LMFDB - Embedded newform 387.3.j.f.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,3,Mod(37,387)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("387.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	387.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.5449862307$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	387.37
Dual form			387.3.j.f.136.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.70884i q^{2} +1.07986 q^{4} +(7.97167 + 4.60245i) q^{5} +(-1.33514 + 0.770846i) q^{7} +8.68068i q^{8} +O(q^{10})$	\(q+1.70884i q^{2} +1.07986 q^{4} +(7.97167 + 4.60245i) q^{5} +(-1.33514 + 0.770846i) q^{7} +8.68068i q^{8} +(-7.86485 + 13.6223i) q^{10} +5.84910 q^{11} +(2.25989 + 3.91424i) q^{13} +(-1.31725 - 2.28155i) q^{14} -10.5145 q^{16} +(-7.87698 - 13.6433i) q^{17} +(-9.62715 - 5.55824i) q^{19} +(8.60829 + 4.97000i) q^{20} +9.99518i q^{22} +(12.4615 - 21.5840i) q^{23} +(29.8650 + 51.7278i) q^{25} +(-6.68882 + 3.86179i) q^{26} +(-1.44177 + 0.832405i) q^{28} +(18.6860 - 10.7884i) q^{29} +(-2.22288 + 3.85015i) q^{31} +16.7551i q^{32} +(23.3143 - 13.4605i) q^{34} -14.1911 q^{35} +(-43.1990 - 24.9410i) q^{37} +(9.49814 - 16.4513i) q^{38} +(-39.9524 + 69.1995i) q^{40} +18.1706 q^{41} +(-34.2424 - 26.0088i) q^{43} +6.31621 q^{44} +(36.8836 + 21.2948i) q^{46} +2.15381 q^{47} +(-23.3116 + 40.3769i) q^{49} +(-88.3946 + 51.0346i) q^{50} +(2.44036 + 4.22683i) q^{52} +(-23.4374 + 40.5948i) q^{53} +(46.6271 + 26.9202i) q^{55} +(-6.69146 - 11.5900i) q^{56} +(18.4356 + 31.9315i) q^{58} -0.247991 q^{59} +(-28.1059 + 16.2269i) q^{61} +(-6.57930 - 3.79856i) q^{62} -70.6898 q^{64} +41.6041i q^{65} +(27.6303 - 47.8570i) q^{67} +(-8.50604 - 14.7329i) q^{68} -24.2504i q^{70} +(-67.4807 + 38.9600i) q^{71} +(77.7797 - 44.9061i) q^{73} +(42.6202 - 73.8203i) q^{74} +(-10.3960 - 6.00211i) q^{76} +(-7.80939 + 4.50875i) q^{77} +(24.9588 + 43.2299i) q^{79} +(-83.8179 - 48.3923i) q^{80} +31.0507i q^{82} +(59.4374 - 102.949i) q^{83} -145.014i q^{85} +(44.4450 - 58.5148i) q^{86} +50.7741i q^{88} +(36.1635 + 20.8790i) q^{89} +(-6.03455 - 3.48405i) q^{91} +(13.4567 - 23.3077i) q^{92} +3.68053i q^{94} +(-51.1630 - 88.6169i) q^{95} -46.2596 q^{97} +(-68.9977 - 39.8358i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 84 q^{4} - 30 q^{7}+O(q^{10}) $ 28 * q - 84 * q^4 - 30 * q^7	$ 28 q - 84 q^{4} - 30 q^{7} + 4 q^{10} - 34 q^{13} + 164 q^{16} - 78 q^{19} + 112 q^{25} + 342 q^{28} - 74 q^{31} + 192 q^{34} - 222 q^{37} + 104 q^{40} + 104 q^{43} + 150 q^{46} + 112 q^{49} - 64 q^{52} - 450 q^{55} + 346 q^{58} - 198 q^{61} - 1264 q^{64} - 26 q^{67} + 342 q^{73} + 282 q^{76} - 48 q^{79} + 684 q^{91} - 480 q^{97}+O(q^{100}) $ 28 * q - 84 * q^4 - 30 * q^7 + 4 * q^10 - 34 * q^13 + 164 * q^16 - 78 * q^19 + 112 * q^25 + 342 * q^28 - 74 * q^31 + 192 * q^34 - 222 * q^37 + 104 * q^40 + 104 * q^43 + 150 * q^46 + 112 * q^49 - 64 * q^52 - 450 * q^55 + 346 * q^58 - 198 * q^61 - 1264 * q^64 - 26 * q^67 + 342 * q^73 + 282 * q^76 - 48 * q^79 + 684 * q^91 - 480 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$			1.70884i			0.854421i	0.904152	+	0.427210i	$0.140504\pi$
$2$			1.70884i			0.854421i	−0.904152	+	0.427210i	$0.859496\pi$
$3$		0			0
$3$		0			0
$4$	1.07986			0.269965
$5$	7.97167	+	4.60245i	1.59433	+	0.920489i	0.992551	+	0.121830i	$0.0388763\pi$
$5$	7.97167	+	4.60245i	1.59433	+	0.920489i	0.601783	+	0.798659i	$0.294457\pi$
$6$		0			0
$7$	−1.33514	+	0.770846i	−0.190735	+	0.110121i	−0.592327	−	0.805698i	$-0.701790\pi$
$7$	−1.33514	+	0.770846i	−0.190735	+	0.110121i	0.401592	+	0.915819i	$0.368457\pi$
$8$			8.68068i			1.08508i
$9$		0			0
$10$	−7.86485	+	13.6223i	−0.786485	+	1.36223i
$11$	5.84910			0.531736			0.265868	−	0.964009i	$-0.414341\pi$
$11$	5.84910			0.531736			0.265868	+	0.964009i	$0.414341\pi$
$12$		0			0
$13$	2.25989	+	3.91424i	0.173838	+	0.301095i	0.939758	−	0.341839i	$-0.111050\pi$
$13$	2.25989	+	3.91424i	0.173838	+	0.301095i	−0.765921	+	0.642935i	$0.777717\pi$
$14$	−1.31725	−	2.28155i	−0.0940895	−	0.162968i
$15$		0			0
$16$	−10.5145			−0.657154
$17$	−7.87698	−	13.6433i	−0.463352	−	0.802549i	0.535773	−	0.844362i	$-0.320020\pi$
$17$	−7.87698	−	13.6433i	−0.463352	−	0.802549i	−0.999125	+	0.0418126i	$0.986687\pi$
$18$		0			0
$19$	−9.62715	−	5.55824i	−0.506692	−	0.292539i	0.224781	−	0.974409i	$-0.427833\pi$
$19$	−9.62715	−	5.55824i	−0.506692	−	0.292539i	−0.731473	+	0.681871i	$0.761167\pi$
$20$	8.60829	+	4.97000i	0.430414	+	0.248500i
$21$		0			0
$22$			9.99518i			0.454327i
$23$	12.4615	−	21.5840i	0.541805	−	0.938434i	−0.456996	−	0.889469i	$-0.651074\pi$
$23$	12.4615	−	21.5840i	0.541805	−	0.938434i	0.998801	−	0.0489647i	$-0.0155922\pi$
$24$		0			0
$25$	29.8650	+	51.7278i	1.19460	+	2.06911i
$26$	−6.68882	+	3.86179i	−0.257262	+	0.148530i
$27$		0			0
$28$	−1.44177	+	0.832405i	−0.0514917	+	0.0297288i
$29$	18.6860	−	10.7884i	0.644346	−	0.372013i	−0.141941	−	0.989875i	$-0.545334\pi$
$29$	18.6860	−	10.7884i	0.644346	−	0.372013i	0.786287	+	0.617862i	$0.212001\pi$
$30$		0			0
$31$	−2.22288	+	3.85015i	−0.0717060	+	0.124198i	−0.899649	−	0.436614i	$-0.856178\pi$
$31$	−2.22288	+	3.85015i	−0.0717060	+	0.124198i	0.827943	+	0.560812i	$0.189511\pi$
$32$			16.7551i			0.523598i
$33$		0			0
$34$	23.3143	−	13.4605i	0.685715	−	0.395898i
$35$	−14.1911			−0.405460
$36$		0			0
$37$	−43.1990	−	24.9410i	−1.16754	−	0.674080i	−0.214442	−	0.976737i	$-0.568793\pi$
$37$	−43.1990	−	24.9410i	−1.16754	−	0.674080i	−0.953100	+	0.302657i	$0.902127\pi$
$38$	9.49814	−	16.4513i	0.249951	−	0.432928i
$39$		0			0
$40$	−39.9524	+	69.1995i	−0.998809	+	1.72999i
$41$	18.1706			0.443186			0.221593	−	0.975139i	$-0.428874\pi$
$41$	18.1706			0.443186			0.221593	+	0.975139i	$0.428874\pi$
$42$		0			0
$43$	−34.2424	−	26.0088i	−0.796335	−	0.604856i
$43$	−34.2424	−	26.0088i	−0.796335	−	0.604856i
$44$	6.31621			0.143550
$45$		0			0
$46$	36.8836	+	21.2948i	0.801817	+	0.462929i
$47$	2.15381			0.0458258			0.0229129	−	0.999737i	$-0.492706\pi$
$47$	2.15381			0.0458258			0.0229129	+	0.999737i	$0.492706\pi$
$48$		0			0
$49$	−23.3116	+	40.3769i	−0.475747	+	0.824018i
$50$	−88.3946	+	51.0346i	−1.76789	+	1.02069i
$51$		0			0
$52$	2.44036	+	4.22683i	0.0469300	+	0.0812852i
$53$	−23.4374	+	40.5948i	−0.442215	+	0.765939i	−0.997854	−	0.0654848i	$-0.979141\pi$
$53$	−23.4374	+	40.5948i	−0.442215	+	0.765939i	0.555638	+	0.831424i	$0.312474\pi$
$54$		0			0
$55$	46.6271	+	26.9202i	0.847765	+	0.489458i
$56$	−6.69146	−	11.5900i	−0.119490	−	0.206963i
$57$		0			0
$58$	18.4356	+	31.9315i	0.317856	+	0.550543i
$59$	−0.247991			−0.00420324			−0.00210162	−	0.999998i	$-0.500669\pi$
$59$	−0.247991			−0.00420324			−0.00210162	+	0.999998i	$0.500669\pi$
$60$		0			0
$61$	−28.1059	+	16.2269i	−0.460752	+	0.266015i	−0.712360	−	0.701814i	$-0.752374\pi$
$61$	−28.1059	+	16.2269i	−0.460752	+	0.266015i	0.251609	+	0.967829i	$0.419040\pi$
$62$	−6.57930	−	3.79856i	−0.106118	−	0.0612671i
$63$		0			0
$64$	−70.6898			−1.10453
$65$			41.6041i			0.640062i
$66$		0			0
$67$	27.6303	−	47.8570i	0.412392	−	0.714284i	−0.582759	−	0.812645i	$-0.698027\pi$
$67$	27.6303	−	47.8570i	0.412392	−	0.714284i	0.995151	+	0.0983615i	$0.0313601\pi$
$68$	−8.50604	−	14.7329i	−0.125089	−	0.216660i
$69$		0			0
$70$		−	24.2504i		−	0.346434i
$71$	−67.4807	+	38.9600i	−0.950432	+	0.548732i	−0.893215	−	0.449630i	$-0.851556\pi$
$71$	−67.4807	+	38.9600i	−0.950432	+	0.548732i	−0.0572169	+	0.998362i	$0.518223\pi$
$72$		0			0
$73$	77.7797	−	44.9061i	1.06548	−	0.615152i	0.138533	−	0.990358i	$-0.455761\pi$
$73$	77.7797	−	44.9061i	1.06548	−	0.615152i	0.926942	+	0.375205i	$0.122428\pi$
$74$	42.6202	−	73.8203i	0.575948	−	0.997572i
$75$		0			0
$76$	−10.3960	−	6.00211i	−0.136789	−	0.0789752i
$77$	−7.80939	+	4.50875i	−0.101421	+	0.0585552i
$78$		0			0
$79$	24.9588	+	43.2299i	0.315934	+	0.547213i	0.979636	−	0.200784i	$-0.0643489\pi$
$79$	24.9588	+	43.2299i	0.315934	+	0.547213i	−0.663702	+	0.747997i	$0.731016\pi$
$80$	−83.8179	−	48.3923i	−1.04772	−	0.604903i
$81$		0			0
$82$			31.0507i			0.378667i
$83$	59.4374	−	102.949i	0.716114	−	1.24035i	−0.246415	−	0.969164i	$-0.579253\pi$
$83$	59.4374	−	102.949i	0.716114	−	1.24035i	0.962528	−	0.271181i	$-0.0874141\pi$
$84$		0			0
$85$		−	145.014i		−	1.70604i
$86$	44.4450	−	58.5148i	0.516802	−	0.680405i
$87$		0			0
$88$			50.7741i			0.576979i
$89$	36.1635	+	20.8790i	0.406331	+	0.234596i	0.689212	−	0.724560i	$-0.257957\pi$
$89$	36.1635	+	20.8790i	0.406331	+	0.234596i	−0.282881	+	0.959155i	$0.591290\pi$
$90$		0			0
$91$	−6.03455	−	3.48405i	−0.0663138	−	0.0382863i
$92$	13.4567	−	23.3077i	0.146268	−	0.253344i
$93$		0			0
$94$			3.68053i			0.0391545i
$95$	−51.1630	−	88.6169i	−0.538558	−	0.932809i
$96$		0			0
$97$	−46.2596			−0.476903			−0.238451	−	0.971154i	$-0.576640\pi$
$97$	−46.2596			−0.476903			−0.238451	+	0.971154i	$0.576640\pi$
$98$	−68.9977	−	39.8358i	−0.704058	−	0.406488i
$99$		0			0
$100$	32.2500	+	55.8587i	0.322500	+	0.558587i
$101$	93.8463	+	162.547i	0.929172	+	1.60937i	0.784711	+	0.619862i	$0.212811\pi$
$101$	93.8463	+	162.547i	0.929172	+	1.60937i	0.144460	+	0.989511i	$0.453855\pi$
$102$		0			0
$103$	−83.5698	−	144.747i	−0.811357	−	1.40531i	−0.911914	−	0.410381i	$-0.865396\pi$
$103$	−83.5698	−	144.747i	−0.811357	−	1.40531i	0.100557	−	0.994931i	$-0.467938\pi$
$104$	−33.9783	+	19.6174i	−0.326714	+	0.188628i
$105$		0			0
$106$	−69.3701	−	40.0508i	−0.654435	−	0.377838i
$107$	120.107			1.12250			0.561248	−	0.827648i	$-0.310321\pi$
$107$	120.107			1.12250			0.561248	+	0.827648i	$0.310321\pi$
$108$		0			0
$109$	77.5526	−	134.325i	0.711492	−	1.23234i	−0.252805	−	0.967517i	$-0.581353\pi$
$109$	77.5526	−	134.325i	0.711492	−	1.23234i	0.964297	−	0.264823i	$-0.0853134\pi$
$110$	−46.0023	+	79.6783i	−0.418203	+	0.724348i
$111$		0			0
$112$	14.0383	−	8.10503i	0.125342	−	0.0723663i
$113$		−	121.935i		−	1.07907i	−0.841962	−	0.539537i	$-0.818599\pi$
$113$		−	121.935i		−	1.07907i	0.841962	−	0.539537i	$-0.181401\pi$
$114$		0			0
$115$	198.678	−	114.707i	1.72764	−	0.997451i
$116$	20.1783	−	11.6499i	0.173951	−	0.100431i
$117$		0			0
$118$		−	0.423778i		−	0.00359134i
$119$	21.0338	+	12.1439i	0.176755	+	0.102049i
$120$		0			0
$121$	−86.7880			−0.717257
$122$	−27.7292	−	48.0285i	−0.227289	−	0.393676i
$123$		0			0
$124$	−2.40040	+	4.15762i	−0.0193581	+	0.0335292i
$125$			319.687i			2.55749i
$126$		0			0
$127$	155.902			1.22758			0.613788	−	0.789471i	$-0.289645\pi$
$127$	155.902			1.22758			0.613788	+	0.789471i	$0.289645\pi$
$128$		−	53.7770i		−	0.420133i
$129$		0			0
$130$	−71.0948			−0.546883
$131$		−	70.3790i		−	0.537245i	−0.963246	−	0.268622i	$-0.913432\pi$
$131$		−	70.3790i		−	0.537245i	0.963246	−	0.268622i	$-0.0865683\pi$
$132$		0			0
$133$	17.1382			0.128858
$134$	81.7801	+	47.2157i	0.610299	+	0.352356i
$135$		0			0
$136$	118.433	−	68.3775i	0.870834	−	0.502776i
$137$			133.621i			0.975336i	0.873029	+	0.487668i	$0.162152\pi$
$137$			133.621i			0.975336i	−0.873029	+	0.487668i	$0.837848\pi$
$138$		0			0
$139$	32.2309	−	55.8256i	0.231877	−	0.401623i	−0.726483	−	0.687184i	$-0.758847\pi$
$139$	32.2309	−	55.8256i	0.231877	−	0.401623i	0.958361	+	0.285561i	$0.0921799\pi$
$140$	−15.3244			−0.109460
$141$		0			0
$142$	−66.5765	−	115.314i	−0.468848	−	0.812069i
$143$	13.2183	+	22.8948i	0.0924357	+	0.160103i
$144$		0			0
$145$	198.612			1.36974
$146$	76.7375	+	132.913i	0.525599	+	0.910364i
$147$		0			0
$148$	−46.6489	−	26.9327i	−0.315195	−	0.181978i
$149$	209.806	+	121.131i	1.40809	+	0.812962i	0.995204	−	0.0978195i	$-0.0311868\pi$
$149$	209.806	+	121.131i	1.40809	+	0.812962i	0.412888	+	0.910782i	$0.364520\pi$
$150$		0			0
$151$		−	239.189i		−	1.58404i	−0.610498	−	0.792018i	$-0.709031\pi$
$151$		−	239.189i		−	1.58404i	0.610498	−	0.792018i	$-0.290969\pi$
$152$	48.2492	−	83.5701i	0.317429	−	0.549804i
$153$		0			0
$154$	−7.70474	−	13.3450i	−0.0500308	−	0.0866559i
$155$	−35.4402	+	20.4614i	−0.228647	+	0.132009i
$156$		0			0
$157$	−245.133	+	141.528i	−1.56136	+	0.901451i	−0.564238	+	0.825612i	$0.690830\pi$
$157$	−245.133	+	141.528i	−1.56136	+	0.901451i	−0.997120	+	0.0758383i	$0.975837\pi$
$158$	−73.8730	+	42.6506i	−0.467551	+	0.269940i
$159$		0			0
$160$	−77.1147	+	133.567i	−0.481967	+	0.834791i
$161$			38.4236i			0.238656i
$162$		0			0
$163$	−206.547	+	119.250i	−1.26716	+	0.731596i	−0.974450	−	0.224606i	$-0.927891\pi$
$163$	−206.547	+	119.250i	−1.26716	+	0.731596i	−0.292711	+	0.956201i	$0.594557\pi$
$164$	19.6217			0.119645
$165$		0			0
$166$	175.923	+	101.569i	1.05978	+	0.611862i
$167$	150.436	−	260.564i	0.900817	−	1.56026i	0.0743819	−	0.997230i	$-0.476302\pi$
$167$	150.436	−	260.564i	0.900817	−	1.56026i	0.826435	−	0.563032i	$-0.190365\pi$
$168$		0			0
$169$	74.2858	−	128.667i	0.439561	−	0.761342i
$170$	247.805			1.45768
$171$		0			0
$172$	−36.9770	−	28.0859i	−0.214982	−	0.163290i
$173$	−18.8457			−0.108935			−0.0544675	−	0.998516i	$-0.517346\pi$
$173$	−18.8457			−0.108935			−0.0544675	+	0.998516i	$0.517346\pi$
$174$		0			0
$175$	−79.7482	−	46.0427i	−0.455704	−	0.263101i
$176$	−61.5001			−0.349433
$177$		0			0
$178$	−35.6789	+	61.7977i	−0.200443	+	0.347178i
$179$	−171.526	+	99.0305i	−0.958245	+	0.553243i	−0.895632	−	0.444795i	$-0.853277\pi$
$179$	−171.526	+	99.0305i	−0.958245	+	0.553243i	−0.0626124	+	0.998038i	$0.519943\pi$
$180$		0			0
$181$	51.2468	+	88.7620i	0.283131	+	0.490398i	0.972154	−	0.234342i	$-0.0752934\pi$
$181$	51.2468	+	88.7620i	0.283131	+	0.490398i	−0.689023	+	0.724740i	$0.741960\pi$
$182$	5.95369	−	10.3121i	0.0327126	−	0.0566599i
$183$		0			0
$184$	187.364	+	108.174i	1.01828	+	0.587904i
$185$	−229.579	−	397.642i	−1.24097	−	2.14942i
$186$		0			0
$187$	−46.0733	−	79.8012i	−0.246381	−	0.426744i
$188$	2.32582			0.0123714
$189$		0			0
$190$	151.432	−	87.4294i	0.797012	−	0.460155i
$191$	−138.649	−	80.0491i	−0.725912	−	0.419105i	0.0910130	−	0.995850i	$-0.470990\pi$
$191$	−138.649	−	80.0491i	−0.725912	−	0.419105i	−0.816925	+	0.576744i	$0.804323\pi$
$192$		0			0
$193$	−59.1113			−0.306276			−0.153138	−	0.988205i	$-0.548938\pi$
$193$	−59.1113			−0.306276			−0.153138	+	0.988205i	$0.548938\pi$
$194$		−	79.0503i		−	0.407476i
$195$		0			0
$196$	−25.1732	+	43.6013i	−0.128435	+	0.222456i
$197$	−80.1417	−	138.810i	−0.406811	−	0.704617i	0.587720	−	0.809065i	$-0.300026\pi$
$197$	−80.1417	−	138.810i	−0.406811	−	0.704617i	−0.994530	+	0.104448i	$0.966692\pi$
$198$		0			0
$199$		−	261.180i		−	1.31246i	−0.754559	−	0.656232i	$-0.772149\pi$
$199$		−	261.180i		−	1.31246i	0.754559	−	0.656232i	$-0.227851\pi$
$200$	−449.032	+	259.249i	−2.24516	+	1.29624i
$201$		0			0
$202$	−277.766	+	160.369i	−1.37508	+	0.793904i
$203$	−16.6324	+	28.8081i	−0.0819328	+	0.141912i
$204$		0			0
$205$	144.850	+	83.6293i	0.706587	+	0.407948i
$206$	247.350	−	142.808i	1.20073	−	0.693241i
$207$		0			0
$208$	−23.7615	−	41.1562i	−0.114238	−	0.197866i
$209$	−56.3101	−	32.5107i	−0.269426	−	0.155553i
$210$		0			0
$211$		−	167.698i		−	0.794775i	−0.917651	−	0.397388i	$-0.869917\pi$
$211$		−	167.698i		−	0.794775i	0.917651	−	0.397388i	$-0.130083\pi$
$212$	−25.3091	+	43.8367i	−0.119383	+	0.206777i
$213$		0			0
$214$			205.244i			0.959084i
$215$	−153.265	−	364.933i	−0.712860	−	1.69736i
$216$		0			0
$217$		−	6.85400i		−	0.0315853i
$218$	229.540	+	132.525i	1.05294	+	0.607913i
$219$		0			0
$220$	50.3507	+	29.0700i	0.228867	+	0.132136i
$221$	35.6022	−	61.6648i	0.161096	−	0.279026i
$222$		0			0
$223$			155.244i			0.696160i	0.937465	+	0.348080i	$0.113166\pi$
$223$			155.244i			0.696160i	−0.937465	+	0.348080i	$0.886834\pi$
$224$	−12.9156	−	22.3705i	−0.0576591	−	0.0998685i
$225$		0			0
$226$	208.368			0.921984
$227$	−369.523	−	213.344i	−1.62785	−	0.939842i	−0.984732	−	0.174078i	$-0.944305\pi$
$227$	−369.523	−	213.344i	−1.62785	−	0.939842i	−0.643122	−	0.765764i	$-0.722361\pi$
$228$		0			0
$229$	145.684	+	252.333i	0.636176	+	1.10189i	0.986265	+	0.165173i	$0.0528182\pi$
$229$	145.684	+	252.333i	0.636176	+	1.10189i	−0.350089	+	0.936717i	$0.613849\pi$
$230$	196.016	+	339.510i	0.852243	+	1.47613i
$231$		0			0
$232$	93.6505	+	162.207i	0.403666	+	0.699170i
$233$	84.3217	−	48.6832i	0.361896	−	0.208941i	−0.308016	−	0.951381i	$-0.599665\pi$
$233$	84.3217	−	48.6832i	0.361896	−	0.208941i	0.669912	+	0.742440i	$0.266332\pi$
$234$		0			0
$235$	17.1695	+	9.91281i	0.0730617	+	0.0421822i
$236$	−0.267796			−0.00113473
$237$		0			0
$238$	−20.7520	+	35.9435i	−0.0871931	+	0.151023i
$239$	−129.298	+	223.950i	−0.540995	+	0.937031i	0.457852	+	0.889028i	$0.348619\pi$
$239$	−129.298	+	223.950i	−0.540995	+	0.937031i	−0.998847	+	0.0480025i	$0.984714\pi$
$240$		0			0
$241$	−366.083	+	211.358i	−1.51902	+	0.877006i	−0.519269	+	0.854611i	$0.673796\pi$
$241$	−366.083	+	211.358i	−1.51902	+	0.877006i	−0.999749	+	0.0223946i	$0.992871\pi$
$242$		−	148.307i		−	0.612839i
$243$		0			0
$244$	−30.3504	+	17.5228i	−0.124387	+	0.0718148i
$245$	−371.665	+	214.581i	−1.51700	+	0.875840i
$246$		0			0
$247$		−	50.2440i		−	0.203417i
$248$	−33.4219	−	19.2961i	−0.134766	−	0.0778070i
$249$		0			0
$250$	−546.294			−2.18518
$251$	62.1427	+	107.634i	0.247580	+	0.428822i	0.962854	−	0.270023i	$-0.0870312\pi$
$251$	62.1427	+	107.634i	0.247580	+	0.428822i	−0.715273	+	0.698845i	$0.753698\pi$
$252$		0			0
$253$	72.8886	−	126.247i	0.288097	−	0.498999i
$254$			266.412i			1.04887i
$255$		0			0
$256$	−190.863			−0.745557
$257$		−	417.246i		−	1.62353i	−0.583987	−	0.811763i	$-0.698508\pi$
$257$		−	417.246i		−	1.62353i	0.583987	−	0.811763i	$-0.301492\pi$
$258$		0			0
$259$	76.9026			0.296921
$260$			44.9265i			0.172794i
$261$		0			0
$262$	120.267			0.459033
$263$	376.260	+	217.234i	1.43065	+	0.825985i	0.997170	−	0.0751798i	$-0.0239531\pi$
$263$	376.260	+	217.234i	1.43065	+	0.825985i	0.433477	+	0.901164i	$0.357286\pi$
$264$		0			0
$265$	−373.671	+	215.739i	−1.41008	+	0.814109i
$266$			29.2864i			0.110099i
$267$		0			0
$268$	29.8368	−	51.6788i	0.111331	−	0.192832i
$269$	66.7250			0.248049			0.124024	−	0.992279i	$-0.460420\pi$
$269$	66.7250			0.248049			0.124024	+	0.992279i	$0.460420\pi$
$270$		0			0
$271$	196.977	+	341.174i	0.726852	+	1.25895i	0.958207	+	0.286076i	$0.0923509\pi$
$271$	196.977	+	341.174i	0.726852	+	1.25895i	−0.231355	+	0.972869i	$0.574316\pi$
$272$	82.8223	+	143.452i	0.304494	+	0.527398i
$273$		0			0
$274$	−228.337			−0.833348
$275$	174.684	+	302.561i	0.635213	+	1.10022i
$276$		0			0
$277$	211.120	+	121.890i	0.762165	+	0.440036i	0.830072	−	0.557656i	$-0.188299\pi$
$277$	211.120	+	121.890i	0.762165	+	0.440036i	−0.0679076	+	0.997692i	$0.521632\pi$
$278$	95.3971	+	55.0776i	0.343155	+	0.198121i
$279$		0			0
$280$		−	123.188i		−	0.439959i
$281$	−22.7131	+	39.3402i	−0.0808295	+	0.140001i	−0.903606	−	0.428364i	$-0.859090\pi$
$281$	−22.7131	+	39.3402i	−0.0808295	+	0.140001i	0.822777	+	0.568364i	$0.192424\pi$
$282$		0			0
$283$	132.974	+	230.318i	0.469874	+	0.813846i	0.999407	−	0.0344440i	$-0.0109660\pi$
$283$	132.974	+	230.318i	0.469874	+	0.813846i	−0.529533	+	0.848290i	$0.677633\pi$
$284$	−72.8697	+	42.0713i	−0.256583	+	0.148138i
$285$		0			0
$286$	−39.1236	+	22.5880i	−0.136796	+	0.0789790i
$287$	−24.2604	+	14.0067i	−0.0845310	+	0.0488040i
$288$		0			0
$289$	20.4063	−	35.3447i	0.0706099	−	0.122300i
$290$			339.396i			1.17033i
$291$		0			0
$292$	83.9911	−	48.4923i	0.287641	−	0.166070i
$293$	−99.0485			−0.338049			−0.169025	−	0.985612i	$-0.554062\pi$
$293$	−99.0485			−0.338049			−0.169025	+	0.985612i	$0.554062\pi$
$294$		0			0
$295$	−1.97691	−	1.14137i	−0.00670137	−	0.00386904i
$296$	216.505	−	374.997i	0.731434	−	1.26688i
$297$		0			0
$298$	−206.994	+	358.525i	−0.694612	+	1.20310i
$299$	112.647			0.376744
$300$		0			0
$301$	65.7673	+	8.32992i	0.218496	+	0.0276742i
$302$	408.737			1.35343
$303$		0			0
$304$	101.224	+	58.4419i	0.332975	+	0.192243i
$305$	−298.734			−0.979457
$306$		0			0
$307$	169.160	−	292.995i	0.551011	−	0.954380i	−0.447191	−	0.894439i	$-0.647575\pi$
$307$	169.160	−	292.995i	0.551011	−	0.954380i	0.998202	−	0.0599409i	$-0.0190912\pi$
$308$	−8.43304	+	4.86882i	−0.0273800	+	0.0158079i
$309$		0			0
$310$	−34.9653	−	60.5617i	−0.112791	−	0.195360i
$311$	−56.1999	+	97.3411i	−0.180707	+	0.312994i	−0.942122	−	0.335271i	$-0.891172\pi$
$311$	−56.1999	+	97.3411i	−0.180707	+	0.312994i	0.761414	+	0.648265i	$0.224505\pi$
$312$		0			0
$313$	−96.5588	−	55.7482i	−0.308494	−	0.178109i	0.337758	−	0.941233i	$-0.390331\pi$
$313$	−96.5588	−	55.7482i	−0.308494	−	0.178109i	−0.646253	+	0.763124i	$0.723665\pi$
$314$	−241.849	−	418.894i	−0.770218	−	1.33406i
$315$		0			0
$316$	26.9520	+	46.6822i	0.0852910	+	0.147728i
$317$	86.1990			0.271921			0.135961	−	0.990714i	$-0.456588\pi$
$317$	86.1990			0.271921			0.135961	+	0.990714i	$0.456588\pi$
$318$		0			0
$319$	109.296	−	63.1023i	0.342622	−	0.197813i
$320$	−563.516	−	325.346i	−1.76099	−	1.01671i
$321$		0			0
$322$	−65.6599			−0.203913
$323$			175.129i			0.542194i
$324$		0			0
$325$	−134.983	+	233.798i	−0.415333	+	0.719378i
$326$	−203.780	−	352.956i	−0.625090	−	1.08269i
$327$		0			0
$328$			157.733i			0.480894i
$329$	−2.87565	+	1.66026i	−0.00874058	+	0.00504638i
$330$		0			0
$331$	−37.6886	+	21.7595i	−0.113863	+	0.0657388i	−0.555850	−	0.831283i	$-0.687607\pi$
$331$	−37.6886	+	21.7595i	−0.113863	+	0.0657388i	0.441987	+	0.897021i	$0.354274\pi$
$332$	64.1841	−	111.170i	0.193326	−	0.334850i
$333$		0			0
$334$	445.262	+	257.072i	1.33312	+	0.769677i
$335$	440.519	−	254.334i	1.31498	−	0.759205i
$336$		0			0
$337$	49.9012	+	86.4314i	0.148075	+	0.256473i	0.930516	−	0.366252i	$-0.119359\pi$
$337$	49.9012	+	86.4314i	0.148075	+	0.256473i	−0.782441	+	0.622725i	$0.786026\pi$
$338$	219.871	+	126.943i	0.650507	+	0.375570i
$339$		0			0
$340$		−	156.594i		−	0.460572i
$341$	−13.0019	+	22.5199i	−0.0381287	+	0.0660408i
$342$		0			0
$343$		−	147.421i		−	0.429800i
$344$	225.774	−	297.247i	0.656320	−	0.864090i
$345$		0			0
$346$		−	32.2044i		−	0.0930763i
$347$	−183.902	−	106.176i	−0.529978	−	0.305983i	0.211029	−	0.977480i	$-0.432318\pi$
$347$	−183.902	−	106.176i	−0.529978	−	0.305983i	−0.741008	+	0.671497i	$0.765652\pi$
$348$		0			0
$349$	146.920	+	84.8242i	0.420974	+	0.243049i	0.695494	−	0.718532i	$-0.255186\pi$
$349$	146.920	+	84.8242i	0.420974	+	0.243049i	−0.274520	+	0.961581i	$0.588519\pi$
$350$	78.6796	−	136.277i	0.224799	−	0.389363i
$351$		0			0
$352$			98.0025i			0.278416i
$353$	−267.568	−	463.442i	−0.757983	−	1.31287i	−0.943877	−	0.330296i	$-0.892851\pi$
$353$	−267.568	−	463.442i	−0.757983	−	1.31287i	0.185894	−	0.982570i	$-0.440482\pi$
$354$		0			0
$355$	−717.245			−2.02041
$356$	39.0515	+	22.5464i	0.109695	+	0.0633326i
$357$		0			0
$358$	−169.227	−	293.110i	−0.472702	−	0.818744i
$359$	316.831	+	548.767i	0.882537	+	1.52860i	0.848511	+	0.529178i	$0.177500\pi$
$359$	316.831	+	548.767i	0.882537	+	1.52860i	0.0340267	+	0.999421i	$0.489167\pi$
$360$		0			0
$361$	−118.712	−	205.615i	−0.328842	−	0.569571i
$362$	−151.680	+	87.5726i	−0.419006	+	0.241913i
$363$		0			0
$364$	−6.51647	−	3.76228i	−0.0179024	−	0.0103359i
$365$	826.712			2.26496
$366$		0			0
$367$	−87.6583	+	151.829i	−0.238851	+	0.413702i	−0.960385	−	0.278677i	$-0.910104\pi$
$367$	−87.6583	+	151.829i	−0.238851	+	0.413702i	0.721534	+	0.692379i	$0.243437\pi$
$368$	−131.026	+	226.944i	−0.356049	+	0.616696i
$369$		0			0
$370$	679.508	−	392.314i	1.83651	−	1.06031i
$371$		−	72.2665i		−	0.194788i
$372$		0			0
$373$	−549.878	+	317.472i	−1.47420	+	0.851131i	−0.999578	−	0.0290566i	$-0.990750\pi$
$373$	−549.878	+	317.472i	−1.47420	+	0.851131i	−0.474625	+	0.880188i	$0.657416\pi$
$374$	136.368	−	78.7319i	0.364619	−	0.210513i
$375$		0			0
$376$			18.6966i			0.0497249i
$377$	84.4567	+	48.7611i	0.224023	+	0.129340i
$378$		0			0
$379$	338.400			0.892877			0.446438	−	0.894814i	$-0.352692\pi$
$379$	338.400			0.892877			0.446438	+	0.894814i	$0.352692\pi$
$380$	−55.2488	−	95.6938i	−0.145392	−	0.251826i
$381$		0			0
$382$	136.791	−	236.929i	0.358092	−	0.620234i
$383$			593.761i			1.55029i	0.631783	+	0.775145i	$0.282323\pi$
$383$			593.761i			1.55029i	−0.631783	+	0.775145i	$0.717677\pi$
$384$		0			0
$385$	−83.0052			−0.215598
$386$		−	101.012i		−	0.261689i
$387$		0			0
$388$	−49.9538			−0.128747
$389$			430.497i			1.10668i	0.832957	+	0.553338i	$0.186646\pi$
$389$			430.497i			1.10668i	−0.832957	+	0.553338i	$0.813354\pi$
$390$		0			0
$391$	−392.637			−1.00419
$392$	−350.499	−	202.360i	−0.894129	−	0.516226i
$393$		0			0
$394$	237.203	−	136.950i	0.602039	−	0.347588i
$395$			459.486i			1.16325i
$396$		0			0
$397$	−63.1007	+	109.294i	−0.158944	+	0.275299i	−0.934488	−	0.355994i	$-0.884142\pi$
$397$	−63.1007	+	109.294i	−0.158944	+	0.275299i	0.775544	+	0.631293i	$0.217476\pi$
$398$	446.316			1.12140
$399$		0			0
$400$	−314.015	−	543.890i	−0.785037	−	1.35972i
$401$	86.4732	+	149.776i	0.215644	+	0.373506i	0.953472	−	0.301483i	$-0.0974817\pi$
$401$	86.4732	+	149.776i	0.215644	+	0.373506i	−0.737828	+	0.674989i	$0.764148\pi$
$402$		0			0
$403$	−20.0939			−0.0498608
$404$	101.341	+	175.528i	0.250844	+	0.434474i
$405$		0			0
$406$	−49.2285	−	28.4221i	−0.121252	−	0.0700051i
$407$	−252.675	−	145.882i	−0.620824	−	0.358433i
$408$		0			0
$409$			18.0602i			0.0441570i	0.999756	+	0.0220785i	$0.00702838\pi$
$409$			18.0602i			0.0441570i	−0.999756	+	0.0220785i	$0.992972\pi$
$410$	−142.909	+	247.526i	−0.348559	+	0.603722i
$411$		0			0
$412$	−90.2437	−	156.307i	−0.219038	−	0.379385i
$413$	0.331104	−	0.191163i	0.000801705	−	0.000462864i
$414$		0			0
$415$	947.631	−	547.115i	2.28345	−	1.31835i
$416$	−65.5837	+	37.8648i	−0.157653	+	0.0910211i
$417$		0			0
$418$	55.5556	−	96.2251i	0.132908	−	0.230204i
$419$			270.830i			0.646372i	0.946335	+	0.323186i	$0.104754\pi$
$419$			270.830i			0.646372i	−0.946335	+	0.323186i	$0.895246\pi$
$420$		0			0
$421$	92.3827	−	53.3372i	0.219436	−	0.126692i	−0.386253	−	0.922393i	$-0.626231\pi$
$421$	92.3827	−	53.3372i	0.219436	−	0.126692i	0.605689	+	0.795701i	$0.292897\pi$
$422$	286.569			0.679073
$423$		0			0
$424$	−352.390	−	203.453i	−0.831109	−	0.479841i
$425$	470.493	−	814.917i	1.10704	−	1.91745i
$426$		0			0
$427$	25.0169	−	43.3306i	0.0585876	−	0.101477i
$428$	129.699			0.303035
$429$		0			0
$430$	623.612	−	261.905i	1.45026	−	0.609082i
$431$	−410.636			−0.952752			−0.476376	−	0.879242i	$-0.658050\pi$
$431$	−410.636			−0.952752			−0.476376	+	0.879242i	$0.658050\pi$
$432$		0			0
$433$	559.028	+	322.755i	1.29106	+	0.745392i	0.978842	−	0.204619i	$-0.0655956\pi$
$433$	559.028	+	322.755i	1.29106	+	0.745392i	0.312215	+	0.950011i	$0.398929\pi$
$434$	11.7124			0.0269871
$435$		0			0
$436$	83.7459	−	145.052i	0.192078	−	0.332689i
$437$	−239.938	+	138.528i	−0.549056	+	0.316998i
$438$		0			0
$439$	−165.315	−	286.334i	−0.376571	−	0.652241i	0.613990	−	0.789314i	$-0.289564\pi$
$439$	−165.315	−	286.334i	−0.376571	−	0.652241i	−0.990561	+	0.137074i	$0.956230\pi$
$440$	−233.685	+	404.755i	−0.531103	+	0.919897i
$441$		0			0
$442$	105.375	+	60.8385i	0.238406	+	0.137644i
$443$	234.995	+	407.023i	0.530462	+	0.918788i	0.999368	+	0.0355395i	$0.0113149\pi$
$443$	234.995	+	407.023i	0.530462	+	0.918788i	−0.468906	+	0.883248i	$0.655352\pi$
$444$		0			0
$445$	192.189	+	332.881i	0.431885	+	0.748047i
$446$	−265.287			−0.594814
$447$		0			0
$448$	94.3810	−	54.4909i	0.210672	−	0.121631i
$449$	−511.770	−	295.471i	−1.13980	−	0.658064i	−0.193419	−	0.981116i	$-0.561958\pi$
$449$	−511.770	−	295.471i	−1.13980	−	0.658064i	−0.946381	+	0.323053i	$0.895291\pi$
$450$		0			0
$451$	106.282			0.235658
$452$		−	131.673i		−	0.291312i
$453$		0			0
$454$	364.571	−	631.456i	0.803021	−	1.39087i
$455$	−32.0703	−	55.5474i	−0.0704842	−	0.122082i
$456$		0			0
$457$			571.268i			1.25004i	0.780609	+	0.625020i	$0.214909\pi$
$457$			571.268i			1.25004i	−0.780609	+	0.625020i	$0.785091\pi$
$458$	−431.197	+	248.951i	−0.941477	+	0.543562i
$459$		0			0
$460$	214.545	−	123.867i	0.466401	−	0.269277i
$461$	76.1726	−	131.935i	0.165233	−	0.286193i	−0.771505	−	0.636224i	$-0.780496\pi$
$461$	76.1726	−	131.935i	0.165233	−	0.286193i	0.936738	+	0.350031i	$0.113829\pi$
$462$		0			0
$463$	−597.602	−	345.026i	−1.29072	−	0.745196i	−0.311936	−	0.950103i	$-0.600977\pi$
$463$	−597.602	−	345.026i	−1.29072	−	0.745196i	−0.978781	+	0.204907i	$0.934311\pi$
$464$	−196.474	+	113.434i	−0.423435	+	0.244470i
$465$		0			0
$466$	83.1918	+	144.092i	0.178523	+	0.309211i
$467$	201.537	+	116.357i	0.431557	+	0.249159i	0.700010	−	0.714133i	$-0.253179\pi$
$467$	201.537	+	116.357i	0.431557	+	0.249159i	−0.268453	+	0.963293i	$0.586512\pi$
$468$		0			0
$469$			85.1946i			0.181652i
$470$	−16.9394	+	29.3400i	−0.0360413	+	0.0624254i
$471$		0			0
$472$		−	2.15273i		−	0.00456087i
$473$	−200.287	−	152.128i	−0.423440	−	0.321624i
$474$		0			0
$475$		−	663.988i		−	1.39787i
$476$	22.7136	+	13.1137i	0.0477176	+	0.0275498i
$477$		0			0
$478$	−382.696	−	220.949i	−0.800619	−	0.462237i
$479$	209.102	−	362.175i	0.436538	−	0.756106i	−0.560882	−	0.827896i	$-0.689538\pi$
$479$	209.102	−	362.175i	0.436538	−	0.756106i	0.997420	+	0.0717898i	$0.0228711\pi$
$480$		0			0
$481$		−	225.455i		−	0.468722i
$482$	−361.178	−	625.579i	−0.749332	−	1.29788i
$483$		0			0
$484$	−93.7189			−0.193634
$485$	−368.766	−	212.907i	−0.760343	−	0.438984i
$486$		0			0
$487$	−465.856	−	806.886i	−0.956583	−	1.65685i	−0.730704	−	0.682695i	$-0.760808\pi$
$487$	−465.856	−	806.886i	−0.956583	−	1.65685i	−0.225879	−	0.974155i	$-0.572525\pi$
$488$	−140.861	−	243.978i	−0.288649	−	0.499955i
$489$		0			0
$490$	−366.685	−	635.116i	−0.748336	−	1.29616i
$491$	−208.100	+	120.146i	−0.423828	+	0.244697i	−0.696714	−	0.717349i	$-0.745355\pi$
$491$	−208.100	+	120.146i	−0.423828	+	0.244697i	0.272886	+	0.962046i	$0.412022\pi$
$492$		0			0
$493$	−294.379	−	169.960i	−0.597118	−	0.344746i
$494$	85.8590			0.173804
$495$		0			0
$496$	23.3724	−	40.4823i	0.0471219	−	0.0816175i
$497$	60.0643	−	104.034i	0.120854	−	0.209325i
$498$		0			0
$499$	42.4869	−	24.5298i	0.0851441	−	0.0491580i	−0.456823	−	0.889557i	$-0.651013\pi$
$499$	42.4869	−	24.5298i	0.0851441	−	0.0491580i	0.541968	+	0.840399i	$0.317680\pi$
$500$			345.217i			0.690433i
$501$		0			0
$502$	−183.930	+	106.192i	−0.366394	+	0.211538i
$503$	−497.428	+	287.190i	−0.988923	+	0.570955i	−0.904952	−	0.425513i	$-0.860094\pi$
$503$	−497.428	+	287.190i	−0.988923	+	0.570955i	−0.0839707	+	0.996468i	$0.526760\pi$
$504$		0			0
$505$			1727.69i			3.42117i
$506$	215.736	+	124.555i	0.426355	+	0.246156i
$507$		0			0
$508$	168.353			0.331403
$509$	90.3672	+	156.521i	0.177539	+	0.307506i	0.941037	−	0.338304i	$-0.109853\pi$
$509$	90.3672	+	156.521i	0.177539	+	0.307506i	−0.763498	+	0.645810i	$0.776520\pi$
$510$		0			0
$511$	−69.2314	+	119.912i	−0.135482	+	0.234662i
$512$		−	541.262i		−	1.05715i
$513$		0			0
$514$	713.008			1.38717
$515$		−	1538.50i		−	2.98738i
$516$		0			0
$517$	12.5979			0.0243673
$518$			131.414i			0.253696i
$519$		0			0
$520$	−361.151			−0.694522
$521$	−13.0375	−	7.52720i	−0.0250240	−	0.0144476i	0.487436	−	0.873159i	$-0.337932\pi$
$521$	−13.0375	−	7.52720i	−0.0250240	−	0.0144476i	−0.512460	+	0.858711i	$0.671266\pi$
$522$		0			0
$523$	360.748	−	208.278i	0.689767	−	0.398237i	−0.113758	−	0.993509i	$-0.536289\pi$
$523$	360.748	−	208.278i	0.689767	−	0.398237i	0.803525	+	0.595271i	$0.202955\pi$
$524$		−	75.9995i		−	0.145037i
$525$		0			0
$526$	−371.218	+	642.969i	−0.705739	+	1.22238i
$527$	70.0385			0.132900
$528$		0			0
$529$	−46.0787	−	79.8106i	−0.0871052	−	0.150871i
$530$	−368.664	−	638.544i	−0.695592	−	1.20480i
$531$		0			0
$532$	18.5068			0.0347872
$533$	41.0636	+	71.1242i	0.0770423	+	0.133441i
$534$		0			0
$535$	957.455	+	552.787i	1.78963	+	1.03325i
$536$	415.431	+	239.849i	0.775058	+	0.447480i
$537$		0			0
$538$			114.023i			0.211938i
$539$	−136.352	+	236.168i	−0.252972	+	0.438160i
$540$		0			0
$541$	−305.359	−	528.897i	−0.564435	−	0.977629i	−0.997102	−	0.0760757i	$-0.975761\pi$
$541$	−305.359	−	528.897i	−0.564435	−	0.977629i	0.432667	−	0.901554i	$-0.357572\pi$
$542$	−583.013	+	336.603i	−1.07567	+	0.621038i
$543$		0			0
$544$	228.596	−	131.980i	0.420213	−	0.242610i
$545$	1236.45	−	713.863i	2.26871	−	1.30984i
$546$		0			0
$547$	−108.798	+	188.445i	−0.198900	+	0.344505i	−0.948172	−	0.317757i	$-0.897070\pi$
$547$	−108.798	+	188.445i	−0.198900	+	0.344505i	0.749272	+	0.662263i	$0.230404\pi$
$548$			144.292i			0.263307i
$549$		0			0
$550$	−517.028	+	298.507i	−0.940052	+	0.542739i
$551$	−239.858			−0.435313
$552$		0			0
$553$	−66.6471	−	38.4787i	−0.120519	−	0.0695818i
$554$	−208.291	+	360.770i	−0.375976	+	0.651210i
$555$		0			0
$556$	34.8049	−	60.2838i	0.0625987	−	0.108424i
$557$	−181.751			−0.326304			−0.163152	−	0.986601i	$-0.552166\pi$
$557$	−181.751			−0.326304			−0.163152	+	0.986601i	$0.552166\pi$
$558$		0			0
$559$	24.4208	−	192.810i	0.0436866	−	0.344919i
$560$	149.212			0.266450
$561$		0			0
$562$	−67.2262	−	38.8131i	−0.119620	−	0.0690624i
$563$	−752.100			−1.33588			−0.667940	−	0.744215i	$-0.732824\pi$
$563$	−752.100			−1.33588			−0.667940	+	0.744215i	$0.732824\pi$
$564$		0			0
$565$	561.201	−	972.029i	0.993277	−	1.72041i
$566$	−393.578	+	227.232i	−0.695367	+	0.401470i
$567$		0			0
$568$	−338.199	−	585.778i	−0.595421	−	1.03130i
$569$	55.0568	−	95.3612i	0.0967607	−	0.167594i	−0.813581	−	0.581451i	$-0.802485\pi$
$569$	55.0568	−	95.3612i	0.0967607	−	0.167594i	0.910342	+	0.413857i	$0.135819\pi$
$570$		0			0
$571$	371.250	+	214.341i	0.650174	+	0.375378i	0.788523	−	0.615005i	$-0.210846\pi$
$571$	371.250	+	214.341i	0.650174	+	0.375378i	−0.138349	+	0.990384i	$0.544179\pi$
$572$	14.2739	+	24.7231i	0.0249544	+	0.0432223i
$573$		0			0
$574$	−23.9353	−	41.4572i	−0.0416991	−	0.0722250i
$575$	1488.65			2.58896
$576$		0			0
$577$	−299.662	+	173.010i	−0.519345	+	0.299844i	−0.736667	−	0.676256i	$-0.763601\pi$
$577$	−299.662	+	173.010i	−0.519345	+	0.299844i	0.217321	+	0.976100i	$0.430268\pi$
$578$	60.3985	+	34.8711i	0.104496	+	0.0603306i
$579$		0			0
$580$	214.473			0.369781
$581$			183.268i			0.315436i
$582$		0			0
$583$	−137.088	+	237.443i	−0.235142	+	0.407278i
$584$	389.815	+	675.180i	0.667492	+	1.15613i
$585$		0			0
$586$		−	169.258i		−	0.288837i
$587$	432.398	−	249.645i	0.736624	−	0.425290i	−0.0842164	−	0.996447i	$-0.526839\pi$
$587$	432.398	−	249.645i	0.736624	−	0.425290i	0.820841	+	0.571157i	$0.193505\pi$
$588$		0			0
$589$	42.8001	−	24.7106i	0.0726657	−	0.0419535i
$590$	1.95042	−	3.37822i	0.00330579	−	0.00572579i
$591$		0			0
$592$	454.215	+	262.241i	0.767254	+	0.442975i
$593$	29.2731	−	16.9009i	0.0493645	−	0.0285006i	−0.475115	−	0.879924i	$-0.657593\pi$
$593$	29.2731	−	16.9009i	0.0493645	−	0.0285006i	0.524479	+	0.851423i	$0.324260\pi$
$594$		0			0
$595$	111.783	+	193.614i	0.187871	+	0.325402i
$596$	226.561	+	130.805i	0.380135	+	0.219471i
$597$		0			0
$598$			192.495i			0.321898i
$599$	−337.276	+	584.180i	−0.563066	+	0.975258i	0.434161	+	0.900835i	$0.357045\pi$
$599$	−337.276	+	584.180i	−0.563066	+	0.975258i	−0.997227	+	0.0744231i	$0.976288\pi$
$600$		0			0
$601$			611.550i			1.01755i	0.860898	+	0.508777i	$0.169902\pi$
$601$			611.550i			1.01755i	−0.860898	+	0.508777i	$0.830098\pi$
$602$	−14.2345	+	112.386i	−0.0236454	+	0.186688i
$603$		0			0
$604$		−	258.291i		−	0.427634i
$605$	−691.846	−	399.437i	−1.14355	−	0.660227i
$606$		0			0
$607$	842.867	+	486.630i	1.38858	+	0.801696i	0.993155	−	0.116803i	$-0.0372646\pi$
$607$	842.867	+	486.630i	1.38858	+	0.801696i	0.395423	+	0.918499i	$0.370598\pi$
$608$	93.1291	−	161.304i	0.153173	−	0.265303i
$609$		0			0
$610$		−	510.490i		−	0.836868i
$611$	4.86738	+	8.43055i	0.00796625	+	0.0137979i
$612$		0			0
$613$	−608.002			−0.991847			−0.495923	−	0.868366i	$-0.665170\pi$
$613$	−608.002			−0.991847			−0.495923	+	0.868366i	$0.665170\pi$
$614$	500.681	+	289.068i	0.815442	+	0.470796i
$615$		0			0
$616$	−39.1390	−	67.7908i	−0.0635374	−	0.110050i
$617$	−115.795	−	200.562i	−0.187673	−	0.325060i	0.756801	−	0.653646i	$-0.226761\pi$
$617$	−115.795	−	200.562i	−0.187673	−	0.325060i	−0.944474	+	0.328586i	$0.893428\pi$
$618$		0			0
$619$	430.174	+	745.083i	0.694950	+	1.20369i	0.970198	+	0.242315i	$0.0779066\pi$
$619$	430.174	+	745.083i	0.694950	+	1.20369i	−0.275248	+	0.961373i	$0.588760\pi$
$620$	−38.2705	+	22.0955i	−0.0617265	+	0.0356378i
$621$		0			0
$622$	−166.341	−	96.0368i	−0.267429	−	0.154400i
$623$	−64.3780			−0.103335
$624$		0			0
$625$	−724.715	+	1255.24i	−1.15954	+	2.00839i
$626$	95.2649	−	165.004i	0.152180	−	0.263584i
$627$		0			0
$628$	−264.709	+	152.830i	−0.421512	+	0.243360i
$629$			785.838i			1.24935i
$630$		0			0
$631$	−551.610	+	318.472i	−0.874184	+	0.504710i	−0.868736	−	0.495275i	$-0.835067\pi$
$631$	−551.610	+	318.472i	−0.874184	+	0.504710i	−0.00544773	+	0.999985i	$0.501734\pi$
$632$	−375.264	+	216.659i	−0.593773	+	0.342815i
$633$		0			0
$634$			147.300i			0.232335i
$635$	1242.80	+	717.532i	1.95717	+	1.12997i
$636$		0			0
$637$	−210.726			−0.330811
$638$	107.832	+	186.770i	0.169016	+	0.292743i
$639$		0			0
$640$	247.506	−	428.693i	0.386728	−	0.669832i
$641$			579.876i			0.904643i	0.891855	+	0.452321i	$0.149404\pi$
$641$			579.876i			0.904643i	−0.891855	+	0.452321i	$0.850596\pi$
$642$		0			0
$643$	−807.091			−1.25520			−0.627598	−	0.778537i	$-0.715962\pi$
$643$	−807.091			−1.25520			−0.627598	+	0.778537i	$0.715962\pi$
$644$			41.4921i			0.0644287i
$645$		0			0
$646$	−299.267			−0.463261
$647$		−	88.5932i		−	0.136929i	−0.997654	−	0.0684646i	$-0.978190\pi$
$647$		−	88.5932i		−	0.136929i	0.997654	−	0.0684646i	$-0.0218100\pi$
$648$		0			0
$649$	−1.45053			−0.00223502
$650$	−399.524	−	230.665i	−0.614652	−	0.354869i
$651$		0			0
$652$	−223.042	+	128.773i	−0.342089	+	0.197505i
$653$			439.732i			0.673403i	0.941611	+	0.336702i	$0.109311\pi$
$653$			439.732i			0.673403i	−0.941611	+	0.336702i	$0.890689\pi$
$654$		0			0
$655$	323.916	−	561.039i	0.494528	−	0.856548i
$656$	−191.054			−0.291241
$657$		0			0
$658$	−2.83712	−	4.91403i	−0.00431173	−	0.00746814i
$659$	−109.882	−	190.322i	−0.166741	−	0.288804i	0.770531	−	0.637402i	$-0.219991\pi$
$659$	−109.882	−	190.322i	−0.166741	−	0.288804i	−0.937272	+	0.348598i	$0.886658\pi$
$660$		0			0
$661$	−789.061			−1.19374			−0.596869	−	0.802338i	$-0.703589\pi$
$661$	−789.061			−1.19374			−0.596869	+	0.802338i	$0.703589\pi$
$662$	−37.1836	−	64.4039i	−0.0561686	−	0.0972869i
$663$		0			0
$664$	893.664	+	515.957i	1.34588	+	0.777044i
$665$	136.620	+	78.8775i	0.205443	+	0.118613i
$666$		0			0
$667$		−	537.759i		−	0.806235i
$668$	162.450	−	281.372i	0.243189	−	0.421216i
$669$		0			0
$670$	434.616	+	752.777i	0.648680	+	1.12355i
$671$	−164.394	+	94.9129i	−0.244998	+	0.141450i
$672$		0			0
$673$	−736.188	+	425.038i	−1.09389	+	0.631558i	−0.934610	−	0.355675i	$-0.884251\pi$
$673$	−736.188	+	425.038i	−1.09389	+	0.631558i	−0.159281	+	0.987233i	$0.550918\pi$
$674$	−147.698	+	85.2732i	−0.219136	+	0.126518i
$675$		0			0
$676$	80.2182	−	138.942i	0.118666	−	0.205536i
$677$			77.7283i			0.114813i	0.998351	+	0.0574065i	$0.0182831\pi$
$677$			77.7283i			0.114813i	−0.998351	+	0.0574065i	$0.981717\pi$
$678$		0			0
$679$	61.7632	−	35.6590i	0.0909620	−	0.0525169i
$680$	1258.82			1.85120
$681$		0			0
$682$	−38.4829	−	22.2181i	−0.0564266	−	0.0325779i
$683$	166.636	−	288.622i	0.243976	−	0.422579i	−0.717867	−	0.696180i	$-0.754881\pi$
$683$	166.636	−	288.622i	0.243976	−	0.422579i	0.961843	+	0.273601i	$0.0882147\pi$
$684$		0			0
$685$	−614.984	+	1065.18i	−0.897787	+	1.55501i
$686$	251.920			0.367230
$687$		0			0
$688$	360.040	+	273.469i	0.523315	+	0.397484i
$689$	−211.864			−0.307495
$690$		0			0
$691$	−792.253	−	457.407i	−1.14653	−	0.661950i	−0.198491	−	0.980103i	$-0.563604\pi$
$691$	−792.253	−	457.407i	−1.14653	−	0.661950i	−0.948039	+	0.318153i	$0.896937\pi$
$692$	−20.3508			−0.0294086
$693$		0			0
$694$	181.438	−	314.260i	0.261438	−	0.452824i
$695$	513.869	−	296.682i	0.739380	−	0.426881i
$696$		0			0
$697$	−143.130	−	247.908i	−0.205351	−	0.355678i
$698$	−144.951	+	251.063i	−0.207666	+	0.359689i
$699$		0			0
$700$	−86.1169	−	49.7196i	−0.123024	−	0.0710280i
$701$	310.815	+	538.347i	0.443388	+	0.767971i	0.997938	−	0.0641796i	$-0.0204431\pi$
$701$	310.815	+	538.347i	0.443388	+	0.767971i	−0.554550	+	0.832150i	$0.687110\pi$
$702$		0			0
$703$	277.256	+	480.221i	0.394389	+	0.683102i
$704$	−413.471			−0.587317
$705$		0			0
$706$	791.948	−	457.232i	1.12174	−	0.647637i
$707$	−250.597	−	144.682i	−0.354451	−	0.204642i
$708$		0			0
$709$	1066.56			1.50432			0.752160	−	0.658980i	$-0.229012\pi$
$709$	1066.56			1.50432			0.752160	+	0.658980i	$0.229012\pi$
$710$		−	1225.66i		−	1.72628i
$711$		0			0
$712$	−181.244	+	313.924i	−0.254556	+	0.440904i
$713$	55.4010	+	95.9574i	0.0777013	+	0.134583i
$714$		0			0
$715$			243.346i			0.340344i
$716$	−185.224	+	106.939i	−0.258692	+	0.149356i
$717$		0			0
$718$	−937.756	+	541.414i	−1.30607	+	0.754058i
$719$	333.496	−	577.632i	0.463833	−	0.803383i	−0.535315	−	0.844653i	$-0.679807\pi$
$719$	333.496	−	577.632i	0.463833	−	0.803383i	0.999148	+	0.0412698i	$0.0131403\pi$
$720$		0			0
$721$	223.155	+	128.839i	0.309508	+	0.178695i
$722$	351.364	−	202.860i	0.486654	−	0.280970i
$723$		0			0
$724$	55.3393	+	95.8505i	0.0764355	+	0.132390i
$725$	1116.12	+	644.391i	1.53947	+	0.888815i
$726$		0			0
$727$		−	874.234i		−	1.20252i	−0.799052	−	0.601261i	$-0.794665\pi$
$727$		−	874.234i		−	1.20252i	0.799052	−	0.601261i	$-0.205335\pi$
$728$	30.2439	−	52.3840i	0.0415438	−	0.0719560i
$729$		0			0
$730$			1412.72i			1.93523i
$731$	−85.1204	+	672.051i	−0.116444	+	0.919359i
$732$		0			0
$733$		−	83.5186i		−	0.113941i	−0.998376	−	0.0569704i	$-0.981856\pi$
$733$		−	83.5186i		−	0.113941i	0.998376	−	0.0569704i	$-0.0181441\pi$
$734$	−259.451	−	149.794i	−0.353475	−	0.204079i
$735$		0			0
$736$	361.643	+	208.795i	0.491362	+	0.283688i
$737$	161.612	−	279.920i	0.219284	−	0.379810i
$738$		0			0
$739$			64.3077i			0.0870199i	0.999053	+	0.0435100i	$0.0138540\pi$
$739$			64.3077i			0.0870199i	−0.999053	+	0.0435100i	$0.986146\pi$
$740$	−247.913	−	429.398i	−0.335018	−	0.580268i
$741$		0			0
$742$	123.492			0.166431
$743$	−704.792	−	406.912i	−0.948576	−	0.547660i	−0.0559375	−	0.998434i	$-0.517815\pi$
$743$	−704.792	−	406.912i	−0.948576	−	0.547660i	−0.892638	+	0.450774i	$0.851148\pi$
$744$		0			0
$745$	1115.00	+	1931.24i	1.49665	+	2.59227i
$746$	−542.509	−	939.654i	−0.727224	−	1.25959i
$747$		0			0
$748$	−49.7526	−	86.1741i	−0.0665142	−	0.115206i
$749$	−160.360	+	92.5841i	−0.214099	+	0.123610i
$750$		0			0
$751$	−703.564	−	406.203i	−0.936836	−	0.540883i	−0.0478692	−	0.998854i	$-0.515243\pi$
$751$	−703.564	−	406.203i	−0.936836	−	0.540883i	−0.888967	+	0.457971i	$0.848576\pi$
$752$	−22.6462			−0.0301146
$753$		0			0
$754$	−83.3250	+	144.323i	−0.110511	+	0.191410i
$755$	1100.86	−	1906.74i	1.45809	−	2.52548i
$756$		0			0
$757$	−32.4334	+	18.7254i	−0.0428446	+	0.0247363i	−0.521269	−	0.853392i	$-0.674541\pi$
$757$	−32.4334	+	18.7254i	−0.0428446	+	0.0247363i	0.478425	+	0.878129i	$0.341208\pi$
$758$			578.272i			0.762892i
$759$		0			0
$760$	769.254	−	444.129i	1.01218	−	0.584380i
$761$	174.329	−	100.649i	0.229078	−	0.132258i	−0.381068	−	0.924547i	$-0.624444\pi$
$761$	174.329	−	100.649i	0.229078	−	0.132258i	0.610147	+	0.792288i	$0.291110\pi$
$762$		0			0
$763$			239.124i			0.313400i
$764$	−149.722	−	86.4418i	−0.195971	−	0.113144i
$765$		0			0
$766$	−1014.64			−1.32460
$767$	−0.560433	−	0.970698i	−0.000730681	−	0.00126558i
$768$		0			0
$769$	586.172	−	1015.28i	0.762252	−	1.32026i	−0.179435	−	0.983770i	$-0.557427\pi$
$769$	586.172	−	1015.28i	0.762252	−	1.32026i	0.941687	−	0.336490i	$-0.109240\pi$
$770$		−	141.843i		−	0.184211i
$771$		0			0
$772$	−63.8319			−0.0826838
$773$			748.974i			0.968918i	0.874814	+	0.484459i	$0.160984\pi$
$773$			748.974i			0.968918i	−0.874814	+	0.484459i	$0.839016\pi$
$774$		0			0
$775$	−265.546			−0.342640
$776$		−	401.564i		−	0.517480i
$777$		0			0
$778$	−735.651			−0.945566
$779$	−174.931	−	100.997i	−0.224559	−	0.129649i
$780$		0			0
$781$	−394.701	+	227.881i	−0.505379	+	0.291781i
$782$		−	670.954i		−	0.857997i
$783$		0			0
$784$	245.109	−	424.541i	0.312639	−	0.541507i
$785$	−2605.50			−3.31910
$786$		0			0
$787$	185.174	+	320.731i	0.235291	+	0.407536i	0.959357	−	0.282195i	$-0.0910624\pi$
$787$	185.174	+	320.731i	0.235291	+	0.407536i	−0.724066	+	0.689730i	$0.757729\pi$
$788$	−86.5418	−	149.895i	−0.109825	−	0.190222i
$789$		0			0
$790$	−785.188			−0.993909
$791$	93.9934	+	162.801i	0.118829	+	0.205817i
$792$		0			0
$793$	−127.032	−	73.3421i	−0.160192	−	0.0924869i
$794$	−186.766	−	107.829i	−0.235221	−	0.135805i
$795$		0			0
$796$		−	282.038i		−	0.354319i
$797$	−439.622	+	761.447i	−0.551596	+	0.955392i	0.446564	+	0.894752i	$0.352647\pi$
$797$	−439.622	+	761.447i	−0.551596	+	0.955392i	−0.998160	+	0.0606400i	$0.980686\pi$
$798$		0			0
$799$	−16.9656	−	29.3852i	−0.0212335	−	0.0367775i
$800$	−866.706	+	500.393i	−1.08338	+	0.625491i
$801$		0			0
$802$	−255.943	+	147.769i	−0.319131	+	0.184251i
$803$	454.941	−	262.660i	0.566552	−	0.327099i
$804$		0			0
$805$	−176.843	+	306.300i	−0.219680	+	0.380497i
$806$		−	34.3373i		−	0.0426021i
$807$		0			0
$808$	−1411.01	+	814.650i	−1.74631	+	1.00823i
$809$	−261.631			−0.323400			−0.161700	−	0.986840i	$-0.551698\pi$
$809$	−261.631			−0.323400			−0.161700	+	0.986840i	$0.551698\pi$
$810$		0			0
$811$	−854.030	−	493.075i	−1.05306	−	0.607984i	−0.129554	−	0.991572i	$-0.541355\pi$
$811$	−854.030	−	493.075i	−1.05306	−	0.607984i	−0.923504	+	0.383589i	$0.874688\pi$
$812$	−17.9606	+	31.1087i	−0.0221190	+	0.0383112i
$813$		0			0
$814$	249.290	−	431.782i	0.306253	−	0.530445i
$815$	−2195.37			−2.69370
$816$		0			0
$817$	185.093	+	440.718i	0.226552	+	0.539434i
$818$	−30.8621			−0.0377287
$819$		0			0
$820$	156.418	+	90.3079i	0.190754	+	0.110132i
$821$	−329.837			−0.401751			−0.200875	−	0.979617i	$-0.564379\pi$
$821$	−329.837			−0.401751			−0.200875	+	0.979617i	$0.564379\pi$
$822$		0			0
$823$	132.664	−	229.781i	0.161196	−	0.279200i	−0.774102	−	0.633061i	$-0.781798\pi$
$823$	132.664	−	229.781i	0.161196	−	0.279200i	0.935298	+	0.353861i	$0.115132\pi$
$824$	1256.50	−	725.442i	1.52488	−	0.880391i
$825$		0			0
$826$	0.326667	+	0.565804i	0.000395481	+	0.000684993i
$827$	2.27610	−	3.94231i	0.00275223	−	0.00476700i	−0.864646	−	0.502382i	$-0.832457\pi$
$827$	2.27610	−	3.94231i	0.00275223	−	0.00476700i	0.867398	+	0.497615i	$0.165791\pi$
$828$		0			0
$829$	984.924	+	568.646i	1.18809	+	0.685942i	0.957871	−	0.287197i	$-0.0927235\pi$
$829$	984.924	+	568.646i	1.18809	+	0.685942i	0.230216	+	0.973140i	$0.426057\pi$
$830$	934.933	+	1619.35i	1.12643	+	1.95103i
$831$		0			0
$832$	−159.751	−	276.697i	−0.192008	−	0.332568i
$833$	734.500			0.881753
$834$		0			0
$835$	2398.46	−	1384.75i	2.87241	−	1.65839i
$836$	−60.8070	−	35.1070i	−0.0727357	−	0.0419940i
$837$		0			0
$838$	−462.805			−0.552274
$839$			1480.37i			1.76444i	0.470835	+	0.882221i	$0.343953\pi$
$839$			1480.37i			1.76444i	−0.470835	+	0.882221i	$0.656047\pi$
$840$		0			0
$841$	−187.721	+	325.143i	−0.223212	+	0.386615i
$842$	91.1448	+	157.867i	0.108248	+	0.187491i
$843$		0			0
$844$		−	181.090i		−	0.214561i
$845$	1184.36	−	683.793i	1.40161	−	0.809223i
$846$		0			0
$847$	115.875	−	66.9002i	0.136806	−	0.0789849i
$848$	246.432	−	426.832i	0.290604	−	0.503340i
$849$		0			0
$850$	1392.57	+	803.998i	1.63831	+	0.945880i
$851$	−1076.65	+	621.605i	−1.26516	+	0.730440i
$852$		0			0
$853$	−283.296	−	490.682i	−0.332117	−	0.575243i	0.650810	−	0.759241i	$-0.274429\pi$
$853$	−283.296	−	490.682i	−0.332117	−	0.575243i	−0.982927	+	0.183998i	$0.941096\pi$
$854$	74.0451	+	42.7499i	0.0867038	+	0.0500585i
$855$		0			0
$856$			1042.61i			1.21800i
$857$	−558.557	+	967.449i	−0.651758	+	1.12888i	0.330938	+	0.943653i	$0.392635\pi$
$857$	−558.557	+	967.449i	−0.651758	+	1.12888i	−0.982696	+	0.185226i	$0.940698\pi$
$858$		0			0
$859$		−	635.376i		−	0.739669i	−0.929098	−	0.369834i	$-0.879414\pi$
$859$		−	635.376i		−	0.739669i	0.929098	−	0.369834i	$-0.120586\pi$
$860$	−165.505	−	394.076i	−0.192447	−	0.458228i
$861$		0			0
$862$		−	701.712i		−	0.814051i
$863$	−1282.55	−	740.483i	−1.48616	−	0.858034i	−0.486283	−	0.873802i	$-0.661647\pi$
$863$	−1282.55	−	740.483i	−1.48616	−	0.858034i	−0.999876	+	0.0157678i	$0.994981\pi$
$864$		0			0
$865$	−150.232	−	86.7365i	−0.173679	−	0.100273i
$866$	−551.537	+	955.290i	−0.636879	+	1.10311i
$867$		0			0
$868$		−	7.40136i		−	0.00852692i
$869$	145.986	+	252.856i	0.167993	+	0.290973i
$870$		0			0
$871$	249.765			0.286757
$872$	1166.03	+	673.209i	1.33719	+	0.772029i
$873$		0			0
$874$	−236.723	−	410.015i	−0.270850	−	0.469125i
$875$	−246.429	−	426.828i	−0.281633	−	0.487803i
$876$		0			0
$877$	−395.936	−	685.781i	−0.451466	−	0.781963i	0.547011	−	0.837125i	$-0.315766\pi$
$877$	−395.936	−	685.781i	−0.451466	−	0.781963i	−0.998477	+	0.0551628i	$0.982432\pi$
$878$	489.299	−	282.497i	0.557288	−	0.321750i
$879$		0			0
$880$	−490.259	−	283.051i	−0.557112	−	0.321649i
$881$	853.589			0.968887			0.484443	−	0.874823i	$-0.339022\pi$
$881$	853.589			0.968887			0.484443	+	0.874823i	$0.339022\pi$
$882$		0			0
$883$	90.0630	−	155.994i	0.101997	−	0.176663i	−0.810511	−	0.585724i	$-0.800810\pi$
$883$	90.0630	−	155.994i	0.101997	−	0.176663i	0.912507	+	0.409061i	$0.134144\pi$
$884$	38.4454	−	66.5894i	0.0434903	−	0.0753273i
$885$		0			0
$886$	−695.538	+	401.569i	−0.785031	+	0.453238i
$887$			145.647i			0.164202i	0.996624	+	0.0821010i	$0.0261630\pi$
$887$			145.647i			0.164202i	−0.996624	+	0.0821010i	$0.973837\pi$
$888$		0			0
$889$	−208.152	+	120.177i	−0.234142	+	0.135182i
$890$	−568.841	+	328.421i	−0.639147	+	0.369012i
$891$		0			0
$892$			167.641i			0.187939i
$893$	−20.7351	−	11.9714i	−0.0232196	−	0.0134058i
$894$		0			0
$895$	−1823.13			−2.03702
$896$	41.4538	+	71.8001i	0.0462654	+	0.0801340i
$897$		0			0
$898$	504.913	−	874.534i	0.562263	−	0.973869i
$899$			95.9254i			0.106702i
$900$		0			0
$901$	738.464			0.819605
$902$			181.619i			0.201351i
$903$		0			0
$904$	1058.48			1.17089
$905$			943.442i			1.04248i
$906$		0			0
$907$	−120.336			−0.132674			−0.0663372	−	0.997797i	$-0.521131\pi$
$907$	−120.336			−0.132674			−0.0663372	+	0.997797i	$0.521131\pi$
$908$	−399.033	−	230.382i	−0.439463	−	0.253724i
$909$		0			0
$910$	94.9217	−	54.8031i	0.104310	−	0.0602232i
$911$		−	1562.26i		−	1.71489i	−0.514577	−	0.857444i	$-0.672051\pi$
$911$		−	1562.26i		−	1.71489i	0.514577	−	0.857444i	$-0.327949\pi$
$912$		0			0
$913$	347.655	−	602.157i	0.380784	−	0.659536i
$914$	−976.206			−1.06806
$915$		0			0
$916$	157.319	+	272.484i	0.171745	+	0.297471i
$917$	54.2514	+	93.9662i	0.0591618	+	0.102471i
$918$		0			0
$919$	1565.35			1.70332			0.851659	−	0.524097i	$-0.175597\pi$
$919$	1565.35			1.70332			0.851659	+	0.524097i	$0.175597\pi$
$920$	995.734	+	1724.66i	1.08232	+	1.87463i
$921$		0			0
$922$	225.456	+	130.167i	0.244529	+	0.141179i
$923$	−304.998	−	176.090i	−0.330442	−	0.190781i
$924$		0			0
$925$		−	2979.45i		−	3.22103i
$926$	589.594	−	1021.21i	0.636711	−	1.10282i
$927$		0			0
$928$	180.761	+	313.087i	0.194786	+	0.337379i
$929$	633.839	−	365.947i	0.682281	−	0.393915i	−0.118433	−	0.992962i	$-0.537787\pi$
$929$	633.839	−	365.947i	0.682281	−	0.393915i	0.800714	+	0.599047i	$0.204454\pi$
$930$		0			0
$931$	448.848	−	259.143i	0.482114	−	0.278349i
$932$	91.0556	−	52.5710i	0.0976992	−	0.0564066i
$933$		0			0
$934$	−198.836	+	344.395i	−0.212887	+	0.368731i
$935$		−	848.199i		−	0.907164i
$936$		0			0
$937$	243.123	−	140.367i	0.259470	−	0.149805i	−0.364623	−	0.931155i	$-0.618802\pi$
$937$	243.123	−	140.367i	0.259470	−	0.149805i	0.624093	+	0.781350i	$0.285469\pi$
$938$	−145.584			−0.155207
$939$		0			0
$940$	18.5406	+	10.7044i	0.0197241	+	0.0113877i
$941$	−199.682	+	345.859i	−0.212202	+	0.367545i	−0.952403	−	0.304841i	$-0.901397\pi$
$941$	−199.682	+	345.859i	−0.212202	+	0.367545i	0.740201	+	0.672385i	$0.234730\pi$
$942$		0			0
$943$	226.433	−	392.194i	0.240120	−	0.415901i
$944$	2.60750			0.00276218
$945$		0			0
$946$	259.963	−	342.259i	0.274802	−	0.361796i
$947$	−1418.34			−1.49772			−0.748860	−	0.662729i	$-0.769398\pi$
$947$	−1418.34			−1.49772			−0.748860	+	0.662729i	$0.769398\pi$
$948$		0			0
$949$	351.547	+	202.966i	0.370439	+	0.213873i
$950$	1134.65			1.19437
$951$		0			0
$952$	−105.417	+	182.588i	−0.110732	+	0.191794i
$953$	237.044	−	136.857i	0.248734	−	0.143607i	−0.370450	−	0.928852i	$-0.620797\pi$
$953$	237.044	−	136.857i	0.248734	−	0.143607i	0.619184	+	0.785246i	$0.287463\pi$
$954$		0			0
$955$	−736.844	−	1276.25i	−0.771564	−	1.33639i
$956$	−139.623	+	241.835i	−0.146050	+	0.252965i
$957$		0			0
$958$	618.900	+	357.322i	0.646033	+	0.372987i
$959$	−103.001	−	178.403i	−0.107405	−	0.186031i
$960$		0			0
$961$	470.618	+	815.134i	0.489717	+	0.848214i
$962$	385.267			0.400486
$963$		0			0
$964$	−395.319	+	228.237i	−0.410082	+	0.236761i
$965$	−471.216	−	272.057i	−0.488306	−	0.281924i
$966$		0			0
$967$	−768.029			−0.794239			−0.397120	−	0.917767i	$-0.629990\pi$
$967$	−768.029			−0.794239			−0.397120	+	0.917767i	$0.629990\pi$
$968$		−	753.379i		−	0.778284i
$969$		0			0
$970$	363.825	−	630.163i	0.375077	−	0.649653i
$971$	11.6253	+	20.1357i	0.0119725	+	0.0207371i	0.871950	−	0.489596i	$-0.162856\pi$
$971$	11.6253	+	20.1357i	0.0119725	+	0.0207371i	−0.859977	+	0.510333i	$0.829522\pi$
$972$		0			0
$973$			99.3803i			0.102138i
$974$	1378.84	−	796.074i	1.41565	−	0.817324i
$975$		0			0
$976$	295.518	−	170.617i	0.302785	−	0.174813i
$977$	0.843119	−	1.46032i	0.000862967	−	0.00149470i	−0.865594	−	0.500747i	$-0.833059\pi$
$977$	0.843119	−	1.46032i	0.000862967	−	0.00149470i	0.866457	+	0.499252i	$0.166392\pi$
$978$		0			0
$979$	211.524	+	122.123i	0.216061	+	0.124743i
$980$	−401.346	+	231.717i	−0.409537	+	0.236446i
$981$		0			0
$982$	−205.311	−	355.609i	−0.209075	−	0.362128i
$983$	418.112	+	241.397i	0.425343	+	0.245572i	0.697361	−	0.716720i	$-0.254358\pi$
$983$	418.112	+	241.397i	0.425343	+	0.245572i	−0.272018	+	0.962292i	$0.587691\pi$
$984$		0			0
$985$		−	1475.39i		−	1.49786i
$986$	290.435	−	503.047i	0.294558	−	0.510190i
$987$		0			0
$988$		−	54.2564i		−	0.0549154i
$989$	−988.086	+	414.978i	−0.999076	+	0.419593i
$990$		0			0
$991$			326.291i			0.329255i	0.986356	+	0.164627i	$0.0526422\pi$
$991$			326.291i			0.329255i	−0.986356	+	0.164627i	$0.947358\pi$
$992$	−64.5098	−	37.2448i	−0.0650301	−	0.0375451i
$993$		0			0
$994$	177.778	+	102.640i	0.178851	+	0.103260i
$995$	1202.07	−	2082.04i	1.20811	−	2.09251i
$996$		0			0
$997$			324.255i			0.325230i	0.986690	+	0.162615i	$0.0519929\pi$
$997$			324.255i			0.325230i	−0.986690	+	0.162615i	$0.948007\pi$
$998$	41.9176	+	72.6034i	0.0420016	+	0.0727489i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.3.j.f.37.10	yes	28
3.2	odd	2	inner	387.3.j.f.37.5	✓	28
43.7	odd	6	inner	387.3.j.f.136.5	yes	28
129.50	even	6	inner	387.3.j.f.136.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.3.j.f.37.5	✓	28	3.2	odd	2	inner
387.3.j.f.37.10	yes	28	1.1	even	1	trivial
387.3.j.f.136.5	yes	28	43.7	odd	6	inner
387.3.j.f.136.10	yes	28	129.50	even	6	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	387.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.70884i q^{2} +1.07986 q^{4} +(7.97167 + 4.60245i) q^{5} +(-1.33514 + 0.770846i) q^{7} +8.68068i q^{8} +O(q^{10})\)	\(q+1.70884i q^{2} +1.07986 q^{4} +(7.97167 + 4.60245i) q^{5} +(-1.33514 + 0.770846i) q^{7} +8.68068i q^{8} +(-7.86485 + 13.6223i) q^{10} +5.84910 q^{11} +(2.25989 + 3.91424i) q^{13} +(-1.31725 - 2.28155i) q^{14} -10.5145 q^{16} +(-7.87698 - 13.6433i) q^{17} +(-9.62715 - 5.55824i) q^{19} +(8.60829 + 4.97000i) q^{20} +9.99518i q^{22} +(12.4615 - 21.5840i) q^{23} +(29.8650 + 51.7278i) q^{25} +(-6.68882 + 3.86179i) q^{26} +(-1.44177 + 0.832405i) q^{28} +(18.6860 - 10.7884i) q^{29} +(-2.22288 + 3.85015i) q^{31} +16.7551i q^{32} +(23.3143 - 13.4605i) q^{34} -14.1911 q^{35} +(-43.1990 - 24.9410i) q^{37} +(9.49814 - 16.4513i) q^{38} +(-39.9524 + 69.1995i) q^{40} +18.1706 q^{41} +(-34.2424 - 26.0088i) q^{43} +6.31621 q^{44} +(36.8836 + 21.2948i) q^{46} +2.15381 q^{47} +(-23.3116 + 40.3769i) q^{49} +(-88.3946 + 51.0346i) q^{50} +(2.44036 + 4.22683i) q^{52} +(-23.4374 + 40.5948i) q^{53} +(46.6271 + 26.9202i) q^{55} +(-6.69146 - 11.5900i) q^{56} +(18.4356 + 31.9315i) q^{58} -0.247991 q^{59} +(-28.1059 + 16.2269i) q^{61} +(-6.57930 - 3.79856i) q^{62} -70.6898 q^{64} +41.6041i q^{65} +(27.6303 - 47.8570i) q^{67} +(-8.50604 - 14.7329i) q^{68} -24.2504i q^{70} +(-67.4807 + 38.9600i) q^{71} +(77.7797 - 44.9061i) q^{73} +(42.6202 - 73.8203i) q^{74} +(-10.3960 - 6.00211i) q^{76} +(-7.80939 + 4.50875i) q^{77} +(24.9588 + 43.2299i) q^{79} +(-83.8179 - 48.3923i) q^{80} +31.0507i q^{82} +(59.4374 - 102.949i) q^{83} -145.014i q^{85} +(44.4450 - 58.5148i) q^{86} +50.7741i q^{88} +(36.1635 + 20.8790i) q^{89} +(-6.03455 - 3.48405i) q^{91} +(13.4567 - 23.3077i) q^{92} +3.68053i q^{94} +(-51.1630 - 88.6169i) q^{95} -46.2596 q^{97} +(-68.9977 - 39.8358i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 84 q^{4} - 30 q^{7}+O(q^{10}) \) 28 * q - 84 * q^4 - 30 * q^7	\( 28 q - 84 q^{4} - 30 q^{7} + 4 q^{10} - 34 q^{13} + 164 q^{16} - 78 q^{19} + 112 q^{25} + 342 q^{28} - 74 q^{31} + 192 q^{34} - 222 q^{37} + 104 q^{40} + 104 q^{43} + 150 q^{46} + 112 q^{49} - 64 q^{52} - 450 q^{55} + 346 q^{58} - 198 q^{61} - 1264 q^{64} - 26 q^{67} + 342 q^{73} + 282 q^{76} - 48 q^{79} + 684 q^{91} - 480 q^{97}+O(q^{100}) \) 28 * q - 84 * q^4 - 30 * q^7 + 4 * q^10 - 34 * q^13 + 164 * q^16 - 78 * q^19 + 112 * q^25 + 342 * q^28 - 74 * q^31 + 192 * q^34 - 222 * q^37 + 104 * q^40 + 104 * q^43 + 150 * q^46 + 112 * q^49 - 64 * q^52 - 450 * q^55 + 346 * q^58 - 198 * q^61 - 1264 * q^64 - 26 * q^67 + 342 * q^73 + 282 * q^76 - 48 * q^79 + 684 * q^91 - 480 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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