LMFDB - Embedded newform 405.3.i.c.26.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(26,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.26"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-2,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.12960000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 $ x^8 - 3x^6 + 8x^4 - 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.2
Root			$0.535233 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	405.26
Dual form			405.3.i.c.296.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.330792 - 0.190983i) q^{2} +(-1.92705 - 3.33775i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-1.85410 + 3.21140i) q^{7} +3.00000i q^{8} +0.854102 q^{10} +(7.08438 + 4.09017i) q^{11} +(-3.85410 - 6.67550i) q^{13} +(1.22665 - 0.708204i) q^{14} +(-7.13525 + 12.3586i) q^{16} +11.9443i q^{17} +5.58359 q^{19} +(7.46344 + 4.30902i) q^{20} +(-1.56231 - 2.70599i) q^{22} +(24.6093 - 14.2082i) q^{23} +(2.50000 - 4.33013i) q^{25} +2.94427i q^{26} +14.2918 q^{28} +(48.5571 + 28.0344i) q^{29} +(15.6246 + 27.0626i) q^{31} +(15.1129 - 8.72542i) q^{32} +(2.28115 - 3.95107i) q^{34} -8.29180i q^{35} -53.4164 q^{37} +(-1.84701 - 1.06637i) q^{38} +(-3.35410 - 5.80948i) q^{40} +(52.6231 - 30.3820i) q^{41} +(35.6869 - 61.8116i) q^{43} -31.5279i q^{44} -10.8541 q^{46} +(39.9565 + 23.0689i) q^{47} +(17.6246 + 30.5267i) q^{49} +(-1.65396 + 0.954915i) q^{50} +(-14.8541 + 25.7281i) q^{52} +73.3607i q^{53} -18.2918 q^{55} +(-9.63420 - 5.56231i) q^{56} +(-10.7082 - 18.5472i) q^{58} +(-78.6039 + 45.3820i) q^{59} +(-9.50000 + 16.4545i) q^{61} -11.9361i q^{62} +50.4164 q^{64} +(14.9269 + 8.61803i) q^{65} +(-0.167184 - 0.289572i) q^{67} +(39.8670 - 23.0172i) q^{68} +(-1.58359 + 2.74286i) q^{70} +81.2624i q^{71} +50.7902 q^{73} +(17.6697 + 10.2016i) q^{74} +(-10.7599 - 18.6366i) q^{76} +(-26.2703 + 15.1672i) q^{77} +(24.0836 - 41.7140i) q^{79} -31.9098i q^{80} -23.2098 q^{82} +(-54.2700 - 31.3328i) q^{83} +(-13.3541 - 23.1300i) q^{85} +(-23.6099 + 13.6312i) q^{86} +(-12.2705 + 21.2531i) q^{88} -69.7082i q^{89} +28.5836 q^{91} +(-94.8469 - 54.7599i) q^{92} +(-8.81153 - 15.2620i) q^{94} +(-10.8126 + 6.24265i) q^{95} +(-79.7082 + 138.059i) q^{97} -13.4640i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} + 12 q^{7} - 20 q^{10} - 4 q^{13} + 10 q^{16} + 152 q^{19} + 68 q^{22} + 20 q^{25} + 168 q^{28} - 36 q^{31} - 22 q^{34} - 320 q^{37} + 44 q^{43} - 60 q^{46} - 20 q^{49} - 92 q^{52} - 200 q^{55}+ \cdots - 584 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 + 12 * q^7 - 20 * q^10 - 4 * q^13 + 10 * q^16 + 152 * q^19 + 68 * q^22 + 20 * q^25 + 168 * q^28 - 36 * q^31 - 22 * q^34 - 320 * q^37 + 44 * q^43 - 60 * q^46 - 20 * q^49 - 92 * q^52 - 200 * q^55 - 32 * q^58 - 76 * q^61 + 296 * q^64 - 216 * q^67 - 120 * q^70 - 184 * q^73 + 142 * q^76 + 300 * q^79 - 776 * q^82 - 80 * q^85 + 36 * q^88 + 336 * q^91 + 332 * q^94 - 584 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.330792	−	0.190983i	−0.165396	−	0.0954915i	0.415017	−	0.909814i	$-0.363776\pi$
$2$	−0.330792	−	0.190983i	−0.165396	−	0.0954915i	−0.580413	+	0.814322i	$0.697109\pi$
$3$		0			0
$3$		0			0
$4$	−1.92705	−	3.33775i	−0.481763	−	0.834438i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		0			0
$7$	−1.85410	+	3.21140i	−0.264872	+	0.458771i	−0.967530	−	0.252756i	$-0.918663\pi$
$7$	−1.85410	+	3.21140i	−0.264872	+	0.458771i	0.702658	+	0.711527i	$0.251996\pi$
$8$			3.00000i			0.375000i
$9$		0			0
$10$	0.854102			0.0854102
$11$	7.08438	+	4.09017i	0.644035	+	0.371834i	0.786167	−	0.618014i	$-0.212063\pi$
$11$	7.08438	+	4.09017i	0.644035	+	0.371834i	−0.142132	+	0.989848i	$0.545396\pi$
$12$		0			0
$13$	−3.85410	−	6.67550i	−0.296469	−	0.513500i	0.678856	−	0.734271i	$-0.262476\pi$
$13$	−3.85410	−	6.67550i	−0.296469	−	0.513500i	−0.975326	+	0.220771i	$0.929143\pi$
$14$	1.22665	−	0.708204i	0.0876175	−	0.0505860i
$15$		0			0
$16$	−7.13525	+	12.3586i	−0.445953	+	0.772414i
$17$			11.9443i			0.702604i	0.936262	+	0.351302i	$0.114261\pi$
$17$			11.9443i			0.702604i	−0.936262	+	0.351302i	$0.885739\pi$
$18$		0			0
$19$	5.58359			0.293873			0.146937	−	0.989146i	$-0.453059\pi$
$19$	5.58359			0.293873			0.146937	+	0.989146i	$0.453059\pi$
$20$	7.46344	+	4.30902i	0.373172	+	0.215451i
$21$		0			0
$22$	−1.56231	−	2.70599i	−0.0710139	−	0.123000i
$23$	24.6093	−	14.2082i	1.06997	−	0.617748i	0.141797	−	0.989896i	$-0.454712\pi$
$23$	24.6093	−	14.2082i	1.06997	−	0.617748i	0.928174	+	0.372148i	$0.121379\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$			2.94427i			0.113241i
$27$		0			0
$28$	14.2918			0.510421
$29$	48.5571	+	28.0344i	1.67438	+	0.966705i	0.965138	+	0.261742i	$0.0842969\pi$
$29$	48.5571	+	28.0344i	1.67438	+	0.966705i	0.709244	+	0.704963i	$0.249036\pi$
$30$		0			0
$31$	15.6246	+	27.0626i	0.504020	+	0.872988i	0.999989	+	0.00464783i	$0.00147945\pi$
$31$	15.6246	+	27.0626i	0.504020	+	0.872988i	−0.495969	+	0.868340i	$0.665187\pi$
$32$	15.1129	−	8.72542i	0.472277	−	0.272670i
$33$		0			0
$34$	2.28115	−	3.95107i	0.0670927	−	0.116208i
$35$		−	8.29180i		−	0.236908i
$36$		0			0
$37$	−53.4164			−1.44369			−0.721843	−	0.692056i	$-0.756705\pi$
$37$	−53.4164			−1.44369			−0.721843	+	0.692056i	$0.756705\pi$
$38$	−1.84701	−	1.06637i	−0.0486055	−	0.0280624i
$39$		0			0
$40$	−3.35410	−	5.80948i	−0.0838525	−	0.145237i
$41$	52.6231	−	30.3820i	1.28349	−	0.741024i	0.306006	−	0.952030i	$-0.401007\pi$
$41$	52.6231	−	30.3820i	1.28349	−	0.741024i	0.977485	+	0.211006i	$0.0676740\pi$
$42$		0			0
$43$	35.6869	−	61.8116i	0.829928	−	1.43748i	−0.0681655	−	0.997674i	$-0.521715\pi$
$43$	35.6869	−	61.8116i	0.829928	−	1.43748i	0.898094	−	0.439804i	$-0.144952\pi$
$44$		−	31.5279i		−	0.716542i
$45$		0			0
$46$	−10.8541			−0.235959
$47$	39.9565	+	23.0689i	0.850138	+	0.490827i	0.860697	−	0.509117i	$-0.170028\pi$
$47$	39.9565	+	23.0689i	0.850138	+	0.490827i	−0.0105595	+	0.999944i	$0.503361\pi$
$48$		0			0
$49$	17.6246	+	30.5267i	0.359686	+	0.622994i
$50$	−1.65396	+	0.954915i	−0.0330792	+	0.0190983i
$51$		0			0
$52$	−14.8541	+	25.7281i	−0.285656	+	0.494770i
$53$			73.3607i			1.38416i	0.721819	+	0.692082i	$0.243306\pi$
$53$			73.3607i			1.38416i	−0.721819	+	0.692082i	$0.756694\pi$
$54$		0			0
$55$	−18.2918			−0.332578
$56$	−9.63420	−	5.56231i	−0.172039	−	0.0993269i
$57$		0			0
$58$	−10.7082	−	18.5472i	−0.184624	−	0.319779i
$59$	−78.6039	+	45.3820i	−1.33227	+	0.769186i	−0.985647	−	0.168819i	$-0.946005\pi$
$59$	−78.6039	+	45.3820i	−1.33227	+	0.769186i	−0.346622	+	0.938005i	$0.612671\pi$
$60$		0			0
$61$	−9.50000	+	16.4545i	−0.155738	+	0.269746i	−0.933327	−	0.359026i	$-0.883109\pi$
$61$	−9.50000	+	16.4545i	−0.155738	+	0.269746i	0.777590	+	0.628772i	$0.216442\pi$
$62$		−	11.9361i		−	0.192518i
$63$		0			0
$64$	50.4164			0.787756
$65$	14.9269	+	8.61803i	0.229644	+	0.132585i
$66$		0			0
$67$	−0.167184	−	0.289572i	−0.00249529	−	0.00432196i	0.864775	−	0.502159i	$-0.167461\pi$
$67$	−0.167184	−	0.289572i	−0.00249529	−	0.00432196i	−0.867270	+	0.497837i	$0.834128\pi$
$68$	39.8670	−	23.0172i	0.586279	−	0.338489i
$69$		0			0
$70$	−1.58359	+	2.74286i	−0.0226227	+	0.0391837i
$71$			81.2624i			1.14454i	0.820065	+	0.572270i	$0.193937\pi$
$71$			81.2624i			1.14454i	−0.820065	+	0.572270i	$0.806063\pi$
$72$		0			0
$73$	50.7902			0.695757			0.347878	−	0.937540i	$-0.386902\pi$
$73$	50.7902			0.695757			0.347878	+	0.937540i	$0.386902\pi$
$74$	17.6697	+	10.2016i	0.238780	+	0.137860i
$75$		0			0
$76$	−10.7599	−	18.6366i	−0.141577	−	0.245219i
$77$	−26.2703	+	15.1672i	−0.341173	+	0.196976i
$78$		0			0
$79$	24.0836	−	41.7140i	0.304856	−	0.528025i	−0.672374	−	0.740212i	$-0.734725\pi$
$79$	24.0836	−	41.7140i	0.304856	−	0.528025i	0.977229	+	0.212187i	$0.0680585\pi$
$80$		−	31.9098i		−	0.398873i
$81$		0			0
$82$	−23.2098			−0.283046
$83$	−54.2700	−	31.3328i	−0.653856	−	0.377504i	0.136076	−	0.990698i	$-0.456551\pi$
$83$	−54.2700	−	31.3328i	−0.653856	−	0.377504i	−0.789932	+	0.613195i	$0.789884\pi$
$84$		0			0
$85$	−13.3541	−	23.1300i	−0.157107	−	0.272117i
$86$	−23.6099	+	13.6312i	−0.274534	+	0.158502i
$87$		0			0
$88$	−12.2705	+	21.2531i	−0.139438	+	0.241513i
$89$		−	69.7082i		−	0.783238i	−0.920127	−	0.391619i	$-0.871915\pi$
$89$		−	69.7082i		−	0.783238i	0.920127	−	0.391619i	$-0.128085\pi$
$90$		0			0
$91$	28.5836			0.314105
$92$	−94.8469	−	54.7599i	−1.03094	−	0.595216i
$93$		0			0
$94$	−8.81153	−	15.2620i	−0.0937397	−	0.162362i
$95$	−10.8126	+	6.24265i	−0.113817	+	0.0657121i
$96$		0			0
$97$	−79.7082	+	138.059i	−0.821734	+	1.42329i	0.0826559	+	0.996578i	$0.473660\pi$
$97$	−79.7082	+	138.059i	−0.821734	+	1.42329i	−0.904390	+	0.426707i	$0.859674\pi$
$98$		−	13.4640i		−	0.137388i
$99$		0			0
$100$	−19.2705			−0.192705
$101$	−20.7846	−	12.0000i	−0.205788	−	0.118812i	0.393564	−	0.919297i	$-0.371242\pi$
$101$	−20.7846	−	12.0000i	−0.205788	−	0.118812i	−0.599352	+	0.800485i	$0.704575\pi$
$102$		0			0
$103$	12.5836	+	21.7954i	0.122171	+	0.211606i	0.920623	−	0.390452i	$-0.127681\pi$
$103$	12.5836	+	21.7954i	0.122171	+	0.211606i	−0.798453	+	0.602058i	$0.794348\pi$
$104$	20.0265	−	11.5623i	0.192563	−	0.111176i
$105$		0			0
$106$	14.0106	−	24.2671i	0.132176	−	0.228935i
$107$			47.6656i			0.445473i	0.974879	+	0.222737i	$0.0714990\pi$
$107$			47.6656i			0.445473i	−0.974879	+	0.222737i	$0.928501\pi$
$108$		0			0
$109$	164.915			1.51298			0.756490	−	0.654005i	$-0.226913\pi$
$109$	164.915			1.51298			0.756490	+	0.654005i	$0.226913\pi$
$110$	6.05078	+	3.49342i	0.0550071	+	0.0317584i
$111$		0			0
$112$	−26.4590	−	45.8283i	−0.236241	−	0.409181i
$113$	−59.2249	+	34.1935i	−0.524114	+	0.302597i	−0.738616	−	0.674126i	$-0.764520\pi$
$113$	−59.2249	+	34.1935i	−0.524114	+	0.302597i	0.214502	+	0.976723i	$0.431187\pi$
$114$		0			0
$115$	−31.7705	+	55.0281i	−0.276265	+	0.478506i
$116$		−	216.095i		−	1.86289i
$117$		0			0
$118$	34.6687			0.293803
$119$	−38.3578	−	22.1459i	−0.322335	−	0.186100i
$120$		0			0
$121$	−27.0410	−	46.8364i	−0.223480	−	0.387078i
$122$	6.28505	−	3.62868i	0.0515168	−	0.0297433i
$123$		0			0
$124$	60.2188	−	104.302i	0.485636	−	0.841146i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−200.748			−1.58069			−0.790345	−	0.612662i	$-0.790099\pi$
$127$	−200.748			−1.58069			−0.790345	+	0.612662i	$0.790099\pi$
$128$	−77.1289	−	44.5304i	−0.602569	−	0.347894i
$129$		0			0
$130$	−3.29180	−	5.70156i	−0.0253215	−	0.0438581i
$131$	−7.07030	+	4.08204i	−0.0539718	+	0.0311606i	−0.526743	−	0.850025i	$-0.676587\pi$
$131$	−7.07030	+	4.08204i	−0.0539718	+	0.0311606i	0.472771	+	0.881185i	$0.343254\pi$
$132$		0			0
$133$	−10.3525	+	17.9311i	−0.0778387	+	0.134821i
$134$			0.127717i			0.000953115i
$135$		0			0
$136$	−35.8328			−0.263477
$137$	−43.5882	−	25.1656i	−0.318162	−	0.183691i	0.332411	−	0.943135i	$-0.392138\pi$
$137$	−43.5882	−	25.1656i	−0.318162	−	0.183691i	−0.650573	+	0.759444i	$0.725471\pi$
$138$		0			0
$139$	63.2492	+	109.551i	0.455030	+	0.788136i	0.998690	−	0.0511701i	$-0.0162951\pi$
$139$	63.2492	+	109.551i	0.455030	+	0.788136i	−0.543660	+	0.839306i	$0.682962\pi$
$140$	−27.6759	+	15.9787i	−0.197685	+	0.114134i
$141$		0			0
$142$	15.5197	−	26.8810i	0.109294	−	0.189303i
$143$		−	63.0557i		−	0.440949i
$144$		0			0
$145$	−125.374			−0.864647
$146$	−16.8010	−	9.70007i	−0.115075	−	0.0664389i
$147$		0			0
$148$	102.936	+	178.291i	0.695514	+	1.20467i
$149$	−13.7002	+	7.90983i	−0.0919478	+	0.0530861i	−0.545269	−	0.838261i	$-0.683572\pi$
$149$	−13.7002	+	7.90983i	−0.0919478	+	0.0530861i	0.453321	+	0.891347i	$0.350239\pi$
$150$		0			0
$151$	69.4984	−	120.375i	0.460255	−	0.797184i	−0.538719	−	0.842486i	$-0.681091\pi$
$151$	69.4984	−	120.375i	0.460255	−	0.797184i	0.998973	+	0.0453013i	$0.0144248\pi$
$152$			16.7508i			0.110202i
$153$		0			0
$154$	11.5867			0.0752383
$155$	−60.5139	−	34.9377i	−0.390412	−	0.225404i
$156$		0			0
$157$	−95.3525	−	165.155i	−0.607341	−	1.05195i	−0.991677	−	0.128752i	$-0.958903\pi$
$157$	−95.3525	−	165.155i	−0.607341	−	1.05195i	0.384336	−	0.923193i	$-0.374431\pi$
$158$	−15.9333	+	9.19911i	−0.100844	+	0.0582222i
$159$		0			0
$160$	−19.5106	+	33.7934i	−0.121942	+	0.211209i
$161$			105.374i			0.654496i
$162$		0			0
$163$	−36.8328			−0.225968			−0.112984	−	0.993597i	$-0.536041\pi$
$163$	−36.8328			−0.225968			−0.112984	+	0.993597i	$0.536041\pi$
$164$	−202.815	−	117.095i	−1.23668	−	0.713995i
$165$		0			0
$166$	11.9681	+	20.7293i	0.0720968	+	0.124875i
$167$	−223.937	+	129.290i	−1.34094	+	0.774193i	−0.986946	−	0.161054i	$-0.948511\pi$
$167$	−223.937	+	129.290i	−1.34094	+	0.774193i	−0.353996	+	0.935247i	$0.615177\pi$
$168$		0			0
$169$	54.7918	−	94.9022i	0.324212	−	0.561551i
$170$			10.2016i			0.0600096i
$171$		0			0
$172$	−275.082			−1.59931
$173$	157.904	+	91.1656i	0.912737	+	0.526969i	0.881311	−	0.472537i	$-0.156662\pi$
$173$	157.904	+	91.1656i	0.912737	+	0.526969i	0.0314263	+	0.999506i	$0.489995\pi$
$174$		0			0
$175$	9.27051	+	16.0570i	0.0529743	+	0.0917543i
$176$	−101.098	+	58.3688i	−0.574419	+	0.331641i
$177$		0			0
$178$	−13.3131	+	23.0589i	−0.0747926	+	0.129545i
$179$			256.774i			1.43449i	0.696820	+	0.717246i	$0.254598\pi$
$179$			256.774i			1.43449i	−0.696820	+	0.717246i	$0.745402\pi$
$180$		0			0
$181$	180.082			0.994928			0.497464	−	0.867485i	$-0.334265\pi$
$181$	180.082			0.994928			0.497464	+	0.867485i	$0.334265\pi$
$182$	−9.45523	−	5.45898i	−0.0519518	−	0.0299944i
$183$		0			0
$184$	42.6246	+	73.8280i	0.231655	+	0.401239i
$185$	103.440	−	59.7214i	0.559137	−	0.322818i
$186$		0			0
$187$	−48.8541	+	84.6178i	−0.261252	+	0.452502i
$188$		−	177.820i		−	0.945849i
$189$		0			0
$190$	4.76896			0.0250998
$191$	−111.186	−	64.1935i	−0.582128	−	0.336092i	0.179851	−	0.983694i	$-0.442439\pi$
$191$	−111.186	−	64.1935i	−0.582128	−	0.336092i	−0.761979	+	0.647602i	$0.775772\pi$
$192$		0			0
$193$	−32.1459	−	55.6783i	−0.166559	−	0.288489i	0.770649	−	0.637260i	$-0.219932\pi$
$193$	−32.1459	−	55.6783i	−0.166559	−	0.288489i	−0.937208	+	0.348771i	$0.886599\pi$
$194$	52.7337	−	30.4458i	0.271823	−	0.156937i
$195$		0			0
$196$	67.9271	−	117.653i	0.346567	−	0.600271i
$197$		−	217.997i		−	1.10658i	−0.832988	−	0.553292i	$-0.813372\pi$
$197$		−	217.997i		−	1.10658i	0.832988	−	0.553292i	$-0.186628\pi$
$198$		0			0
$199$	320.249			1.60929			0.804646	−	0.593754i	$-0.202355\pi$
$199$	320.249			1.60929			0.804646	+	0.593754i	$0.202355\pi$
$200$	12.9904	+	7.50000i	0.0649519	+	0.0375000i
$201$		0			0
$202$	4.58359	+	7.93901i	0.0226911	+	0.0393021i
$203$	−180.060	+	103.957i	−0.886993	+	0.512106i
$204$		0			0
$205$	−67.9361	+	117.669i	−0.331396	+	0.573994i
$206$		−	9.61301i		−	0.0466651i
$207$		0			0
$208$	110.000			0.528846
$209$	39.5563	+	22.8378i	0.189265	+	0.109272i
$210$		0			0
$211$	31.9164	+	55.2808i	0.151263	+	0.261995i	0.931692	−	0.363250i	$-0.118333\pi$
$211$	31.9164	+	55.2808i	0.151263	+	0.261995i	−0.780429	+	0.625244i	$0.784999\pi$
$212$	244.860	−	141.370i	1.15500	−	0.666839i
$213$		0			0
$214$	9.10333	−	15.7674i	0.0425389	−	0.0736795i
$215$			159.597i			0.742310i
$216$		0			0
$217$	−115.878			−0.534002
$218$	−54.5526	−	31.4959i	−0.250241	−	0.144477i
$219$		0			0
$220$	35.2492	+	61.0534i	0.160224	+	0.277516i
$221$	79.7340	−	46.0344i	0.360787	−	0.208301i
$222$		0			0
$223$	4.12461	−	7.14404i	0.0184960	−	0.0320360i	−0.856629	−	0.515932i	$-0.827446\pi$
$223$	4.12461	−	7.14404i	0.0184960	−	0.0320360i	0.875125	+	0.483896i	$0.160779\pi$
$224$			64.7113i			0.288890i
$225$		0			0
$226$	26.1215			0.115582
$227$	294.037	+	169.762i	1.29532	+	0.747852i	0.979592	−	0.200999i	$-0.0644186\pi$
$227$	294.037	+	169.762i	1.29532	+	0.747852i	0.315726	+	0.948850i	$0.397752\pi$
$228$		0			0
$229$	−101.248	−	175.366i	−0.442130	−	0.765791i	0.555718	−	0.831371i	$-0.312444\pi$
$229$	−101.248	−	175.366i	−0.442130	−	0.765791i	−0.997847	+	0.0655802i	$0.979110\pi$
$230$	21.0189	−	12.1353i	0.0913864	−	0.0527620i
$231$		0			0
$232$	−84.1033	+	145.671i	−0.362514	+	0.627893i
$233$			19.0820i			0.0818972i	0.999161	+	0.0409486i	$0.0130380\pi$
$233$			19.0820i			0.0818972i	−0.999161	+	0.0409486i	$0.986962\pi$
$234$		0			0
$235$	−103.167			−0.439009
$236$	302.947	+	174.907i	1.28368	+	0.741130i
$237$		0			0
$238$	8.45898	+	14.6514i	0.0355419	+	0.0615604i
$239$	236.087	−	136.305i	0.987812	−	0.570314i	0.0831925	−	0.996533i	$-0.473488\pi$
$239$	236.087	−	136.305i	0.987812	−	0.570314i	0.904620	+	0.426220i	$0.140155\pi$
$240$		0			0
$241$	−116.290	+	201.421i	−0.482532	+	0.835770i	−0.999799	−	0.0200541i	$-0.993616\pi$
$241$	−116.290	+	201.421i	−0.482532	+	0.835770i	0.517267	+	0.855824i	$0.326950\pi$
$242$			20.6575i			0.0853616i
$243$		0			0
$244$	73.2279			0.300114
$245$	−68.2598	−	39.4098i	−0.278612	−	0.160856i
$246$		0			0
$247$	−21.5197	−	37.2733i	−0.0871244	−	0.150904i
$248$	−81.1879	+	46.8738i	−0.327370	+	0.189007i
$249$		0			0
$250$	2.13525	−	3.69837i	0.00854102	−	0.0147935i
$251$			14.4195i			0.0574483i	0.999587	+	0.0287241i	$0.00914443\pi$
$251$			14.4195i			0.0574483i	−0.999587	+	0.0287241i	$0.990856\pi$
$252$		0			0
$253$	232.456			0.918798
$254$	66.4058	+	38.3394i	0.261440	+	0.150942i
$255$		0			0
$256$	−83.8237	−	145.187i	−0.327436	−	0.567137i
$257$	143.542	−	82.8738i	0.558528	−	0.322466i	−0.194026	−	0.980996i	$-0.562155\pi$
$257$	143.542	−	82.8738i	0.558528	−	0.322466i	0.752554	+	0.658530i	$0.228821\pi$
$258$		0			0
$259$	99.0395	−	171.541i	0.382392	−	0.662322i
$260$		−	66.4296i		−	0.255498i
$261$		0			0
$262$	3.11840			0.0119023
$263$	450.356	+	260.013i	1.71238	+	0.988643i	0.931331	+	0.364174i	$0.118649\pi$
$263$	450.356	+	260.013i	1.71238	+	0.988643i	0.781049	+	0.624470i	$0.214685\pi$
$264$		0			0
$265$	−82.0197	−	142.062i	−0.309508	−	0.536084i
$266$	6.84909	−	3.95432i	0.0257484	−	0.0148659i
$267$		0			0
$268$	−0.644345	+	1.11604i	−0.00240427	+	0.00416432i
$269$			87.3576i			0.324749i	0.986729	+	0.162375i	$0.0519153\pi$
$269$			87.3576i			0.324749i	−0.986729	+	0.162375i	$0.948085\pi$
$270$		0			0
$271$	35.5836			0.131305			0.0656524	−	0.997843i	$-0.479087\pi$
$271$	35.5836			0.131305			0.0656524	+	0.997843i	$0.479087\pi$
$272$	−147.615	−	85.2254i	−0.542701	−	0.313329i
$273$		0			0
$274$	9.61242	+	16.6492i	0.0350818	+	0.0607635i
$275$	35.4219	−	20.4508i	0.128807	−	0.0743667i
$276$		0			0
$277$	−73.6869	+	127.629i	−0.266018	+	0.460756i	−0.967830	−	0.251606i	$-0.919041\pi$
$277$	−73.6869	+	127.629i	−0.266018	+	0.460756i	0.701812	+	0.712362i	$0.252375\pi$
$278$		−	48.3181i		−	0.173806i
$279$		0			0
$280$	24.8754			0.0888407
$281$	165.298	+	95.4346i	0.588248	+	0.339625i	0.764404	−	0.644737i	$-0.223033\pi$
$281$	165.298	+	95.4346i	0.588248	+	0.339625i	−0.176157	+	0.984362i	$0.556367\pi$
$282$		0			0
$283$	−58.8541	−	101.938i	−0.207965	−	0.360206i	0.743108	−	0.669171i	$-0.233351\pi$
$283$	−58.8541	−	101.938i	−0.207965	−	0.360206i	−0.951073	+	0.308965i	$0.900017\pi$
$284$	271.234	−	156.597i	0.955048	−	0.551397i
$285$		0			0
$286$	−12.0426	+	20.8583i	−0.0421069	+	0.0729313i
$287$			225.325i			0.785105i
$288$		0			0
$289$	146.334			0.506347
$290$	41.4727	+	23.9443i	0.143009	+	0.0825665i
$291$		0			0
$292$	−97.8754	−	169.525i	−0.335190	−	0.580566i
$293$	357.879	−	206.622i	1.22143	−	0.705193i	0.256207	−	0.966622i	$-0.417527\pi$
$293$	357.879	−	206.622i	1.22143	−	0.705193i	0.965223	+	0.261429i	$0.0841937\pi$
$294$		0			0
$295$	101.477	−	175.764i	0.343990	−	0.595809i
$296$		−	160.249i		−	0.541383i
$297$		0			0
$298$	6.04257			0.0202771
$299$	−189.694	−	109.520i	−0.634427	−	0.366287i
$300$		0			0
$301$	132.334	+	229.210i	0.439649	+	0.761495i
$302$	−45.9791	+	26.5460i	−0.152249	+	0.0879008i
$303$		0			0
$304$	−39.8404	+	69.0055i	−0.131054	+	0.226992i
$305$		−	42.4853i		−	0.139296i
$306$		0			0
$307$	−458.158			−1.49237			−0.746185	−	0.665738i	$-0.768117\pi$
$307$	−458.158			−1.49237			−0.746185	+	0.665738i	$0.768117\pi$
$308$	101.249	+	58.4559i	0.328729	+	0.189792i
$309$		0			0
$310$	13.3450	+	23.1142i	0.0430484	+	0.0745621i
$311$	−102.228	+	59.0213i	−0.328707	+	0.189779i	−0.655267	−	0.755397i	$-0.727444\pi$
$311$	−102.228	+	59.0213i	−0.328707	+	0.189779i	0.326560	+	0.945176i	$0.394111\pi$
$312$		0			0
$313$	206.413	−	357.518i	0.659467	−	1.14223i	−0.321286	−	0.946982i	$-0.604115\pi$
$313$	206.413	−	357.518i	0.659467	−	1.14223i	0.980754	−	0.195249i	$-0.0625515\pi$
$314$			72.8429i			0.231984i
$315$		0			0
$316$	−185.641			−0.587472
$317$	233.779	+	134.972i	0.737472	+	0.425780i	0.821149	−	0.570713i	$-0.193333\pi$
$317$	233.779	+	134.972i	0.737472	+	0.425780i	−0.0836775	+	0.996493i	$0.526667\pi$
$318$		0			0
$319$	229.331	+	397.213i	0.718907	+	1.24518i
$320$	−97.6310	+	56.3673i	−0.305097	+	0.176148i
$321$		0			0
$322$	20.1246	−	34.8569i	0.0624988	−	0.108251i
$323$			66.6919i			0.206477i
$324$		0			0
$325$	−38.5410			−0.118588
$326$	12.1840	+	7.03444i	0.0373743	+	0.0215780i
$327$		0			0
$328$	91.1459	+	157.869i	0.277884	+	0.481309i
$329$	−148.167	+	85.5441i	−0.450355	+	0.260013i
$330$		0			0
$331$	−4.95743	+	8.58652i	−0.0149771	+	0.0259411i	−0.873417	−	0.486973i	$-0.838101\pi$
$331$	−4.95743	+	8.58652i	−0.0149771	+	0.0259411i	0.858440	+	0.512914i	$0.171434\pi$
$332$			241.520i			0.727469i
$333$		0			0
$334$	98.7690			0.295715
$335$	0.647502	+	0.373835i	0.00193284	+	0.00111593i
$336$		0			0
$337$	218.225	+	377.976i	0.647551	+	1.12159i	0.983706	+	0.179785i	$0.0575402\pi$
$337$	218.225	+	377.976i	0.647551	+	1.12159i	−0.336154	+	0.941807i	$0.609126\pi$
$338$	−36.2494	+	20.9286i	−0.107247	+	0.0619189i
$339$		0			0
$340$	−51.4681	+	89.1453i	−0.151377	+	0.262192i
$341$			255.629i			0.749646i
$342$		0			0
$343$	−312.413			−0.910826
$344$	185.435	+	107.061i	0.539054	+	0.311223i
$345$		0			0
$346$	−34.8222	−	60.3138i	−0.100642	−	0.174317i
$347$	−21.9831	+	12.6919i	−0.0633518	+	0.0365762i	−0.531341	−	0.847158i	$-0.678312\pi$
$347$	−21.9831	+	12.6919i	−0.0633518	+	0.0365762i	0.467990	+	0.883734i	$0.344978\pi$
$348$		0			0
$349$	36.0410	−	62.4249i	0.103269	−	0.178868i	−0.809760	−	0.586761i	$-0.800403\pi$
$349$	36.0410	−	62.4249i	0.103269	−	0.178868i	0.913030	+	0.407893i	$0.133736\pi$
$350$		−	7.08204i		−	0.0202344i
$351$		0			0
$352$	142.754			0.405551
$353$	−339.624	−	196.082i	−0.962108	−	0.555473i	−0.0652867	−	0.997867i	$-0.520796\pi$
$353$	−339.624	−	196.082i	−0.962108	−	0.555473i	−0.896821	+	0.442393i	$0.854130\pi$
$354$		0			0
$355$	−90.8541	−	157.364i	−0.255927	−	0.443279i
$356$	−232.669	+	134.331i	−0.653563	+	0.377335i
$357$		0			0
$358$	49.0395	−	84.9388i	0.136982	−	0.237259i
$359$		−	399.994i		−	1.11419i	−0.830449	−	0.557094i	$-0.811916\pi$
$359$		−	399.994i		−	1.11419i	0.830449	−	0.557094i	$-0.188084\pi$
$360$		0			0
$361$	−329.823			−0.913639
$362$	−59.5697	−	34.3926i	−0.164557	−	0.0950072i
$363$		0			0
$364$	−55.0820	−	95.4049i	−0.151324	−	0.262101i
$365$	−98.3549	+	56.7852i	−0.269465	+	0.155576i
$366$		0			0
$367$	−103.185	+	178.722i	−0.281159	+	0.486982i	−0.971670	−	0.236340i	$-0.924052\pi$
$367$	−103.185	+	178.722i	−0.281159	+	0.486982i	0.690511	+	0.723321i	$0.257386\pi$
$368$			405.517i			1.10195i
$369$		0			0
$370$	−45.6231			−0.123306
$371$	−235.590	−	136.018i	−0.635015	−	0.366626i
$372$		0			0
$373$	−177.416	−	307.294i	−0.475647	−	0.823845i	0.523964	−	0.851741i	$-0.324453\pi$
$373$	−177.416	−	307.294i	−0.475647	−	0.823845i	−0.999611	+	0.0278955i	$0.991119\pi$
$374$	32.3211	−	18.6606i	0.0864201	−	0.0498947i
$375$		0			0
$376$	−69.2067	+	119.869i	−0.184060	+	0.318802i
$377$		−	432.190i		−	1.14639i
$378$		0			0
$379$	−423.997			−1.11873			−0.559363	−	0.828923i	$-0.688954\pi$
$379$	−423.997			−1.11873			−0.559363	+	0.828923i	$0.688954\pi$
$380$	41.6728	+	24.0598i	0.109665	+	0.0633152i
$381$		0			0
$382$	24.5197	+	42.4694i	0.0641878	+	0.111177i
$383$	−179.404	+	103.579i	−0.468418	+	0.270441i	−0.715577	−	0.698534i	$-0.753836\pi$
$383$	−179.404	+	103.579i	−0.468418	+	0.270441i	0.247159	+	0.968975i	$0.420503\pi$
$384$		0			0
$385$	33.9149	−	58.7423i	0.0880905	−	0.152577i
$386$			24.5573i			0.0636199i
$387$		0			0
$388$	614.407			1.58352
$389$	381.014	+	219.979i	0.979471	+	0.565498i	0.902110	−	0.431505i	$-0.142017\pi$
$389$	381.014	+	219.979i	0.979471	+	0.565498i	0.0773608	+	0.997003i	$0.475351\pi$
$390$		0			0
$391$	169.707	+	293.941i	0.434032	+	0.751766i
$392$	−91.5802	+	52.8738i	−0.233623	+	0.134882i
$393$		0			0
$394$	−41.6337	+	72.1117i	−0.105669	+	0.183025i
$395$			107.705i			0.272671i
$396$		0			0
$397$	453.872			1.14326			0.571628	−	0.820513i	$-0.306312\pi$
$397$	453.872			1.14326			0.571628	+	0.820513i	$0.306312\pi$
$398$	−105.936	−	61.1622i	−0.266171	−	0.153674i
$399$		0			0
$400$	35.6763	+	61.7931i	0.0891907	+	0.154483i
$401$	481.863	−	278.204i	1.20165	−	0.693774i	0.240730	−	0.970592i	$-0.422613\pi$
$401$	481.863	−	278.204i	1.20165	−	0.693774i	0.960922	+	0.276818i	$0.0892798\pi$
$402$		0			0
$403$	120.438	−	208.604i	0.298853	−	0.517628i
$404$			92.4984i			0.228957i
$405$		0			0
$406$	79.4164			0.195607
$407$	−378.422	−	218.482i	−0.929784	−	0.536811i
$408$		0			0
$409$	−37.8313	−	65.5257i	−0.0924970	−	0.160209i	0.816064	−	0.577961i	$-0.196152\pi$
$409$	−37.8313	−	65.5257i	−0.0924970	−	0.160209i	−0.908561	+	0.417752i	$0.862818\pi$
$410$	44.9455	−	25.9493i	0.109623	−	0.0632910i
$411$		0			0
$412$	48.4984	−	84.0018i	0.117715	−	0.203888i
$413$		−	336.571i		−	0.814942i
$414$		0			0
$415$	140.125			0.337650
$416$	−116.493	−	67.2574i	−0.280032	−	0.161676i
$417$		0			0
$418$	−8.72328	−	15.1092i	−0.0208691	−	0.0361463i
$419$	−451.251	+	260.530i	−1.07697	+	0.621789i	−0.930078	−	0.367363i	$-0.880261\pi$
$419$	−451.251	+	260.530i	−1.07697	+	0.621789i	−0.146893	+	0.989152i	$0.546927\pi$
$420$		0			0
$421$	−57.3723	+	99.3717i	−0.136276	+	0.236037i	−0.926084	−	0.377317i	$-0.876847\pi$
$421$	−57.3723	+	99.3717i	−0.136276	+	0.236037i	0.789808	+	0.613354i	$0.210180\pi$
$422$		−	24.3820i		−	0.0577772i
$423$		0			0
$424$	−220.082			−0.519061
$425$	51.7202	+	29.8607i	0.121695	+	0.0702604i
$426$		0			0
$427$	−35.2279	−	61.0166i	−0.0825010	−	0.142896i
$428$	159.096	−	91.8541i	0.371720	−	0.214612i
$429$		0			0
$430$	30.4803	−	52.7934i	0.0708843	−	0.122775i
$431$			233.204i			0.541076i	0.962709	+	0.270538i	$0.0872015\pi$
$431$			233.204i			0.541076i	−0.962709	+	0.270538i	$0.912799\pi$
$432$		0			0
$433$	−501.702			−1.15867			−0.579333	−	0.815091i	$-0.696687\pi$
$433$	−501.702			−1.15867			−0.579333	+	0.815091i	$0.696687\pi$
$434$	38.3317	+	22.1308i	0.0883219	+	0.0509927i
$435$		0			0
$436$	−317.799	−	550.445i	−0.728898	−	1.26249i
$437$	137.408	−	79.3328i	0.314436	−	0.181540i
$438$		0			0
$439$	−182.998	+	316.963i	−0.416853	+	0.722010i	−0.995621	−	0.0934817i	$-0.970200\pi$
$439$	−182.998	+	316.963i	−0.416853	+	0.722010i	0.578768	+	0.815492i	$0.303534\pi$
$440$		−	54.8754i		−	0.124717i
$441$		0			0
$442$	−35.1672			−0.0795638
$443$	−548.110	−	316.451i	−1.23727	−	0.714337i	−0.268733	−	0.963215i	$-0.586605\pi$
$443$	−548.110	−	316.451i	−1.23727	−	0.714337i	−0.968535	+	0.248878i	$0.919938\pi$
$444$		0			0
$445$	77.9361	+	134.989i	0.175137	+	0.303347i
$446$	−2.72878	+	1.57546i	−0.00611834	+	0.00353242i
$447$		0			0
$448$	−93.4772	+	161.907i	−0.208654	+	0.361400i
$449$		−	796.344i		−	1.77360i	−0.462158	−	0.886798i	$-0.652925\pi$
$449$		−	796.344i		−	1.77360i	0.462158	−	0.886798i	$-0.347075\pi$
$450$		0			0
$451$	497.070			1.10215
$452$	228.259	+	131.785i	0.504997	+	0.291560i
$453$		0			0
$454$	−64.8435	−	112.312i	−0.142827	−	0.247384i
$455$	−55.3519	+	31.9574i	−0.121653	+	0.0702361i
$456$		0			0
$457$	101.289	−	175.437i	0.221638	−	0.383889i	−0.733667	−	0.679509i	$-0.762193\pi$
$457$	101.289	−	175.437i	0.221638	−	0.383889i	0.955306	+	0.295620i	$0.0955263\pi$
$458$			77.3463i			0.168878i
$459$		0			0
$460$	244.894			0.532377
$461$	−630.387	−	363.954i	−1.36743	−	0.789489i	−0.376835	−	0.926280i	$-0.622988\pi$
$461$	−630.387	−	363.954i	−1.36743	−	0.789489i	−0.990600	+	0.136792i	$0.956321\pi$
$462$		0			0
$463$	−246.502	−	426.953i	−0.532401	−	0.922145i	−0.999284	−	0.0378264i	$-0.987957\pi$
$463$	−246.502	−	426.953i	−0.532401	−	0.922145i	0.466884	−	0.884319i	$-0.345377\pi$
$464$	−692.934	+	400.066i	−1.49339	+	0.862211i
$465$		0			0
$466$	3.64435	−	6.31219i	0.00782048	−	0.0135455i
$467$		−	453.190i		−	0.970429i	−0.874395	−	0.485215i	$-0.838741\pi$
$467$		−	453.190i		−	0.970429i	0.874395	−	0.485215i	$-0.161259\pi$
$468$		0			0
$469$	1.23991			0.00264372
$470$	34.1269	+	19.7032i	0.0726104	+	0.0419217i
$471$		0			0
$472$	−136.146	−	235.812i	−0.288445	−	0.499601i
$473$	505.640	−	291.931i	1.06901	−	0.617191i
$474$		0			0
$475$	13.9590	−	24.1777i	0.0293873	−	0.0509003i
$476$			170.705i			0.358624i
$477$		0			0
$478$	−104.128			−0.217840
$479$	−276.733	−	159.772i	−0.577731	−	0.333553i	0.182500	−	0.983206i	$-0.441581\pi$
$479$	−276.733	−	159.772i	−0.577731	−	0.333553i	−0.760231	+	0.649653i	$0.774914\pi$
$480$		0			0
$481$	205.872	+	356.581i	0.428009	+	0.741333i
$482$	76.9358	−	44.4189i	0.159618	−	0.0921554i
$483$		0			0
$484$	−104.219	+	180.512i	−0.215328	+	0.372959i
$485$		−	356.466i		−	0.734981i
$486$		0			0
$487$	792.869			1.62807			0.814034	−	0.580817i	$-0.197267\pi$
$487$	792.869			1.62807			0.814034	+	0.580817i	$0.197267\pi$
$488$	−49.3634	−	28.5000i	−0.101155	−	0.0584016i
$489$		0			0
$490$	15.0532	+	26.0729i	0.0307208	+	0.0532101i
$491$	−319.941	+	184.718i	−0.651612	+	0.376208i	−0.789073	−	0.614299i	$-0.789439\pi$
$491$	−319.941	+	184.718i	−0.651612	+	0.376208i	0.137462	+	0.990507i	$0.456106\pi$
$492$		0			0
$493$	−334.851	+	579.979i	−0.679211	+	1.17643i
$494$			16.4396i			0.0332786i
$495$		0			0
$496$	−445.942			−0.899077
$497$	−260.966	−	150.669i	−0.525082	−	0.303156i
$498$		0			0
$499$	−304.956	−	528.199i	−0.611134	−	1.05852i	−0.991050	−	0.133494i	$-0.957380\pi$
$499$	−304.956	−	528.199i	−0.611134	−	1.05852i	0.379916	−	0.925021i	$-0.375953\pi$
$500$	37.3172	−	21.5451i	0.0746344	−	0.0430902i
$501$		0			0
$502$	2.75388	−	4.76986i	0.00548582	−	0.00950172i
$503$			305.308i			0.606974i	0.952836	+	0.303487i	$0.0981509\pi$
$503$			305.308i			0.606974i	−0.952836	+	0.303487i	$0.901849\pi$
$504$		0			0
$505$	53.6656			0.106269
$506$	−76.8946	−	44.3951i	−0.151966	−	0.0877374i
$507$		0			0
$508$	386.851	+	670.046i	0.761518	+	1.31899i
$509$	−177.083	+	102.239i	−0.347905	+	0.200863i	−0.663762	−	0.747944i	$-0.731041\pi$
$509$	−177.083	+	102.239i	−0.347905	+	0.200863i	0.315857	+	0.948807i	$0.397708\pi$
$510$		0			0
$511$	−94.1703	+	163.108i	−0.184286	+	0.319193i
$512$			420.279i			0.820857i
$513$		0			0
$514$	−63.3100			−0.123171
$515$	−48.7360	−	28.1378i	−0.0946331	−	0.0546364i
$516$		0			0
$517$	188.711	+	326.858i	0.365012	+	0.632220i
$518$	−65.5230	+	37.8297i	−0.126492	+	0.0730303i
$519$		0			0
$520$	−25.8541	+	44.7806i	−0.0497194	+	0.0861166i
$521$		−	590.227i		−	1.13287i	−0.824105	−	0.566436i	$-0.808322\pi$
$521$		−	590.227i		−	1.13287i	0.824105	−	0.566436i	$-0.191678\pi$
$522$		0			0
$523$	−19.7933			−0.0378458			−0.0189229	−	0.999821i	$-0.506024\pi$
$523$	−19.7933			−0.0378458			−0.0189229	+	0.999821i	$0.506024\pi$
$524$	27.2497	+	15.7326i	0.0520032	+	0.0300240i
$525$		0			0
$526$	−99.3162	−	172.021i	−0.188814	−	0.327036i
$527$	−323.243	+	186.625i	−0.613365	+	0.354126i
$528$		0			0
$529$	139.246	−	241.181i	0.263225	−	0.455919i
$530$			62.6575i			0.118222i
$531$		0			0
$532$	79.7996			0.149999
$533$	−405.630	−	234.190i	−0.761031	−	0.439382i
$534$		0			0
$535$	−53.2918	−	92.3041i	−0.0996108	−	0.172531i
$536$	0.868715	−	0.501553i	0.00162074	−	0.000935733i
$537$		0			0
$538$	16.6838	−	28.8972i	0.0310108	−	0.0537123i
$539$			288.351i			0.534973i
$540$		0			0
$541$	428.164			0.791431			0.395715	−	0.918373i	$-0.370497\pi$
$541$	428.164			0.791431			0.395715	+	0.918373i	$0.370497\pi$
$542$	−11.7708	−	6.79586i	−0.0217173	−	0.0125385i
$543$		0			0
$544$	104.219	+	180.512i	0.191579	+	0.331824i
$545$	−319.356	+	184.380i	−0.585975	+	0.338313i
$546$		0			0
$547$	491.353	−	851.048i	0.898268	−	1.55585i	0.0685606	−	0.997647i	$-0.478159\pi$
$547$	491.353	−	851.048i	0.898268	−	1.55585i	0.829707	−	0.558199i	$-0.188507\pi$
$548$			193.982i			0.353981i
$549$		0			0
$550$	−15.6231			−0.0284056
$551$	271.123	+	156.533i	0.492056	+	0.284089i
$552$		0			0
$553$	89.3069	+	154.684i	0.161495	+	0.279718i
$554$	48.7501	−	28.1459i	0.0879966	−	0.0508049i
$555$		0			0
$556$	243.769	−	422.220i	0.438433	−	0.759389i
$557$			310.839i			0.558059i	0.960282	+	0.279030i	$0.0900128\pi$
$557$			310.839i			0.558059i	−0.960282	+	0.279030i	$0.909987\pi$
$558$		0			0
$559$	−550.164			−0.984193
$560$	102.475	+	59.1641i	0.182991	+	0.105650i
$561$		0			0
$562$	−36.4528	−	63.1380i	−0.0648626	−	0.112345i
$563$	−736.985	+	425.498i	−1.30903	+	0.755770i	−0.981935	−	0.189221i	$-0.939404\pi$
$563$	−736.985	+	425.498i	−1.30903	+	0.755770i	−0.327097	+	0.944991i	$0.606070\pi$
$564$		0			0
$565$	76.4590	−	132.431i	0.135326	−	0.234391i
$566$			44.9605i			0.0794356i
$567$		0			0
$568$	−243.787			−0.429203
$569$	253.206	+	146.188i	0.445002	+	0.256922i	0.705717	−	0.708494i	$-0.250625\pi$
$569$	253.206	+	146.188i	0.445002	+	0.256922i	−0.260715	+	0.965416i	$0.583958\pi$
$570$		0			0
$571$	178.877	+	309.824i	0.313270	+	0.542599i	0.979068	−	0.203533i	$-0.0652423\pi$
$571$	178.877	+	309.824i	0.313270	+	0.542599i	−0.665799	+	0.746132i	$0.731909\pi$
$572$	−210.464	+	121.512i	−0.367945	+	0.212433i
$573$		0			0
$574$	43.0333	−	74.5358i	0.0749708	−	0.129853i
$575$		−	142.082i		−	0.247099i
$576$		0			0
$577$	216.456			0.375140			0.187570	−	0.982251i	$-0.439939\pi$
$577$	216.456			0.375140			0.187570	+	0.982251i	$0.439939\pi$
$578$	−48.4063	−	27.9474i	−0.0837479	−	0.0483519i
$579$		0			0
$580$	241.602	+	418.467i	0.416555	+	0.721494i
$581$	201.244	−	116.188i	0.346376	−	0.199980i
$582$		0			0
$583$	−300.058	+	519.715i	−0.514679	+	0.891450i
$584$			152.371i			0.260909i
$585$		0			0
$586$	−157.845			−0.269360
$587$	−500.986	−	289.245i	−0.853469	−	0.492751i	0.00835083	−	0.999965i	$-0.497342\pi$
$587$	−500.986	−	289.245i	−0.853469	−	0.492751i	−0.861820	+	0.507215i	$0.830675\pi$
$588$		0			0
$589$	87.2415	+	151.107i	0.148118	+	0.256548i
$590$	−67.1357	+	38.7608i	−0.113789	+	0.0656963i
$591$		0			0
$592$	381.140	−	660.153i	0.643817	−	1.11512i
$593$			159.971i			0.269765i	0.990862	+	0.134882i	$0.0430657\pi$
$593$			159.971i			0.269765i	−0.990862	+	0.134882i	$0.956934\pi$
$594$		0			0
$595$	99.0395			0.166453
$596$	52.8021	+	30.4853i	0.0885941	+	0.0511498i
$597$		0			0
$598$	41.8328	+	72.4566i	0.0699545	+	0.121165i
$599$	392.963	−	226.877i	0.656032	−	0.378760i	−0.134732	−	0.990882i	$-0.543017\pi$
$599$	392.963	−	226.877i	0.656032	−	0.378760i	0.790763	+	0.612122i	$0.209684\pi$
$600$		0			0
$601$	326.792	−	566.020i	0.543747	−	0.941797i	−0.454938	−	0.890523i	$-0.650339\pi$
$601$	326.792	−	566.020i	0.543747	−	0.941797i	0.998685	−	0.0512738i	$-0.0163281\pi$
$602$		−	101.094i		−	0.167931i
$603$		0			0
$604$	−535.708			−0.886934
$605$	104.729	+	60.4656i	0.173106	+	0.0999431i
$606$		0			0
$607$	92.3131	+	159.891i	0.152081	+	0.263412i	0.931992	−	0.362478i	$-0.118069\pi$
$607$	92.3131	+	159.891i	0.152081	+	0.263412i	−0.779911	+	0.625890i	$0.784736\pi$
$608$	84.3842	−	48.7192i	0.138790	−	0.0801303i
$609$		0			0
$610$	−8.11397	+	14.0538i	−0.0133016	+	0.0230390i
$611$		−	355.639i		−	0.582061i
$612$		0			0
$613$	−903.416			−1.47376			−0.736881	−	0.676022i	$-0.763702\pi$
$613$	−903.416			−1.47376			−0.736881	+	0.676022i	$0.763702\pi$
$614$	151.555	+	87.5004i	0.246832	+	0.142509i
$615$		0			0
$616$	−45.5016	−	78.8110i	−0.0738662	−	0.127940i
$617$	334.709	−	193.245i	0.542479	−	0.313200i	−0.203604	−	0.979053i	$-0.565266\pi$
$617$	334.709	−	193.245i	0.542479	−	0.313200i	0.746083	+	0.665853i	$0.231932\pi$
$618$		0			0
$619$	−582.951	+	1009.70i	−0.941763	+	1.63118i	−0.179656	+	0.983729i	$0.557499\pi$
$619$	−582.951	+	1009.70i	−0.941763	+	1.63118i	−0.762106	+	0.647452i	$0.775835\pi$
$620$			269.307i			0.434366i
$621$		0			0
$622$	45.0883			0.0724891
$623$	223.861	+	129.246i	0.359327	+	0.207458i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−136.560	+	78.8429i	−0.218147	+	0.125947i
$627$		0			0
$628$	−367.498	+	636.526i	−0.585189	+	1.01358i
$629$		−	638.020i		−	1.01434i
$630$		0			0
$631$	50.8297			0.0805542			0.0402771	−	0.999189i	$-0.487176\pi$
$631$	50.8297			0.0805542			0.0402771	+	0.999189i	$0.487176\pi$
$632$	125.142	+	72.2508i	0.198010	+	0.114321i
$633$		0			0
$634$	−51.5548	−	89.2955i	−0.0813167	−	0.140845i
$635$	388.746	−	224.443i	0.612199	−	0.353453i
$636$		0			0
$637$	135.854	−	235.306i	0.213272	−	0.369397i
$638$		−	175.193i		−	0.274598i
$639$		0			0
$640$	199.146			0.311165
$641$	475.235	+	274.377i	0.741396	+	0.428045i	0.822577	−	0.568654i	$-0.192536\pi$
$641$	475.235	+	274.377i	0.741396	+	0.428045i	−0.0811807	+	0.996699i	$0.525869\pi$
$642$		0			0
$643$	−263.356	−	456.145i	−0.409573	−	0.709402i	0.585269	−	0.810840i	$-0.300989\pi$
$643$	−263.356	−	456.145i	−0.409573	−	0.709402i	−0.994842	+	0.101438i	$0.967656\pi$
$644$	351.712	−	203.061i	0.546136	−	0.315312i
$645$		0			0
$646$	12.7370	−	22.0612i	0.0197168	−	0.0341504i
$647$			694.607i			1.07358i	0.843716	+	0.536790i	$0.180363\pi$
$647$			694.607i			1.07358i	−0.843716	+	0.536790i	$0.819637\pi$
$648$		0			0
$649$	−742.480			−1.14404
$650$	12.7491	+	7.36068i	0.0196140	+	0.0113241i
$651$		0			0
$652$	70.9787	+	122.939i	0.108863	+	0.188556i
$653$	971.934	−	561.146i	1.48841	−	0.859336i	0.488501	−	0.872563i	$-0.337544\pi$
$653$	971.934	−	561.146i	1.48841	−	0.859336i	0.999913	+	0.0132277i	$0.00421063\pi$
$654$		0			0
$655$	9.12772	−	15.8097i	0.0139354	−	0.0241369i
$656$			867.132i			1.32185i
$657$		0			0
$658$	65.3499			0.0993160
$659$	−580.660	−	335.244i	−0.881123	−	0.508717i	−0.0100944	−	0.999949i	$-0.503213\pi$
$659$	−580.660	−	335.244i	−0.881123	−	0.508717i	−0.871028	+	0.491233i	$0.836547\pi$
$660$		0			0
$661$	−544.076	−	942.367i	−0.823110	−	1.42567i	−0.903355	−	0.428893i	$-0.858904\pi$
$661$	−544.076	−	942.367i	−0.823110	−	1.42567i	0.0802449	−	0.996775i	$-0.474430\pi$
$662$	3.27976	−	1.89357i	0.00495432	−	0.00286038i
$663$		0			0
$664$	93.9984	−	162.810i	0.141564	−	0.245196i
$665$		−	46.2980i		−	0.0696211i
$666$		0			0
$667$	1593.28			2.38872
$668$	863.077	+	498.298i	1.29203	+	0.745955i
$669$		0			0
$670$	−0.142792	−	0.247324i	−0.000213123	−	0.000369140i
$671$	−134.603	+	77.7132i	−0.200601	+	0.115817i
$672$		0			0
$673$	319.185	−	552.845i	0.474272	−	0.821464i	−0.525294	−	0.850921i	$-0.676044\pi$
$673$	319.185	−	552.845i	0.474272	−	0.821464i	0.999566	+	0.0294571i	$0.00937783\pi$
$674$		−	166.709i		−	0.247343i
$675$		0			0
$676$	−422.346			−0.624773
$677$	691.225	+	399.079i	1.02101	+	0.589481i	0.914397	−	0.404819i	$-0.132665\pi$
$677$	691.225	+	399.079i	1.02101	+	0.589481i	0.106615	+	0.994300i	$0.465999\pi$
$678$		0			0
$679$	−295.574	−	511.950i	−0.435308	−	0.753976i
$680$	69.3899	−	40.0623i	0.102044	−	0.0589152i
$681$		0			0
$682$	48.8208	−	84.5602i	0.0715848	−	0.123989i
$683$		−	757.505i		−	1.10908i	−0.832156	−	0.554542i	$-0.812893\pi$
$683$		−	757.505i		−	1.10908i	0.832156	−	0.554542i	$-0.187107\pi$
$684$		0			0
$685$	112.544			0.164298
$686$	103.344	+	59.6656i	0.150647	+	0.0869761i
$687$		0			0
$688$	509.271	+	882.082i	0.740219	+	1.28210i
$689$	489.719	−	282.740i	0.710768	−	0.410362i
$690$		0			0
$691$	−351.166	+	608.237i	−0.508199	+	0.880227i	0.491756	+	0.870733i	$0.336355\pi$
$691$	−351.166	+	608.237i	−0.508199	+	0.880227i	−0.999955	+	0.00949361i	$0.996978\pi$
$692$		−	702.723i		−	1.01550i
$693$		0			0
$694$	9.69578			0.0139709
$695$	−244.963	−	141.430i	−0.352465	−	0.203496i
$696$		0			0
$697$	362.890	+	628.545i	0.520646	+	0.901786i
$698$	−23.8442	+	13.7664i	−0.0341607	+	0.0197227i
$699$		0			0
$700$	35.7295	−	61.8853i	0.0510421	−	0.0884076i
$701$		−	406.616i		−	0.580052i	−0.957019	−	0.290026i	$-0.906336\pi$
$701$		−	406.616i		−	0.580052i	0.957019	−	0.290026i	$-0.0936639\pi$
$702$		0			0
$703$	−298.255			−0.424261
$704$	357.169	+	206.212i	0.507342	+	0.292914i
$705$		0			0
$706$	74.8967	+	129.725i	0.106086	+	0.183746i
$707$	77.0736	−	44.4984i	0.109015	−	0.0629398i
$708$		0			0
$709$	−282.161	+	488.717i	−0.397970	+	0.689305i	−0.993475	−	0.114047i	$-0.963619\pi$
$709$	−282.161	+	488.717i	−0.397970	+	0.689305i	0.595505	+	0.803352i	$0.296952\pi$
$710$			69.4064i			0.0977554i
$711$		0			0
$712$	209.125			0.293714
$713$	769.022	+	443.995i	1.07857	+	0.622714i
$714$		0			0
$715$	70.4984	+	122.107i	0.0985992	+	0.170779i
$716$	857.047	−	494.817i	1.19699	−	0.691085i
$717$		0			0
$718$	−76.3920	+	132.315i	−0.106396	+	0.184283i
$719$			1340.07i			1.86379i	0.362725	+	0.931896i	$0.381846\pi$
$719$			1340.07i			1.86379i	−0.362725	+	0.931896i	$0.618154\pi$
$720$		0			0
$721$	−93.3251			−0.129438
$722$	109.103	+	62.9907i	0.151112	+	0.0872447i
$723$		0			0
$724$	−347.027	−	601.069i	−0.479319	−	0.830206i
$725$	242.785	−	140.172i	0.334876	−	0.193341i
$726$		0			0
$727$	−65.4953	+	113.441i	−0.0900899	+	0.156040i	−0.907549	−	0.419947i	$-0.862049\pi$
$727$	−65.4953	+	113.441i	−0.0900899	+	0.156040i	0.817459	+	0.575987i	$0.195382\pi$
$728$			85.7508i			0.117790i
$729$		0			0
$730$	43.3800			0.0594247
$731$	738.294	+	426.254i	1.00998	+	0.583111i
$732$		0			0
$733$	−707.240	−	1224.98i	−0.964857	−	1.67118i	−0.710000	−	0.704202i	$-0.751305\pi$
$733$	−707.240	−	1224.98i	−0.964857	−	1.67118i	−0.254857	−	0.966979i	$-0.582028\pi$
$734$	68.2658	−	39.4133i	0.0930052	−	0.0536966i
$735$		0			0
$736$	247.945	−	429.454i	0.336882	−	0.583497i
$737$		−	2.73525i		−	0.00371133i
$738$		0			0
$739$	10.5805			0.0143173			0.00715865	−	0.999974i	$-0.497721\pi$
$739$	10.5805			0.0143173			0.00715865	+	0.999974i	$0.497721\pi$
$740$	−398.670	−	230.172i	−0.538743	−	0.311044i
$741$		0			0
$742$	51.9543	+	89.9875i	0.0700193	+	0.121277i
$743$	−687.670	+	397.026i	−0.925531	+	0.534356i	−0.885395	−	0.464838i	$-0.846112\pi$
$743$	−687.670	+	397.026i	−0.925531	+	0.534356i	−0.0401358	+	0.999194i	$0.512779\pi$
$744$		0			0
$745$	17.6869	−	30.6346i	0.0237408	−	0.0411203i
$746$			135.534i			0.181681i
$747$		0			0
$748$	376.577			0.503446
$749$	−153.073	−	88.3769i	−0.204370	−	0.117993i
$750$		0			0
$751$	26.7554	+	46.3418i	0.0356264	+	0.0617068i	0.883289	−	0.468829i	$-0.155324\pi$
$751$	26.7554	+	46.3418i	0.0356264	+	0.0617068i	−0.847662	+	0.530536i	$0.821991\pi$
$752$	−570.199	+	329.205i	−0.758244	+	0.437772i
$753$		0			0
$754$	−82.5410	+	142.965i	−0.109471	+	0.189609i
$755$			310.807i			0.411664i
$756$		0			0
$757$	921.745			1.21763			0.608814	−	0.793313i	$-0.291646\pi$
$757$	921.745			1.21763			0.608814	+	0.793313i	$0.291646\pi$
$758$	140.255	+	80.9762i	0.185033	+	0.106829i
$759$		0			0
$760$	−18.7279	−	32.4377i	−0.0246420	−	0.0426812i
$761$	500.663	−	289.058i	0.657901	−	0.379839i	−0.133576	−	0.991039i	$-0.542646\pi$
$761$	500.663	−	289.058i	0.657901	−	0.379839i	0.791477	+	0.611199i	$0.209313\pi$
$762$		0			0
$763$	−305.769	+	529.607i	−0.400746	+	0.694112i
$764$			494.817i			0.647666i
$765$		0			0
$766$	79.1273			0.103299
$767$	605.895	+	349.813i	0.789954	+	0.456080i
$768$		0			0
$769$	325.828	+	564.351i	0.423704	+	0.733876i	0.996298	−	0.0859622i	$-0.0273964\pi$
$769$	325.828	+	564.351i	0.423704	+	0.733876i	−0.572595	+	0.819839i	$0.694063\pi$
$770$	−22.4375	+	12.9543i	−0.0291397	+	0.0168238i
$771$		0			0
$772$	−123.894	+	214.590i	−0.160484	+	0.277966i
$773$			389.754i			0.504209i	0.967700	+	0.252105i	$0.0811227\pi$
$773$			389.754i			0.504209i	−0.967700	+	0.252105i	$0.918877\pi$
$774$		0			0
$775$	156.246			0.201608
$776$	−414.176	−	239.125i	−0.533732	−	0.308150i
$777$		0			0
$778$	−84.0244	−	145.535i	−0.108001	−	0.187062i
$779$	293.826	−	169.641i	0.377184	−	0.217767i
$780$		0			0
$781$	−332.377	+	575.694i	−0.425579	+	0.737124i
$782$		−	129.644i		−	0.165786i
$783$		0			0
$784$	−503.024			−0.641613
$785$	369.299	+	213.215i	0.470444	+	0.271611i
$786$		0			0
$787$	18.2279	+	31.5717i	0.0231613	+	0.0401165i	0.877374	−	0.479808i	$-0.159294\pi$
$787$	18.2279	+	31.5717i	0.0231613	+	0.0401165i	−0.854212	+	0.519924i	$0.825960\pi$
$788$	−727.619	+	420.091i	−0.923375	+	0.533111i
$789$		0			0
$790$	20.5698	−	35.6280i	0.0260378	−	0.0450988i
$791$		−	253.593i		−	0.320598i
$792$		0			0
$793$	146.456			0.184686
$794$	−150.137	−	86.6819i	−0.189090	−	0.109171i
$795$		0			0
$796$	−617.137	−	1068.91i	−0.775297	−	1.34285i
$797$	633.468	−	365.733i	0.794816	−	0.458887i	−0.0468395	−	0.998902i	$-0.514915\pi$
$797$	633.468	−	365.733i	0.794816	−	0.458887i	0.841655	+	0.540015i	$0.181582\pi$
$798$		0			0
$799$	−275.541	+	477.251i	−0.344857	+	0.597310i
$800$		−	87.2542i		−	0.109068i
$801$		0			0
$802$	−212.529			−0.264998
$803$	359.817	+	207.741i	0.448092	+	0.258706i
$804$		0			0
$805$	−117.812	−	204.056i	−0.146350	−	0.253485i
$806$	−79.6797	+	46.0031i	−0.0988582	+	0.0570758i
$807$		0			0
$808$	36.0000	−	62.3538i	0.0445545	−	0.0771706i
$809$			595.767i			0.736424i	0.929742	+	0.368212i	$0.120030\pi$
$809$			595.767i			0.736424i	−0.929742	+	0.368212i	$0.879970\pi$
$810$		0			0
$811$	180.177			0.222166			0.111083	−	0.993811i	$-0.464568\pi$
$811$	180.177			0.222166			0.111083	+	0.993811i	$0.464568\pi$
$812$	693.968	+	400.663i	0.854640	+	0.493427i
$813$		0			0
$814$	83.4528	+	144.544i	0.102522	+	0.177573i
$815$	71.3264	−	41.1803i	0.0875171	−	0.0505280i
$816$		0			0
$817$	199.261	−	345.131i	0.243894	−	0.422436i
$818$			28.9005i			0.0353307i
$819$		0			0
$820$	523.666			0.638617
$821$	−27.1390	−	15.6687i	−0.0330561	−	0.0190849i	0.483381	−	0.875410i	$-0.339409\pi$
$821$	−27.1390	−	15.6687i	−0.0330561	−	0.0190849i	−0.516437	+	0.856325i	$0.672742\pi$
$822$		0			0
$823$	117.401	+	203.345i	0.142650	+	0.247078i	0.928494	−	0.371348i	$-0.121104\pi$
$823$	117.401	+	203.345i	0.142650	+	0.247078i	−0.785843	+	0.618425i	$0.787771\pi$
$824$	−65.3863	+	37.7508i	−0.0793523	+	0.0458140i
$825$		0			0
$826$	−64.2794	+	111.335i	−0.0778201	+	0.134788i
$827$		−	47.8003i		−	0.0577996i	−0.999582	−	0.0288998i	$-0.990800\pi$
$827$		−	47.8003i		−	0.0577996i	0.999582	−	0.0288998i	$-0.00920038\pi$
$828$		0			0
$829$	−292.760			−0.353148			−0.176574	−	0.984287i	$-0.556502\pi$
$829$	−292.760			−0.353148			−0.176574	+	0.984287i	$0.556502\pi$
$830$	−46.3521	−	26.7614i	−0.0558459	−	0.0322427i
$831$		0			0
$832$	−194.310	−	336.555i	−0.233546	−	0.404513i
$833$	−364.619	+	210.513i	−0.437718	+	0.252717i
$834$		0			0
$835$	289.102	−	500.739i	0.346230	−	0.599687i
$836$		−	176.039i		−	0.210573i
$837$		0			0
$838$	199.027			0.237502
$839$	−428.152	−	247.193i	−0.510312	−	0.294629i	0.222650	−	0.974898i	$-0.428529\pi$
$839$	−428.152	−	247.193i	−0.510312	−	0.294629i	−0.732962	+	0.680270i	$0.761863\pi$
$840$		0			0
$841$	1151.36	+	1994.21i	1.36904	+	2.37124i
$842$	37.9566	−	21.9143i	0.0450791	−	0.0260264i
$843$		0			0
$844$	123.009	−	213.058i	0.145745	−	0.252438i
$845$			245.036i			0.289984i
$846$		0			0
$847$	200.547			0.236774
$848$	−906.637	−	523.447i	−1.06915	−	0.617273i
$849$		0			0
$850$	−11.4058	−	19.7554i	−0.0134185	−	0.0232416i
$851$	−1314.54	+	758.951i	−1.54470	+	0.891835i
$852$		0			0
$853$	575.823	−	997.356i	0.675057	−	1.16923i	−0.301395	−	0.953499i	$-0.597452\pi$
$853$	575.823	−	997.356i	0.675057	−	1.16923i	0.976452	−	0.215734i	$-0.0692143\pi$
$854$			26.9117i			0.0315126i
$855$		0			0
$856$	−142.997			−0.167052
$857$	−950.916	−	549.012i	−1.10959	−	0.640620i	−0.170865	−	0.985295i	$-0.554656\pi$
$857$	−950.916	−	549.012i	−1.10959	−	0.640620i	−0.938722	+	0.344674i	$0.887989\pi$
$858$		0			0
$859$	145.378	+	251.803i	0.169242	+	0.293135i	0.938153	−	0.346220i	$-0.112535\pi$
$859$	145.378	+	251.803i	0.169242	+	0.293135i	−0.768912	+	0.639355i	$0.779202\pi$
$860$	532.694	−	307.551i	0.619412	−	0.357618i
$861$		0			0
$862$	44.5379	−	77.1419i	0.0516681	−	0.0894918i
$863$		−	1069.28i		−	1.23903i	−0.784985	−	0.619514i	$-0.787330\pi$
$863$		−	1069.28i		−	1.23903i	0.784985	−	0.619514i	$-0.212670\pi$
$864$		0			0
$865$	−407.705			−0.471335
$866$	165.959	+	95.8166i	0.191639	+	0.110643i
$867$		0			0
$868$	223.304	+	386.773i	0.257262	+	0.445592i
$869$	341.235	−	197.012i	0.392675	−	0.226711i
$870$		0			0
$871$	−1.28869	+	2.23208i	−0.00147955	+	0.00256266i
$872$			494.745i			0.567368i
$873$		0			0
$874$	−60.6049			−0.0693420
$875$	−35.9045	−	20.7295i	−0.0410337	−	0.0236908i
$876$		0			0
$877$	80.0213	+	138.601i	0.0912443	+	0.158040i	0.908035	−	0.418894i	$-0.137582\pi$
$877$	80.0213	+	138.601i	0.0912443	+	0.158040i	−0.816791	+	0.576934i	$0.804249\pi$
$878$	121.069	−	69.8992i	0.137892	−	0.0796118i
$879$		0			0
$880$	130.517	−	226.061i	0.148314	−	0.256888i
$881$		−	712.502i		−	0.808743i	−0.914595	−	0.404371i	$-0.867490\pi$
$881$		−	712.502i		−	0.808743i	0.914595	−	0.404371i	$-0.132510\pi$
$882$		0			0
$883$	−1244.12			−1.40897			−0.704486	−	0.709718i	$-0.748822\pi$
$883$	−1244.12			−1.40897			−0.704486	+	0.709718i	$0.748822\pi$
$884$	−307.303	−	177.421i	−0.347628	−	0.200703i
$885$		0			0
$886$	120.874	+	209.359i	0.136426	+	0.236297i
$887$	−372.241	+	214.913i	−0.419663	+	0.242292i	−0.694933	−	0.719075i	$-0.744566\pi$
$887$	−372.241	+	214.913i	−0.419663	+	0.242292i	0.275270	+	0.961367i	$0.411233\pi$
$888$		0			0
$889$	372.207	−	644.681i	0.418680	−	0.725175i
$890$		−	59.5379i		−	0.0668965i
$891$		0			0
$892$	−31.7933			−0.0356428
$893$	223.101	+	128.807i	0.249833	+	0.144241i
$894$		0			0
$895$	−287.082	−	497.241i	−0.320762	−	0.555576i
$896$	286.010	−	165.128i	0.319207	−	0.184294i
$897$		0			0
$898$	−152.088	+	263.425i	−0.169363	+	0.293346i
$899$			1752.11i			1.94895i
$900$		0			0
$901$	−876.240			−0.972519
$902$	−164.427	−	94.9318i	−0.182291	−	0.105246i
$903$		0			0
$904$	−102.580	−	177.675i	−0.113474	−	0.196543i
$905$	−348.727	+	201.338i	−0.385334	+	0.222473i
$906$		0			0
$907$	276.620	−	479.120i	0.304983	−	0.528247i	−0.672274	−	0.740302i	$-0.734682\pi$
$907$	276.620	−	479.120i	0.304983	−	0.528247i	0.977258	+	0.212055i	$0.0680157\pi$
$908$		−	1308.56i		−	1.44115i
$909$		0			0
$910$	24.4133			0.0268278
$911$	577.877	+	333.637i	0.634333	+	0.366232i	0.782428	−	0.622741i	$-0.213981\pi$
$911$	577.877	+	333.637i	0.634333	+	0.366232i	−0.148096	+	0.988973i	$0.547314\pi$
$912$		0			0
$913$	−256.313	−	443.947i	−0.280737	−	0.486251i
$914$	−67.0110	+	38.6888i	−0.0733162	+	0.0423291i
$915$		0			0
$916$	−390.219	+	675.879i	−0.426003	+	0.737859i
$917$		−	30.2741i		−	0.0330143i
$918$		0			0
$919$	−338.000			−0.367791			−0.183896	−	0.982946i	$-0.558871\pi$
$919$	−338.000			−0.367791			−0.183896	+	0.982946i	$0.558871\pi$
$920$	−165.084	−	95.3115i	−0.179440	−	0.103599i
$921$		0			0
$922$	139.018	+	240.787i	0.150779	+	0.261157i
$923$	542.467	−	313.193i	0.587722	−	0.339321i
$924$		0			0
$925$	−133.541	+	231.300i	−0.144369	+	0.250054i
$926$			188.310i			0.203359i
$927$		0			0
$928$	978.450			1.05436
$929$	187.779	+	108.414i	0.202131	+	0.116700i	0.597649	−	0.801758i	$-0.296102\pi$
$929$	187.779	+	108.414i	0.202131	+	0.116700i	−0.395518	+	0.918458i	$0.629435\pi$
$930$		0			0
$931$	98.4086	+	170.449i	0.105702	+	0.183081i
$932$	63.6911	−	36.7721i	0.0683381	−	0.0394550i
$933$		0			0
$934$	−86.5517	+	149.912i	−0.0926677	+	0.160505i
$935$		−	218.482i		−	0.233671i
$936$		0			0
$937$	−851.647			−0.908908			−0.454454	−	0.890770i	$-0.650166\pi$
$937$	−851.647			−0.908908			−0.454454	+	0.890770i	$0.650166\pi$
$938$	−0.410152	−	0.236801i	−0.000437262	−	0.000252453i
$939$		0			0
$940$	198.808	+	344.346i	0.211498	+	0.366326i
$941$	−929.613	+	536.712i	−0.987899	+	0.570363i	−0.904645	−	0.426165i	$-0.859864\pi$
$941$	−929.613	+	536.712i	−0.987899	+	0.570363i	−0.0832531	+	0.996528i	$0.526531\pi$
$942$		0			0
$943$	863.346	−	1495.36i	0.915532	−	1.58575i
$944$		−	1295.25i		−	1.37208i
$945$		0			0
$946$	−223.016			−0.235746
$947$	−1425.32	−	822.910i	−1.50509	−	0.868965i	−0.999983	−	0.00591016i	$-0.998119\pi$
$947$	−1425.32	−	822.910i	−1.50509	−	0.868965i	−0.505110	−	0.863055i	$-0.668548\pi$
$948$		0			0
$949$	−195.751	−	339.050i	−0.206271	−	0.357271i
$950$	−9.23505	+	5.33186i	−0.00972110	+	0.00561248i
$951$		0			0
$952$	66.4377	−	115.073i	0.0697875	−	0.120875i
$953$			1139.03i			1.19520i	0.801793	+	0.597602i	$0.203880\pi$
$953$			1139.03i			1.19520i	−0.801793	+	0.597602i	$0.796120\pi$
$954$		0			0
$955$	287.082			0.300609
$956$	−909.904	−	525.333i	−0.951782	−	0.549512i
$957$		0			0
$958$	61.0275	+	105.703i	0.0637030	+	0.110337i
$959$	161.634	−	93.3193i	0.168544	−	0.0973090i
$960$		0			0
$961$	−7.75699	+	13.4355i	−0.00807179	+	0.0139807i
$962$		−	157.272i		−	0.163485i
$963$		0			0
$964$	896.389			0.929864
$965$	124.501	+	71.8804i	0.129016	+	0.0744875i
$966$		0			0
$967$	178.745	+	309.595i	0.184844	+	0.320160i	0.943524	−	0.331304i	$-0.107489\pi$
$967$	178.745	+	309.595i	0.184844	+	0.320160i	−0.758680	+	0.651464i	$0.774155\pi$
$968$	140.509	−	81.1231i	0.145154	−	0.0838048i
$969$		0			0
$970$	−68.0789	+	117.916i	−0.0701845	+	0.121563i
$971$		−	46.5836i		−	0.0479749i	−0.999712	−	0.0239874i	$-0.992364\pi$
$971$		−	46.5836i		−	0.0479749i	0.999712	−	0.0239874i	$-0.00763617\pi$
$972$		0			0
$973$	−469.082			−0.482099
$974$	−262.275	−	151.425i	−0.269276	−	0.155467i
$975$		0			0
$976$	−135.570	−	234.814i	−0.138904	−	0.240588i
$977$	300.178	−	173.308i	0.307245	−	0.177388i	−0.338448	−	0.940985i	$-0.609902\pi$
$977$	300.178	−	173.308i	0.307245	−	0.177388i	0.645693	+	0.763597i	$0.276569\pi$
$978$		0			0
$979$	285.118	−	493.840i	0.291234	−	0.504433i
$980$			303.779i			0.309979i
$981$		0			0
$982$	141.112			0.143699
$983$	733.502	+	423.488i	0.746187	+	0.430811i	0.824315	−	0.566132i	$-0.191561\pi$
$983$	733.502	+	423.488i	0.746187	+	0.430811i	−0.0781274	+	0.996943i	$0.524894\pi$
$984$		0			0
$985$	243.728	+	422.149i	0.247440	+	0.428578i
$986$	221.532	−	127.902i	0.224678	−	0.129718i
$987$		0			0
$988$	−82.9392	+	143.655i	−0.0839466	+	0.145400i
$989$		−	2028.19i		−	2.05075i
$990$		0			0
$991$	1304.33			1.31617			0.658085	−	0.752943i	$-0.271367\pi$
$991$	1304.33			1.31617			0.658085	+	0.752943i	$0.271367\pi$
$992$	472.266	+	272.663i	0.476074	+	0.274862i
$993$		0			0
$994$	57.5503	+	99.6801i	0.0578977	+	0.100282i
$995$	−620.160	+	358.050i	−0.623276	+	0.359849i
$996$		0			0
$997$	−917.887	+	1589.83i	−0.920649	+	1.59461i	−0.122236	+	0.992501i	$0.539007\pi$
$997$	−917.887	+	1589.83i	−0.920649	+	1.59461i	−0.798413	+	0.602110i	$0.794327\pi$
$998$			232.966i			0.233432i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.i.c.26.2		8
3.2	odd	2	inner	405.3.i.c.26.3		8
9.2	odd	6		135.3.c.c.26.2	✓	4
9.4	even	3	inner	405.3.i.c.296.3		8
9.5	odd	6	inner	405.3.i.c.296.2		8
9.7	even	3		135.3.c.c.26.3	yes	4
36.7	odd	6		2160.3.l.g.161.1		4
36.11	even	6		2160.3.l.g.161.3		4
45.2	even	12		675.3.d.i.674.2		4
45.7	odd	12		675.3.d.e.674.4		4
45.29	odd	6		675.3.c.p.26.3		4
45.34	even	6		675.3.c.p.26.2		4
45.38	even	12		675.3.d.e.674.3		4
45.43	odd	12		675.3.d.i.674.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.c.c.26.2	✓	4	9.2	odd	6
135.3.c.c.26.3	yes	4	9.7	even	3
405.3.i.c.26.2		8	1.1	even	1	trivial
405.3.i.c.26.3		8	3.2	odd	2	inner
405.3.i.c.296.2		8	9.5	odd	6	inner
405.3.i.c.296.3		8	9.4	even	3	inner
675.3.c.p.26.2		4	45.34	even	6
675.3.c.p.26.3		4	45.29	odd	6
675.3.d.e.674.3		4	45.38	even	12
675.3.d.e.674.4		4	45.7	odd	12
675.3.d.i.674.1		4	45.43	odd	12
675.3.d.i.674.2		4	45.2	even	12
2160.3.l.g.161.1		4	36.7	odd	6
2160.3.l.g.161.3		4	36.11	even	6

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.330792 - 0.190983i) q^{2} +(-1.92705 - 3.33775i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(-1.85410 + 3.21140i) q^{7} +3.00000i q^{8} +0.854102 q^{10} +(7.08438 + 4.09017i) q^{11} +(-3.85410 - 6.67550i) q^{13} +(1.22665 - 0.708204i) q^{14} +(-7.13525 + 12.3586i) q^{16} +11.9443i q^{17} +5.58359 q^{19} +(7.46344 + 4.30902i) q^{20} +(-1.56231 - 2.70599i) q^{22} +(24.6093 - 14.2082i) q^{23} +(2.50000 - 4.33013i) q^{25} +2.94427i q^{26} +14.2918 q^{28} +(48.5571 + 28.0344i) q^{29} +(15.6246 + 27.0626i) q^{31} +(15.1129 - 8.72542i) q^{32} +(2.28115 - 3.95107i) q^{34} -8.29180i q^{35} -53.4164 q^{37} +(-1.84701 - 1.06637i) q^{38} +(-3.35410 - 5.80948i) q^{40} +(52.6231 - 30.3820i) q^{41} +(35.6869 - 61.8116i) q^{43} -31.5279i q^{44} -10.8541 q^{46} +(39.9565 + 23.0689i) q^{47} +(17.6246 + 30.5267i) q^{49} +(-1.65396 + 0.954915i) q^{50} +(-14.8541 + 25.7281i) q^{52} +73.3607i q^{53} -18.2918 q^{55} +(-9.63420 - 5.56231i) q^{56} +(-10.7082 - 18.5472i) q^{58} +(-78.6039 + 45.3820i) q^{59} +(-9.50000 + 16.4545i) q^{61} -11.9361i q^{62} +50.4164 q^{64} +(14.9269 + 8.61803i) q^{65} +(-0.167184 - 0.289572i) q^{67} +(39.8670 - 23.0172i) q^{68} +(-1.58359 + 2.74286i) q^{70} +81.2624i q^{71} +50.7902 q^{73} +(17.6697 + 10.2016i) q^{74} +(-10.7599 - 18.6366i) q^{76} +(-26.2703 + 15.1672i) q^{77} +(24.0836 - 41.7140i) q^{79} -31.9098i q^{80} -23.2098 q^{82} +(-54.2700 - 31.3328i) q^{83} +(-13.3541 - 23.1300i) q^{85} +(-23.6099 + 13.6312i) q^{86} +(-12.2705 + 21.2531i) q^{88} -69.7082i q^{89} +28.5836 q^{91} +(-94.8469 - 54.7599i) q^{92} +(-8.81153 - 15.2620i) q^{94} +(-10.8126 + 6.24265i) q^{95} +(-79.7082 + 138.059i) q^{97} -13.4640i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 12 q^{7} - 20 q^{10} - 4 q^{13} + 10 q^{16} + 152 q^{19} + 68 q^{22} + 20 q^{25} + 168 q^{28} - 36 q^{31} - 22 q^{34} - 320 q^{37} + 44 q^{43} - 60 q^{46} - 20 q^{49} - 92 q^{52} - 200 q^{55}+ \cdots - 584 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 + 12 * q^7 - 20 * q^10 - 4 * q^13 + 10 * q^16 + 152 * q^19 + 68 * q^22 + 20 * q^25 + 168 * q^28 - 36 * q^31 - 22 * q^34 - 320 * q^37 + 44 * q^43 - 60 * q^46 - 20 * q^49 - 92 * q^52 - 200 * q^55 - 32 * q^58 - 76 * q^61 + 296 * q^64 - 216 * q^67 - 120 * q^70 - 184 * q^73 + 142 * q^76 + 300 * q^79 - 776 * q^82 - 80 * q^85 + 36 * q^88 + 336 * q^91 + 332 * q^94 - 584 * q^97

Introduction

L-functions

Modular forms

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