.693163i
$320$			14.0129i			0.0437904i
$321$		0			0
$322$	207.469	+	175.662i	0.644315	+	0.545534i
$323$			12.3095i			0.0381098i
$324$		0			0
$325$	−105.433	−	182.615i	−0.324409	−	0.561893i
$326$		−	76.0059i		−	0.233147i
$327$		0			0
$328$	45.7983	+	79.3250i	0.139629	+	0.241844i
$329$	249.571	−	294.761i	0.758573	−	0.895930i
$330$		0			0
$331$	98.5084	+	170.622i	0.297609	+	0.515473i	0.975588	−	0.219607i	$-0.0704776\pi$
$331$	98.5084	+	170.622i	0.297609	+	0.515473i	−0.677980	+	0.735081i	$0.737144\pi$
$332$	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	$0.993570\pi$
$338$			108.272i			0.320330i
$339$		0			0
$340$	−1.98693			−0.00584390
$341$	−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
$346$	−64.9902	+	112.566i	−0.187833	+	0.325336i
$347$	−84.4075	−	48.7327i	−0.243249	−	0.140440i	0.373420	−	0.927662i	$-0.378185\pi$
$347$	−84.4075	−	48.7327i	−0.243249	−	0.140440i	−0.616669	+	0.787222i	$0.711518\pi$
$348$		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
$353$			641.700i			1.81785i	0.416962	+	0.908924i	$0.363095\pi$
$353$			641.700i			1.81785i	−0.416962	+	0.908924i	$0.636905\pi$
$354$		0			0
$355$	15.6356			0.0440440
$356$	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	$-0.472817\pi$
$359$	−263.839	−	152.328i	−0.734928	−	0.424311i	−0.820222	+	0.572045i	$0.806150\pi$
$360$		0			0
$361$	−55.0174	−	95.2929i	−0.152403	−	0.263969i
$362$	−299.581	+	172.963i	−0.827571	+	0.477798i
$363$		0			0
$364$	−126.690	+	45.4758i	−0.348049	+	0.124933i
$365$	12.2144	−	7.05200i	0.0334641	−	0.0193205i
$366$		0			0
$367$	125.326			0.341488			0.170744	−	0.985315i	$-0.445383\pi$
$367$	125.326			0.341488			0.170744	+	0.985315i	$0.445383\pi$
$368$	−95.1265	+	54.9213i	−0.258496	+	0.149243i
$369$		0			0
$370$	−36.8610			−0.0996243
$371$	252.616	−	298.357i	0.680905	−	0.804198i
$372$		0			0
$373$	−264.825			−0.709987			−0.354993	−	0.934869i	$-0.615517\pi$
$373$	−264.825			−0.709987			−0.354993	+	0.934869i	$0.615517\pi$
$374$	3.13565	+	1.81037i	0.00838408	+	0.00484055i
$375$		0			0
$376$	78.0291	+	135.150i	0.207524	+	0.359443i
$377$			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	$0.580983\pi$
$380$	65.8455	−	38.0159i	0.173278	−	0.100042i
$381$		0			0
$382$	−103.903	+	179.965i	−0.271997	+	0.471113i
$383$			599.457i			1.56516i	0.622548	+	0.782582i	$0.286098\pi$
$383$			599.457i			1.56516i	−0.622548	+	0.782582i	$0.713902\pi$
$384$		0			0
$385$	−52.0940	+	18.6993i	−0.135309	+	0.0485697i
$386$			358.902i			0.929797i
$387$		0			0
$388$	−76.0637	−	131.746i	−0.196040	−	0.339552i
$389$		−	100.950i		−	0.259512i	−0.991546	−	0.129756i	$-0.958581\pi$
$389$		−	100.950i		−	0.259512i	0.991546	−	0.129756i	$-0.0414193\pi$
$390$		0			0
$391$	−7.78743	−	13.4882i	−0.0199167	−	0.0344967i
$392$	88.1403	+	106.955i	0.224848	+	0.272843i
$393$		0			0
$394$	−224.951	−	389.627i	−0.570942	−	0.988900i
$395$	−148.134	+	85.5250i	−0.375022	+	0.216519i
$396$		0			0
$397$	−154.534	+	267.661i	−0.389255	+	0.674210i	−0.992350	−	0.123460i	$-0.960601\pi$
$397$	−154.534	+	267.661i	−0.389255	+	0.674210i	0.603094	+	0.797670i	$0.293934\pi$
$398$	−302.554	−	174.680i	−0.760185	−	0.438893i
$399$		0			0
$400$	−43.8637	−	75.9741i	−0.109659	−	0.189935i
$401$		−	603.024i		−	1.50380i	−0.659276	−	0.751901i	$-0.729137\pi$
$401$		−	603.024i		−	1.50380i	0.659276	−	0.751901i	$-0.270863\pi$
$402$		0			0
$403$	−384.484			−0.954054
$404$	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
$409$	−219.715	+	380.558i	−0.537201	+	0.930459i	0.461853	+	0.886957i	$0.347185\pi$
$409$	−219.715	+	380.558i	−0.537201	+	0.930459i	−0.999053	+	0.0435023i	$0.986148\pi$
$410$	69.4735	+	40.1105i	0.169447	+	0.0978305i
$411$		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
$416$		−	54.3884i		−	0.130741i
$417$		0			0
$418$	−138.551			−0.331462
$419$	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
$425$	10.7726	−	6.21954i	0.0253472	−	0.0146342i
$426$		0			0
$427$	−424.860	−	359.724i	−0.994989	−	0.842445i
$428$	−131.758	+	76.0704i	−0.307845	+	0.177735i
$429$		0			0
$430$	−7.30692			−0.0169928
$431$	90.4104	−	52.1985i	0.209769	−	0.121110i	−0.391435	−	0.920206i	$-0.628021\pi$
$431$	90.4104	−	52.1985i	0.209769	−	0.121110i	0.601204	+	0.799096i	$0.294688\pi$
$432$		0			0
$433$	426.363			0.984673			0.492337	−	0.870405i	$-0.336143\pi$
$433$	426.363			0.984673			0.492337	+	0.870405i	$0.336143\pi$
$434$	133.746	+	372.599i	0.308171	+	0.858524i
$435$		0			0
$436$	318.414			0.730307
$437$	516.141	+	297.994i	1.18110	+	0.681909i
$438$		0			0
$439$	−142.303	−	246.476i	−0.324153	−	0.561449i	0.657188	−	0.753727i	$-0.271746\pi$
$439$	−142.303	−	246.476i	−0.324153	−	0.561449i	−0.981341	+	0.192278i	$0.938413\pi$
$440$		−	22.3641i		−	0.0508276i
$441$		0			0
$442$	7.71186			0.0174476
$443$	−399.167	+	230.459i	−0.901055	+	0.520224i	−0.877542	−	0.479499i	$-0.840818\pi$
$443$	−399.167	+	230.459i	−0.901055	+	0.520224i	−0.0235125	+	0.999724i	$0.507485\pi$
$444$		0			0
$445$	47.6625	−	82.5539i	0.107107	−	0.185514i
$446$		−	115.813i		−	0.259671i
$447$		0			0
$448$	−52.7072	+	18.9195i	−0.117650	+	0.0422310i
$449$			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
$452$			204.147i			0.451652i
$453$		0			0
$454$	−16.6961	−	28.9184i	−0.0367755	−	0.0636970i
$455$	−76.1766	+	89.9700i	−0.167421	+	0.197736i
$456$		0			0
$457$	79.0457	+	136.911i	0.172967	+	0.299587i	0.939456	−	0.342670i	$-0.111331\pi$
$457$	79.0457	+	136.911i	0.172967	+	0.299587i	−0.766489	+	0.642257i	$0.777998\pi$
$458$	−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	$0.713191\pi$
$464$			226.249i			0.487606i
$465$		0			0
$466$	−194.299			−0.416951
$467$	−222.692	−	128.571i	−0.476856	−	0.275313i	0.242249	−	0.970214i	$-0.422115\pi$
$467$	−222.692	−	128.571i	−0.476856	−	0.275313i	−0.719105	+	0.694901i	$0.755448\pi$
$468$		0			0
$469$	−0.354487	+	1.95952i	−0.000755836	+	0.00417808i
$470$	118.366	+	68.3385i	0.251842	+	0.145401i
$471$		0			0
$472$	−17.5683	+	30.4291i	−0.0372209	+	0.0644684i
$473$	11.5313	+	6.65762i	0.0243791	+	0.0140753i
$474$		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
$479$		−	198.939i		−	0.415322i	−0.978201	−	0.207661i	$-0.933415\pi$
$479$		−	198.939i		−	0.415322i	0.978201	−	0.207661i	$-0.0665851\pi$
$480$		0			0
$481$	143.069			0.297440
$482$	−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	0.523912	−	0.851772i	$-0.324472\pi$
$487$	−231.666	−	401.257i	−0.475700	−	0.823937i	−0.999613	+	0.0278350i	$0.991139\pi$
$488$	194.802	−	112.469i	0.399185	−	0.230469i
$489$		0			0
$490$	113.688	+	42.5251i	0.232016	+	0.0867859i
$491$	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
$493$	−32.0805			−0.0650719
$494$	−255.566	+	147.551i	−0.517340	+	0.298687i
$495$		0			0
$496$	−159.958			−0.322497
$497$	21.1103	+	58.8107i	0.0424755	+	0.118331i
$498$		0			0
$499$	15.1998			0.0304606			0.0152303	−	0.999884i	$-0.495152\pi$
$499$	15.1998			0.0304606			0.0152303	+	0.999884i	$0.495152\pi$
$500$	−142.386	−	82.2066i	−0.284772	−	0.164413i
$501$		0			0
$502$	−80.6818	−	139.745i	−0.160721	−	0.278377i
$503$			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
$506$	151.819	−	87.6525i	0.300037	−	0.173226i
$507$		0			0
$508$	−221.800	+	384.169i	−0.436614	+	0.756237i
$509$		−	200.767i		−	0.394435i	−0.980360	−	0.197217i	$-0.936810\pi$
$509$		−	200.767i		−	0.394435i	0.980360	−	0.197217i	$-0.0631905\pi$
$510$		0			0
$511$	43.0161	+	36.4212i	0.0841802	+	0.0712744i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	−212.372	−	367.838i	−0.413174	−	0.715639i
$515$			204.108i			0.396326i
$516$		0			0
$517$	−124.532	−	215.695i	−0.240874	−	0.417206i
$518$	−49.7677	−	138.646i	−0.0960766	−	0.267657i
$519$		0			0
$520$	−23.8169	−	41.2521i	−0.0458017	−	0.0793309i
$521$	−248.569	+	143.512i	−0.477101	+	0.275454i	−0.719207	−	0.694795i	$-0.755495\pi$
$521$	−248.569	+	143.512i	−0.477101	+	0.275454i	0.242107	+	0.970250i	$0.422162\pi$
$522$		0			0
$523$	−280.624	+	486.054i	−0.536565	+	0.929358i	0.462520	+	0.886609i	$0.346945\pi$
$523$	−280.624	+	486.054i	−0.536565	+	0.929358i	−0.999086	+	0.0427498i	$0.986388\pi$
$524$	−4.19174	−	2.42010i	−0.00799951	−	0.00461852i
$525$		0			0
$526$	298.067	+	516.267i	0.566667	+	0.981495i
$527$		−	22.6809i		−	0.0430377i
$528$		0			0
$529$	−225.088			−0.425498
$530$	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
$535$	−66.6231	+	115.395i	−0.124529	+	0.215691i
$536$	−0.696819	−	0.402309i	−0.00130004	−	0.000750576i
$537$		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	−0.914851	−	0.403791i	$-0.867692\pi$
$541$	−58.2830	+	100.949i	−0.107732	+	0.186597i	0.807119	+	0.590389i	$0.201026\pi$
$542$			682.769i			1.25972i
$543$		0			0
$544$	3.20840			0.00589779
$545$	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
$551$	1063.13	−	613.796i	1.92945	−	1.11397i
$552$		0			0
$553$	−521.689	−	441.708i	−0.943380	−	0.798749i
$554$	−183.138	+	105.735i	−0.330573	+	0.190857i
$555$		0			0
$556$	448.899			0.807373
$557$	772.053	−	445.745i	1.38609	−	0.800260i	0.393219	−	0.919445i	$-0.371361\pi$
$557$	772.053	−	445.745i	1.38609	−	0.800260i	0.992872	+	0.119185i	$0.0380280\pi$
$558$		0			0
$559$	28.3604			0.0507341
$560$	−31.6921	+	37.4306i	−0.0565929	+	0.0668404i
$561$		0			0
$562$	−27.9630			−0.0497562
$563$	−290.660	−	167.813i	−0.516270	−	0.298069i	0.219137	−	0.975694i	$-0.429676\pi$
$563$	−290.660	−	167.813i	−0.516270	−	0.298069i	−0.735407	+	0.677625i	$0.763009\pi$
$564$		0			0
$565$	89.3967	+	154.840i	0.158224	+	0.274052i
$566$		−	777.752i		−	1.37412i
$567$		0			0
$568$	−25.2477			−0.0444501
$569$	−818.812	+	472.741i	−1.43904	+	0.830828i	−0.997783	−	0.0665539i	$-0.978800\pi$
$569$	−818.812	+	472.741i	−1.43904	+	0.830828i	−0.441254	+	0.897382i	$0.645466\pi$
$570$		0			0
$571$	258.155	−	447.138i	0.452111	−	0.783079i	−0.546406	−	0.837520i	$-0.684005\pi$
$571$	258.155	−	447.138i	0.452111	−	0.783079i	0.998517	+	0.0544416i	$0.0173379\pi$
$572$			86.8019i			0.151752i
$573$		0			0
$574$	−57.0697	+	315.468i	−0.0994246	+	0.549595i
$575$		−	602.263i		−	1.04741i
$576$		0			0
$577$	−222.167	−	384.804i	−0.385038	−	0.666905i	0.606737	−	0.794903i	$-0.292478\pi$
$577$	−222.167	−	384.804i	−0.385038	−	0.666905i	−0.991774	+	0.127998i	$0.959145\pi$
$578$		−	408.253i		−	0.706320i
$579$		0			0
$580$	99.0755	+	171.604i	0.170820	+	0.295869i
$581$	155.695	+	28.1660i	0.267977	+	0.0484784i
$582$		0			0
$583$	−126.051	−	218.327i	−0.216211	−	0.374489i
$584$	−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
$590$			30.7728i			0.0521573i
$591$		0			0
$592$	59.5214			0.100543
$593$	−234.426	−	135.346i	−0.395321	−	0.228239i	0.289142	−	0.957286i	$-0.406630\pi$
$593$	−234.426	−	135.346i	−0.395321	−	0.228239i	−0.684463	+	0.729047i	$0.739963\pi$
$594$		0			0
$595$	−5.30738	−	4.49369i	−0.00891996	−	0.00755243i
$596$	−143.047	−	82.5884i	−0.240012	−	0.138571i
$597$		0			0
$598$	186.693	−	323.361i	0.312195	−	0.540738i
$599$	251.273	+	145.073i	0.419488	+	0.242191i	0.694858	−	0.719147i	$-0.255467\pi$
$599$	251.273	+	145.073i	0.419488	+	0.242191i	−0.275370	+	0.961338i	$0.588800\pi$
$600$		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
$605$		−	176.253i		−	0.291328i
$606$		0			0
$607$	−275.607			−0.454048			−0.227024	−	0.973889i	$-0.572900\pi$
$607$	−275.607			−0.454048			−0.227024	+	0.973889i	$0.572900\pi$
$608$	−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	0.890447	−	0.455086i	$-0.150392\pi$
$613$	31.3289	+	54.2633i	0.0511075	+	0.0885209i	−0.839340	+	0.543607i	$0.817058\pi$
$614$	−309.233	+	178.536i	−0.503638	+	0.290775i
$615$		0			0
$616$	84.1189	−	30.1948i	0.136557	−	0.0490176i
$617$	−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
$619$	1078.54			1.74239			0.871194	−	0.490939i	$-0.163346\pi$
$619$	1078.54			1.74239			0.871194	+	0.490939i	$0.163346\pi$
$620$	−121.324	+	70.0464i	−0.195684	+	0.112978i
$621$		0			0
$622$	292.631			0.470467
$623$	374.864	+	67.8148i	0.601708	+	0.108852i
$624$		0			0
$625$	404.302			0.646883
$626$	−416.341	−	240.375i	−0.665082	−	0.383985i
$627$		0			0
$628$	161.794	+	280.235i	0.257634	+	0.446235i
$629$			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	$0.483465\pi$
$632$	239.199	−	138.102i	0.378480	−	0.218515i
$633$		0			0
$634$	194.253	−	336.457i	0.306393	−	0.530689i
$635$			388.508i			0.611824i
$636$		0			0
$637$	−441.256	−	165.053i	−0.692710	−	0.259109i
$638$		−	361.086i		−	0.565966i
$639$		0			0
$640$	−9.90864	−	17.1623i	−0.0154822	−	0.0268160i
$641$		−	791.031i		−	1.23406i	−0.786940	−	0.617029i	$-0.788336\pi$
$641$		−	791.031i		−	1.23406i	0.786940	−	0.617029i	$-0.211664\pi$
$642$		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	$-0.389523\pi$
$644$	−378.309	−	68.4380i	−0.587436	−	0.106270i
$645$		0			0
$646$	−8.70411	−	15.0760i	−0.0134739	−	0.0233374i
$647$	54.8043	−	31.6413i	0.0847053	−	0.0489046i	−0.457049	−	0.889441i	$-0.651094\pi$
$647$	54.8043	−	31.6413i	0.0847053	−	0.0489046i	0.541754	+	0.840537i	$0.317760\pi$
$648$		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
$653$			651.734i			0.998062i	0.866584	+	0.499031i	$0.166311\pi$
$653$			651.734i			0.998062i	−0.866584	+	0.499031i	$0.833689\pi$
$654$		0			0
$655$	−4.23909			−0.00647189
$656$	−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
$661$	243.282	−	421.376i	0.368051	−	0.637483i	−0.621210	−	0.783644i	$-0.713358\pi$
$661$	243.282	−	421.376i	0.368051	−	0.637483i	0.989261	+	0.146161i	$0.0466918\pi$
$662$	−241.295	−	139.312i	−0.364495	−	0.210441i
$663$		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
$668$		−	94.9178i		−	0.142093i
$669$		0			0
$670$	−0.704690			−0.00105178
$671$	−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
$677$	513.950	−	296.729i	0.759158	−	0.438300i	−0.0698351	−	0.997559i	$-0.522247\pi$
$677$	513.950	−	296.729i	0.759158	−	0.438300i	0.828994	+	0.559258i	$0.188914\pi$
$678$		0			0
$679$	94.7837	−	523.942i	0.139593	−	0.771637i
$680$	2.43348	−	1.40497i	0.00357865	−	0.00206613i
$681$		0			0
$682$	255.288			0.374322
$683$	−763.359	+	440.725i	−1.11766	+	0.645279i	−0.940801	−	0.338958i	$-0.889925\pi$
$683$	−763.359	+	440.725i	−1.11766	+	0.645279i	−0.176854	+	0.984237i	$0.556592\pi$
$684$		0			0
$685$	414.836			0.605600
$686$	−6.45604	+	485.032i	−0.00941113	+	0.707044i
$687$		0			0
$688$	11.7989			0.0171495
$689$	−465.019	−	268.479i	−0.674919	−	0.389665i
$690$		0			0
$691$	−438.204	−	758.992i	−0.634159	−	1.09840i	−0.986693	−	0.162597i	$-0.948013\pi$
$691$	−438.204	−	758.992i	−0.634159	−	1.09840i	0.352533	−	0.935799i	$-0.385320\pi$
$692$		−	183.820i		−	0.265636i
$693$		0			0
$694$	137.837			0.198612
$695$	340.478	−	196.575i	0.489896	−	0.282841i
$696$		0			0
$697$	9.18370	−	15.9066i	0.0131760	−	0.0228216i
$698$		−	302.124i		−	0.432842i
$699$		0			0
$700$	54.6589	−	302.142i	0.0780842	−	0.431631i
$701$			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
$704$			36.1126i			0.0512962i
$705$		0			0
$706$	−453.751	−	785.919i	−0.642706	−	1.11320i
$707$	460.967	+	1284.19i	0.652004	+	1.81640i
$708$		0			0
$709$	−328.602	−	569.156i	−0.463473	−	0.802758i	0.535659	−	0.844435i	$-0.320063\pi$
$709$	−328.602	−	569.156i	−0.463473	−	0.802758i	−0.999131	+	0.0416765i	$0.986730\pi$
$710$	−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
$716$		−	330.527i		−	0.461629i
$717$		0			0
$718$	430.848			0.600066
$719$	404.412	+	233.488i	0.562465	+	0.324739i	0.754134	−	0.656720i	$-0.228057\pi$
$719$	404.412	+	233.488i	0.562465	+	0.324739i	−0.191669	+	0.981460i	$0.561390\pi$
$720$		0			0
$721$	−767.717	+	275.575i	−1.06480	+	0.382212i
$722$	134.765	+	77.8064i	0.186655	+	0.107765i
$723$		0			0
$724$	244.607	−	423.671i	0.337854	−	0.585181i
$725$	−1074.32	−	620.258i	−1.48182	−	0.855529i
$726$		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
$731$			1.67299i			0.00228863i
$732$		0			0
$733$	1118.07			1.52533			0.762665	−	0.646794i	$-0.223891\pi$
$733$	1118.07			1.52533			0.762665	+	0.646794i	$0.223891\pi$
$734$	−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	0.997404	+	0.0720041i	$0.0229395\pi$
$739$	414.623	+	718.148i	0.561060	+	0.971784i	−0.436345	+	0.899780i	$0.643727\pi$
$740$	45.1453	−	26.0647i	0.0610072	−	0.0352225i
$741$		0			0
$742$	−98.4193	+	544.038i	−0.132641	+	0.733205i
$743$	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
$745$	−144.663			−0.194179
$746$	324.343	−	187.260i	0.434776	−	0.251018i
$747$		0			0
$748$	−5.12049			−0.00684557
$749$	−523.988	−	94.7921i	−0.699583	−	0.126558i
$750$		0			0
$751$	1217.73			1.62147			0.810737	−	0.585411i	$-0.199067\pi$
$751$	1217.73			1.62147			0.810737	+	0.585411i	$0.199067\pi$
$752$	−191.132	−	110.350i	−0.254164	−	0.146742i
$753$		0			0
$754$	−384.542	−	666.046i	−0.510002	−	0.883350i
$755$			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	$0.455256\pi$
$758$	233.648	−	134.897i	0.308243	−	0.177964i
$759$		0			0
$760$	−53.7626	+	93.1196i	−0.0707403	+	0.122526i
$761$		−	1021.32i		−	1.34208i	−0.741423	−	0.671038i	$-0.765849\pi$
$761$		−	1021.32i		−	1.34208i	0.741423	−	0.671038i	$-0.234151\pi$
$762$		0			0
$763$	850.530	+	720.134i	1.11472	+	0.943819i
$764$		−	293.882i		−	0.384662i
$765$		0			0
$766$	−423.880	−	734.182i	−0.553369	−	0.958463i
$767$		−	119.439i		−	0.155722i
$768$		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	$0.841257\pi$
$770$	50.5794	−	59.7379i	0.0656875	−	0.0775817i
$771$		0			0
$772$	−253.782	−	439.563i	−0.328733	−	0.569382i
$773$	329.696	−	190.350i	0.426515	−	0.246249i	−0.271346	−	0.962482i	$-0.587469\pi$
$773$	329.696	−	190.350i	0.426515	−	0.246249i	0.697861	+	0.716233i	$0.254135\pi$
$774$		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
$779$			702.847i			0.902243i
$780$		0			0
$781$	40.2944			0.0515933
$782$	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
$787$	−427.833	+	741.028i	−0.543625	+	0.941586i	0.455067	+	0.890457i	$0.349615\pi$
$787$	−427.833	+	741.028i	−0.543625	+	0.941586i	−0.998692	+	0.0511290i	$0.983718\pi$
$788$	551.015	+	318.129i	0.699258	+	0.403717i
$789$		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
$794$		−	437.089i		−	0.550490i
$795$		0			0
$796$	494.068			0.620689
$797$	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
$803$	31.4776	−	18.1736i	0.0392000	−	0.0226322i
$804$		0			0
$805$	−316.906	+	113.755i	−0.393672	+	0.141310i
$806$	470.894	−	271.871i	0.584236	−	0.337309i
$807$		0			0
$808$	−551.309			−0.682313
$809$	366.440	−	211.564i	0.452955	−	0.261514i	−0.256123	−	0.966644i	$-0.582445\pi$
$809$	366.440	−	211.564i	0.452955	−	0.261514i	0.709077	+	0.705131i	$0.249112\pi$
$810$		0			0
$811$	695.569			0.857668			0.428834	−	0.903383i	$-0.358925\pi$
$811$	695.569			0.857668			0.428834	+	0.903383i	$0.358925\pi$
$812$	−511.692	+	604.346i	−0.630163	+	0.744268i
$813$		0			0
$814$	−94.9940			−0.116700
$815$	81.5270	+	47.0697i	0.100033	+	0.0577542i
$816$		0			0
$817$	−32.0094	−	55.4419i	−0.0391792	−	0.0678603i
$818$		−	621.448i		−	0.759717i
$819$		0			0
$820$	−113.450			−0.138353
$821$	−79.1142	+	45.6766i	−0.0963632	+	0.0556353i	−0.547407	−	0.836866i	$-0.684385\pi$
$821$	−79.1142	+	45.6766i	−0.0963632	+	0.0556353i	0.451044	+	0.892502i	$0.351052\pi$
$822$		0			0
$823$	328.999	−	569.843i	0.399755	−	0.692397i	−0.593940	−	0.804509i	$-0.702428\pi$
$823$	328.999	−	569.843i	0.399755	−	0.692397i	0.993696	+	0.112113i	$0.0357617\pi$
$824$		−	329.584i		−	0.399980i
$825$		0			0
$826$	−115.747	+	41.5478i	−0.140129	+	0.0503000i
$827$		−	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	0.530160	−	0.847898i	$-0.322132\pi$
$829$	−388.984	−	673.740i	−0.469221	−	0.812715i	−0.999381	+	0.0351831i	$0.988799\pi$
$830$			55.9915i			0.0674597i
$831$		0			0
$832$	38.4584	+	66.6119i	0.0462240	+	0.0800624i
$833$	9.73654	−	26.0299i	0.0116885	−	0.0312484i
$834$		0			0
$835$	−41.5649	−	71.9925i	−0.0497783	−	0.0862186i
$836$	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
$842$			463.049i			0.549940i
$843$		0			0
$844$	−430.106			−0.509605
$845$	−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
$850$	−8.79576	+	15.2347i	−0.0103479	+	0.0179232i
$851$	353.879	+	204.312i	0.415839	+	0.240085i
$852$		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
$857$		−	1327.16i		−	1.54861i	−0.632814	−	0.774304i	$-0.718100\pi$
$857$		−	1327.16i		−	1.54861i	0.632814	−	0.774304i	$-0.281900\pi$
$858$		0			0
$859$	362.201			0.421654			0.210827	−	0.977523i	$-0.432384\pi$
$859$	362.201			0.421654			0.210827	+	0.977523i	$0.432384\pi$
$860$	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	$-0.117390\pi$
$863$	938.041	+	541.578i	1.08695	+	0.627553i	0.154190	+	0.988041i	$0.450723\pi$
$864$		0			0
$865$	−80.4956	−	139.422i	−0.0930584	−	0.161182i
$866$	−522.186	+	301.484i	−0.602987	+	0.348134i
$867$		0			0
$868$	−427.272	−	361.766i	−0.492249	−	0.416782i
$869$	−381.753	+	220.405i	−0.439302	+	0.253631i
$870$		0			0
$871$	2.73511			0.00314020
$872$	−389.975	+	225.152i	−0.447220	+	0.258202i
$873$		0			0
$874$	−842.854			−0.964364
$875$	−194.413	−	541.610i	−0.222186	−	0.618983i
$876$		0			0
$877$	−1141.56			−1.30166			−0.650830	−	0.759223i	$-0.725579\pi$
$877$	−1141.56			−1.30166			−0.650830	+	0.759223i	$0.725579\pi$
$878$	348.570	+	201.247i	0.397004	+	0.229211i
$879$		0			0
$880$	15.8138	+	27.3904i	0.0179703	+	0.0311254i
$881$			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	$0.575315\pi$
$884$	−9.44506	+	5.45311i	−0.0106845	+	0.00616868i
$885$		0			0
$886$	325.919	−	564.508i	0.367854	−	0.637142i
$887$			115.461i			0.130171i	0.997880	+	0.0650853i	$0.0207320\pi$
$887$			115.461i			0.130171i	−0.997880	+	0.0650853i	$0.979268\pi$
$888$		0			0
$889$	−1461.31	+	524.542i	−1.64377	+	0.590036i
$890$			134.810i			0.151472i
$891$		0			0
$892$	81.8923	+	141.842i	0.0918076	+	0.159015i
$893$			1197.48i			1.34096i
$894$		0			0
$895$	−144.739	−	250.695i	−0.161719	−	0.280106i
$896$	51.1748	−	60.4412i	0.0571148	−	0.0674567i
$897$		0			0
$898$	−130.429	−	225.909i	−0.145244	−	0.251570i
$899$	−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
$905$		−	428.457i		−	0.473433i
$906$		0			0
$907$	−182.571			−0.201291			−0.100646	−	0.994922i	$-0.532091\pi$
$907$	−182.571			−0.201291			−0.100646	+	0.994922i	$0.532091\pi$
$908$	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
$913$	51.0160	−	88.3624i	0.0558774	−	0.0967824i
$914$	−193.622	−	111.788i	−0.211840	−	0.122306i
$915$		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	0.341785	+	0.939778i	$0.388969\pi$
$919$	−590.898	+	1023.47i	−0.642979	+	1.11367i	−0.984764	+	0.173895i	$0.944365\pi$
$920$		−	136.049i		−	0.147879i
$921$		0			0
$922$	−491.719			−0.533318
$923$	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
$929$	−760.239	+	438.924i	−0.818341	+	0.472469i	−0.849844	−	0.527034i	$-0.823304\pi$
$929$	−760.239	+	438.924i	−0.818341	+	0.472469i	0.0315030	+	0.999504i	$0.489971\pi$
$930$		0			0
$931$	175.368	+	1048.90i	0.188366	+	1.12664i
$932$	237.967	−	137.390i	0.255330	−	0.147415i
$933$		0			0
$934$	363.654			0.389351
$935$	−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	$0.606995\pi$
$938$	−0.951433	−	2.65057i	−0.00101432	−	0.00282577i
$939$		0			0
$940$	−193.291			−0.205628
$941$	−831.225	−	479.908i	−0.883342	−	0.509998i	−0.0115830	−	0.999933i	$-0.503687\pi$
$941$	−831.225	−	479.908i	−0.883342	−	0.509998i	−0.871759	+	0.489935i	$0.837020\pi$
$942$		0			0
$943$	−444.647	−	770.151i	−0.471524	−	0.816704i
$944$		−	49.6905i		−	0.0526383i
$945$		0			0
$946$	−18.8306			−0.0199055
$947$	−646.600	+	373.315i	−0.682788	+	0.394208i	−0.800905	−	0.598792i	$-0.795648\pi$
$947$	−646.600	+	373.315i	−0.682788	+	0.394208i	0.118117	+	0.993000i	$0.462314\pi$
$948$		0			0
$949$	38.7083	−	67.0448i	0.0407885	−	0.0706478i
$950$		−	673.157i		−	0.708587i
$951$		0			0
$952$	8.57010	+	7.25620i	0.00900221	+	0.00762206i
$953$			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
$956$			803.760i			0.840753i
$957$		0			0
$958$	140.671	+	243.650i	0.146839	+	0.254332i
$959$	560.088	+	1560.33i	0.584033	+	1.62704i
$960$		0			0
$961$	−319.083	−	552.668i	−0.332032	−	0.575097i
$962$	−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	$0.806633\pi$
$968$			284.605i			0.294014i
$969$		0			0
$970$	188.422			0.194249
$971$	−1063.88	−	614.232i	−1.09565	−	0.632577i	−0.160579	−	0.987023i	$-0.551336\pi$
$971$	−1063.88	−	614.232i	−1.09565	−	0.632577i	−0.935076	+	0.354446i	$0.884669\pi$
$972$		0			0
$973$	1199.08	+	1015.24i	1.23235	+	1.04342i
$974$	567.464	+	327.625i	0.582612	+	0.336371i
$975$		0			0
$976$	−159.055	+	275.492i	−0.162966	+	0.282266i
$977$	902.636	+	521.137i	0.923885	+	0.533405i	0.884872	−	0.465833i	$-0.154245\pi$
$977$	902.636	+	521.137i	0.923885	+	0.533405i	0.0390127	+	0.999239i	$0.487579\pi$
$978$		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
$983$		−	784.219i		−	0.797782i	−0.916998	−	0.398891i	$-0.869395\pi$
$983$		−	784.219i		−	0.797782i	0.916998	−	0.398891i	$-0.130605\pi$
$984$		0			0
$985$	557.240			0.565726
$986$	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	0.821944	−	0.569569i	$-0.192890\pi$
$991$	−81.5488	−	141.247i	−0.0822894	−	0.142529i	−0.904233	+	0.427040i	$0.859557\pi$
$992$	195.908	−	113.108i	0.197488	−	0.114020i
$993$		0			0
$994$	−67.4402	−	57.1009i	−0.0678473	−	0.0574455i
$995$	374.737	−	216.354i	0.376620	−	0.217442i
$996$		0			0
$997$	−226.432			−0.227113			−0.113557	−	0.993532i	$-0.536224\pi$
$997$	−226.432			−0.227113			−0.113557	+	0.993532i	$0.536224\pi$
$998$	−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.i.a.359.4		32
3.2	odd	2		126.3.i.a.65.12	✓	32
7.4	even	3		378.3.r.a.305.5		32
9.4	even	3		126.3.r.a.23.1	yes	32
9.5	odd	6		378.3.r.a.233.13		32
21.11	odd	6		126.3.r.a.11.9	yes	32
63.4	even	3		126.3.i.a.95.12	yes	32
63.32	odd	6	inner	378.3.i.a.179.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.i.a.65.12	✓	32	3.2	odd	2
126.3.i.a.95.12	yes	32	63.4	even	3
126.3.r.a.11.9	yes	32	21.11	odd	6
126.3.r.a.23.1	yes	32	9.4	even	3
378.3.i.a.179.5		32	63.32	odd	6	inner
378.3.i.a.359.4		32	1.1	even	1	trivial
378.3.r.a.233.13		32	9.5	odd	6
378.3.r.a.305.5		32	7.4	even	3

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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} -1.75162i q^{5} +(6.58841 - 2.36493i) q^{7} +2.82843i q^{8} +(1.23858 + 2.14528i) q^{10} -4.51407i q^{11} +(-4.80730 - 8.32649i) q^{13} +(-6.39685 + 7.55515i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(0.491183 - 0.283585i) q^{17} +(-10.8517 + 18.7956i) q^{19} +(-3.03389 - 1.75162i) q^{20} +(3.19193 + 5.52858i) q^{22} -27.4607i q^{23} +21.9318 q^{25} +(11.7754 + 6.79855i) q^{26} +(2.49222 - 13.7764i) q^{28} +(-48.9844 - 28.2812i) q^{29} +(19.9948 - 34.6320i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-0.401050 + 0.694638i) q^{34} +(-4.14246 - 11.5404i) q^{35} +(-7.44017 + 12.8868i) q^{37} -30.6932i q^{38} +4.95432 q^{40} +(28.0456 - 16.1921i) q^{41} +(-1.47486 + 2.55453i) q^{43} +(-7.81860 - 4.51407i) q^{44} +(19.4176 + 33.6323i) q^{46} +(47.7829 - 27.5875i) q^{47} +(37.8142 - 31.1623i) q^{49} +(-26.8609 + 15.5082i) q^{50} -19.2292 q^{52} +(48.3659 - 27.9241i) q^{53} -7.90692 q^{55} +(6.68904 + 18.6348i) q^{56} +79.9912 q^{58} +(10.7583 + 6.21132i) q^{59} +(-39.7638 - 68.8730i) q^{61} +56.5538i q^{62} -8.00000 q^{64} +(-14.5848 + 8.42054i) q^{65} +(-0.142238 + 0.246363i) q^{67} -1.13434i q^{68} +(13.2337 + 11.2048i) q^{70} +8.92640i q^{71} +(4.02599 + 6.97323i) q^{73} -21.0440i q^{74} +(21.7033 + 37.5913i) q^{76} +(-10.6755 - 29.7405i) q^{77} +(-48.8263 - 84.5697i) q^{79} +(-6.06778 + 3.50323i) q^{80} +(-22.8992 + 39.6625i) q^{82} +(19.5749 + 11.3016i) q^{83} +(-0.496732 - 0.860365i) q^{85} -4.17153i q^{86} +12.7677 q^{88} +(47.1301 + 27.2106i) q^{89} +(-51.3640 - 43.4893i) q^{91} +(-47.5633 - 27.4607i) q^{92} +(-39.0146 + 67.5752i) q^{94} +(32.9227 + 19.0080i) q^{95} +(38.0319 - 65.8731i) q^{97} +(-24.2776 + 64.9045i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 2 q^{7} + 10 q^{13} - 36 q^{14} - 64 q^{16} - 54 q^{17} + 28 q^{19} - 160 q^{25} - 72 q^{26} - 4 q^{28} - 36 q^{29} - 8 q^{31} - 90 q^{35} + 22 q^{37} - 72 q^{41} + 16 q^{43} + 72 q^{44}+ \cdots + 288 q^{98}+O(q^{100}) \) 32 * q + 32 * q^4 + 2 * q^7 + 10 * q^13 - 36 * q^14 - 64 * q^16 - 54 * q^17 + 28 * q^19 - 160 * q^25 - 72 * q^26 - 4 * q^28 - 36 * q^29 - 8 * q^31 - 90 * q^35 + 22 * q^37 - 72 * q^41 + 16 * q^43 + 72 * q^44 - 12 * q^46 + 108 * q^47 + 74 * q^49 + 288 * q^50 + 40 * q^52 - 72 * q^53 - 24 * q^55 + 48 * q^58 + 90 * q^59 - 62 * q^61 - 256 * q^64 - 378 * q^65 + 70 * q^67 - 108 * q^70 + 196 * q^73 - 56 * q^76 - 630 * q^77 - 38 * q^79 + 60 * q^85 - 486 * q^89 - 122 * q^91 - 252 * q^92 + 168 * q^94 + 72 * q^95 - 38 * q^97 + 288 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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