LMFDB - Embedded newform 720.3.bs.d.401.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [720,3,Mod(401,720)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(720, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("720.401"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$N$	$=$	$720 = 2^{4} \cdot 3^{2} \cdot 5$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	720.bs (of order $6$ , degree $2$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$19.6185790339$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 12x^{14} + 138x^{12} - 1040x^{10} + 5541x^{8} - 26220x^{6} + 99328x^{4} - 202728x^{2} + 181476$ x^16 - 12x^14 + 138x^12 - 1040x^10 + 5541x^8 - 26220x^6 + 99328x^4 - 202728*x^2 + 181476
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$2^{4}\cdot 3^{6}$
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			401.5
Root			$-2.11536 + 0.410927i$ of defining polynomial
Character	$\chi$	$=$	720.401
Dual form			720.3.bs.d.641.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.129213 - 2.99722i) q^{3} +(1.93649 + 1.11803i) q^{5} +(-3.31598 - 5.74345i) q^{7} +(-8.96661 - 0.774559i) q^{9} +(18.2172 - 10.5177i) q^{11} +(4.89124 - 8.47187i) q^{13} +(3.60121 - 5.65962i) q^{15} +12.9017i q^{17} -16.1821 q^{19} +(-17.6428 + 9.19659i) q^{21} +(-14.6674 - 8.46823i) q^{23} +(2.50000 + 4.33013i) q^{25} +(-3.48012 + 26.7748i) q^{27} +(43.3525 - 25.0296i) q^{29} +(-5.03212 + 8.71588i) q^{31} +(-29.1700 - 55.9600i) q^{33} -14.8295i q^{35} +2.54425 q^{37} +(-24.7600 - 15.7548i) q^{39} +(-46.5617 - 26.8824i) q^{41} +(-37.4175 - 64.8089i) q^{43} +(-16.4978 - 11.5249i) q^{45} +(-40.8766 + 23.6001i) q^{47} +(2.50850 - 4.34485i) q^{49} +(38.6691 + 1.66706i) q^{51} +1.08813i q^{53} +47.0367 q^{55} +(-2.09094 + 48.5013i) q^{57} +(-8.34807 - 4.81976i) q^{59} +(22.4573 + 38.8971i) q^{61} +(25.2845 + 54.0677i) q^{63} +(18.9437 - 10.9371i) q^{65} +(-1.67067 + 2.89369i) q^{67} +(-27.2763 + 42.8672i) q^{69} -38.4670i q^{71} -88.9201 q^{73} +(13.3014 - 6.93353i) q^{75} +(-120.816 - 69.7532i) q^{77} +(58.8235 + 101.885i) q^{79} +(79.8001 + 13.8903i) q^{81} +(-127.412 + 73.5614i) q^{83} +(-14.4245 + 24.9840i) q^{85} +(-69.4173 - 133.171i) q^{87} -145.331i q^{89} -64.8771 q^{91} +(25.4732 + 16.2086i) q^{93} +(-31.3365 - 18.0922i) q^{95} +(23.5267 + 40.7494i) q^{97} +(-171.493 + 80.1980i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 4 q^{3} + 4 q^{7} - 4 q^{9} + 20 q^{13} + 20 q^{15} - 80 q^{19} - 44 q^{21} - 108 q^{23} + 40 q^{25} + 124 q^{27} - 72 q^{29} + 16 q^{31} - 264 q^{33} - 88 q^{37} + 8 q^{39} + 108 q^{41} - 92 q^{43}+ \cdots - 816 q^{99}+O(q^{100})$ 16 * q + 4 * q^3 + 4 * q^7 - 4 * q^9 + 20 * q^13 + 20 * q^15 - 80 * q^19 - 44 * q^21 - 108 * q^23 + 40 * q^25 + 124 * q^27 - 72 * q^29 + 16 * q^31 - 264 * q^33 - 88 * q^37 + 8 * q^39 + 108 * q^41 - 92 * q^43 - 80 * q^45 - 216 * q^47 - 84 * q^49 - 168 * q^51 + 28 * q^57 - 144 * q^59 - 76 * q^61 + 104 * q^63 + 180 * q^65 - 56 * q^67 - 72 * q^69 + 416 * q^73 - 20 * q^75 - 684 * q^77 - 80 * q^79 + 320 * q^81 - 396 * q^83 - 60 * q^85 - 420 * q^87 + 656 * q^91 - 356 * q^93 + 360 * q^95 - 16 * q^97 - 816 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$ .

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	0.129213	−	2.99722i	0.0430710	−	0.999072i
$3$	0.129213	−	2.99722i	0.0430710	−	0.999072i
$4$		0			0
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$5$	1.93649	+	1.11803i	0.387298	+	0.223607i
$6$		0			0
$7$	−3.31598	−	5.74345i	−0.473712	−	0.820493i	0.525835	−	0.850587i	$-0.323753\pi$
$7$	−3.31598	−	5.74345i	−0.473712	−	0.820493i	−0.999547	+	0.0300933i	$0.990420\pi$
$8$		0			0
$9$	−8.96661	−	0.774559i	−0.996290	−	0.0860621i
$10$		0			0
$11$	18.2172	−	10.5177i	1.65611	−	0.956156i	0.681627	−	0.731699i	$-0.261273\pi$
$11$	18.2172	−	10.5177i	1.65611	−	0.956156i	0.974484	−	0.224457i	$-0.0720608\pi$
$12$		0			0
$13$	4.89124	−	8.47187i	0.376249	−	0.651683i	−0.614264	−	0.789101i	$-0.710547\pi$
$13$	4.89124	−	8.47187i	0.376249	−	0.651683i	0.990513	+	0.137418i	$0.0438803\pi$
$14$		0			0
$15$	3.60121	−	5.65962i	0.240081	−	0.377308i
$16$		0			0
$17$			12.9017i			0.758921i	0.925208	+	0.379460i	$0.123890\pi$
$17$			12.9017i			0.758921i	−0.925208	+	0.379460i	$0.876110\pi$
$18$		0			0
$19$	−16.1821			−0.851691			−0.425845	−	0.904796i	$-0.640023\pi$
$19$	−16.1821			−0.851691			−0.425845	+	0.904796i	$0.640023\pi$
$20$		0			0
$21$	−17.6428	+	9.19659i	−0.840135	+	0.437933i
$22$		0			0
$23$	−14.6674	−	8.46823i	−0.637713	−	0.368184i	0.146020	−	0.989282i	$-0.453354\pi$
$23$	−14.6674	−	8.46823i	−0.637713	−	0.368184i	−0.783733	+	0.621098i	$0.786687\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$		0			0
$27$	−3.48012	+	26.7748i	−0.128893	+	0.991658i
$28$		0			0
$29$	43.3525	−	25.0296i	1.49491	−	0.863089i	0.494930	−	0.868933i	$-0.335194\pi$
$29$	43.3525	−	25.0296i	1.49491	−	0.863089i	0.999983	+	0.00584415i	$0.00186026\pi$
$30$		0			0
$31$	−5.03212	+	8.71588i	−0.162326	+	0.281158i	−0.935703	−	0.352790i	$-0.885233\pi$
$31$	−5.03212	+	8.71588i	−0.162326	+	0.281158i	0.773376	+	0.633947i	$0.218566\pi$
$32$		0			0
$33$	−29.1700	−	55.9600i	−0.883939	−	1.69576i
$34$		0			0
$35$		−	14.8295i		−	0.423701i
$36$		0			0
$37$	2.54425			0.0687635			0.0343817	−	0.999409i	$-0.489054\pi$
$37$	2.54425			0.0687635			0.0343817	+	0.999409i	$0.489054\pi$
$38$		0			0
$39$	−24.7600	−	15.7548i	−0.634872	−	0.403969i
$40$		0			0
$41$	−46.5617	−	26.8824i	−1.13565	−	0.655669i	−0.190301	−	0.981726i	$-0.560946\pi$
$41$	−46.5617	−	26.8824i	−1.13565	−	0.655669i	−0.945350	+	0.326057i	$0.894280\pi$
$42$		0			0
$43$	−37.4175	−	64.8089i	−0.870173	−	1.50718i	−0.861817	−	0.507219i	$-0.830673\pi$
$43$	−37.4175	−	64.8089i	−0.870173	−	1.50718i	−0.00835640	−	0.999965i	$-0.502660\pi$
$44$		0			0
$45$	−16.4978	−	11.5249i	−0.366617	−	0.256109i
$46$		0			0
$47$	−40.8766	+	23.6001i	−0.869716	+	0.502131i	−0.867254	−	0.497866i	$-0.834117\pi$
$47$	−40.8766	+	23.6001i	−0.869716	+	0.502131i	−0.00246200	+	0.999997i	$0.500784\pi$
$48$		0			0
$49$	2.50850	−	4.34485i	0.0511939	−	0.0886704i
$50$		0			0
$51$	38.6691	+	1.66706i	0.758217	+	0.0326875i
$52$		0			0
$53$			1.08813i			0.0205307i	0.999947	+	0.0102654i	$0.00326762\pi$
$53$			1.08813i			0.0205307i	−0.999947	+	0.0102654i	$0.996732\pi$
$54$		0			0
$55$	47.0367			0.855212
$56$		0			0
$57$	−2.09094	+	48.5013i	−0.0366832	+	0.850900i
$58$		0			0
$59$	−8.34807	−	4.81976i	−0.141493	−	0.0816908i	0.427583	−	0.903976i	$-0.359365\pi$
$59$	−8.34807	−	4.81976i	−0.141493	−	0.0816908i	−0.569075	+	0.822285i	$0.692699\pi$
$60$		0			0
$61$	22.4573	+	38.8971i	0.368152	+	0.637657i	0.989277	−	0.146054i	$-0.0466574\pi$
$61$	22.4573	+	38.8971i	0.368152	+	0.637657i	−0.621125	+	0.783712i	$0.713324\pi$
$62$		0			0
$63$	25.2845	+	54.0677i	0.401341	+	0.858218i
$64$		0			0
$65$	18.9437	−	10.9371i	0.291441	−	0.168264i
$66$		0			0
$67$	−1.67067	+	2.89369i	−0.0249354	+	0.0431894i	−0.878224	−	0.478250i	$-0.841271\pi$
$67$	−1.67067	+	2.89369i	−0.0249354	+	0.0431894i	0.853288	+	0.521439i	$0.174605\pi$
$68$		0			0
$69$	−27.2763	+	42.8672i	−0.395309	+	0.621263i
$70$		0			0
$71$		−	38.4670i		−	0.541788i	−0.962609	−	0.270894i	$-0.912681\pi$
$71$		−	38.4670i		−	0.541788i	0.962609	−	0.270894i	$-0.0873193\pi$
$72$		0			0
$73$	−88.9201			−1.21808			−0.609042	−	0.793138i	$-0.708446\pi$
$73$	−88.9201			−1.21808			−0.609042	+	0.793138i	$0.708446\pi$
$74$		0			0
$75$	13.3014	−	6.93353i	0.177351	−	0.0924471i
$76$		0			0
$77$	−120.816	−	69.7532i	−1.56904	−	0.905885i
$78$		0			0
$79$	58.8235	+	101.885i	0.744602	+	1.28969i	0.950381	+	0.311090i	$0.100694\pi$
$79$	58.8235	+	101.885i	0.744602	+	1.28969i	−0.205779	+	0.978599i	$0.565973\pi$
$80$		0			0
$81$	79.8001	+	13.8903i	0.985187	+	0.171486i
$82$		0			0
$83$	−127.412	+	73.5614i	−1.53509	+	0.886282i	−0.535970	+	0.844237i	$0.680054\pi$
$83$	−127.412	+	73.5614i	−1.53509	+	0.886282i	−0.999116	+	0.0420449i	$0.986613\pi$
$84$		0			0
$85$	−14.4245	+	24.9840i	−0.169700	+	0.293929i
$86$		0			0
$87$	−69.4173	−	133.171i	−0.797900	−	1.53070i
$88$		0			0
$89$		−	145.331i		−	1.63293i	−0.577396	−	0.816464i	$-0.695931\pi$
$89$		−	145.331i		−	1.63293i	0.577396	−	0.816464i	$-0.304069\pi$
$90$		0			0
$91$	−64.8771			−0.712935
$92$		0			0
$93$	25.4732	+	16.2086i	0.273905	+	0.174285i
$94$		0			0
$95$	−31.3365	−	18.0922i	−0.329858	−	0.190444i
$96$		0			0
$97$	23.5267	+	40.7494i	0.242543	+	0.420097i	0.961438	−	0.275022i	$-0.0886851\pi$
$97$	23.5267	+	40.7494i	0.242543	+	0.420097i	−0.718895	+	0.695119i	$0.755352\pi$
$98$		0			0
$99$	−171.493	+	80.1980i	−1.73226	+	0.810080i
$100$		0			0
$101$	−19.3600	+	11.1775i	−0.191683	+	0.110668i	−0.592770	−	0.805372i	$-0.701966\pi$
$101$	−19.3600	+	11.1775i	−0.191683	+	0.110668i	0.401087	+	0.916040i	$0.368632\pi$
$102$		0			0
$103$	61.9495	−	107.300i	0.601452	−	1.04174i	−0.391150	−	0.920327i	$-0.627923\pi$
$103$	61.9495	−	107.300i	0.601452	−	1.04174i	0.992601	−	0.121418i	$-0.0387441\pi$
$104$		0			0
$105$	−44.4473	−	1.91617i	−0.423308	−	0.0182492i
$106$		0			0
$107$		−	47.3690i		−	0.442701i	−0.975194	−	0.221351i	$-0.928954\pi$
$107$		−	47.3690i		−	0.442701i	0.975194	−	0.221351i	$-0.0710465\pi$
$108$		0			0
$109$	−26.8745			−0.246555			−0.123278	−	0.992372i	$-0.539341\pi$
$109$	−26.8745			−0.246555			−0.123278	+	0.992372i	$0.539341\pi$
$110$		0			0
$111$	0.328750	−	7.62567i	0.00296171	−	0.0686997i
$112$		0			0
$113$	−16.2899	−	9.40495i	−0.144158	−	0.0832297i	0.426186	−	0.904635i	$-0.359857\pi$
$113$	−16.2899	−	9.40495i	−0.144158	−	0.0832297i	−0.570344	+	0.821406i	$0.693190\pi$
$114$		0			0
$115$	−18.9355	−	32.7973i	−0.164657	−	0.285194i
$116$		0			0
$117$	−50.4198	+	72.1754i	−0.430938	+	0.616884i
$118$		0			0
$119$	74.1001	−	42.7817i	0.622690	−	0.359510i
$120$		0			0
$121$	160.745	−	278.418i	1.32847	−	2.30098i
$122$		0			0
$123$	−86.5888	+	136.082i	−0.703974	+	1.10636i
$124$		0			0
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	128.820			1.01433			0.507166	−	0.861849i	$-0.330693\pi$
$127$	128.820			1.01433			0.507166	+	0.861849i	$0.330693\pi$
$128$		0			0
$129$	−199.081	+	103.774i	−1.54327	+	0.804450i
$130$		0			0
$131$	26.6836	+	15.4058i	0.203692	+	0.117601i	0.598376	−	0.801215i	$-0.295813\pi$
$131$	26.6836	+	15.4058i	0.203692	+	0.117601i	−0.394685	+	0.918817i	$0.629146\pi$
$132$		0			0
$133$	53.6597	+	92.9413i	0.403456	+	0.698806i
$134$		0			0
$135$	−36.6743	+	47.9582i	−0.271662	+	0.355246i
$136$		0			0
$137$	−92.2703	+	53.2723i	−0.673506	+	0.388849i	−0.797404	−	0.603446i	$-0.793794\pi$
$137$	−92.2703	+	53.2723i	−0.673506	+	0.388849i	0.123898	+	0.992295i	$0.460460\pi$
$138$		0			0
$139$	57.1183	−	98.9317i	0.410923	−	0.711739i	−0.584068	−	0.811705i	$-0.698540\pi$
$139$	57.1183	−	98.9317i	0.410923	−	0.711739i	0.994991	+	0.0999656i	$0.0318733\pi$
$140$		0			0
$141$	65.4529	+	125.566i	0.464205	+	0.890536i
$142$		0			0
$143$		−	205.779i		−	1.43901i
$144$		0			0
$145$	111.936			0.771970
$146$		0			0
$147$	−12.6983	−	8.07993i	−0.0863832	−	0.0549655i
$148$		0			0
$149$	104.689	+	60.4419i	0.702607	+	0.405651i	0.808318	−	0.588746i	$-0.200378\pi$
$149$	104.689	+	60.4419i	0.702607	+	0.405651i	−0.105710	+	0.994397i	$0.533712\pi$
$150$		0			0
$151$	63.4938	+	109.975i	0.420489	+	0.728308i	0.995987	−	0.0894947i	$-0.0285252\pi$
$151$	63.4938	+	109.975i	0.420489	+	0.728308i	−0.575498	+	0.817803i	$0.695192\pi$
$152$		0			0
$153$	9.99310	−	115.684i	0.0653144	−	0.756105i
$154$		0			0
$155$	−19.4893	+	11.2522i	−0.125737	+	0.0725946i
$156$		0			0
$157$	−52.1064	+	90.2510i	−0.331888	+	0.574847i	−0.982882	−	0.184236i	$-0.941019\pi$
$157$	−52.1064	+	90.2510i	−0.331888	+	0.574847i	0.650994	+	0.759083i	$0.274352\pi$
$158$		0			0
$159$	3.26135	+	0.140600i	0.0205117	+	0.000884279i
$160$		0			0
$161$			112.322i			0.697652i
$162$		0			0
$163$	188.533			1.15664			0.578321	−	0.815809i	$-0.303708\pi$
$163$	188.533			1.15664			0.578321	+	0.815809i	$0.303708\pi$
$164$		0			0
$165$	6.07775	−	140.979i	0.0368349	−	0.854419i
$166$		0			0
$167$	58.8172	+	33.9581i	0.352199	+	0.203342i	0.665653	−	0.746261i	$-0.268153\pi$
$167$	58.8172	+	33.9581i	0.352199	+	0.203342i	−0.313454	+	0.949603i	$0.601486\pi$
$168$		0			0
$169$	36.6516	+	63.4824i	0.216873	+	0.375635i
$170$		0			0
$171$	145.099	+	12.5340i	0.848531	+	0.0732983i
$172$		0			0
$173$	105.995	−	61.1963i	0.612689	−	0.353736i	−0.161328	−	0.986901i	$-0.551578\pi$
$173$	105.995	−	61.1963i	0.612689	−	0.353736i	0.774017	+	0.633165i	$0.218244\pi$
$174$		0			0
$175$	16.5799	−	28.7173i	0.0947424	−	0.164099i
$176$		0			0
$177$	−15.5245	+	24.3982i	−0.0877093	+	0.137843i
$178$		0			0
$179$		−	78.4259i		−	0.438134i	−0.975710	−	0.219067i	$-0.929699\pi$
$179$		−	78.4259i		−	0.438134i	0.975710	−	0.219067i	$-0.0703013\pi$
$180$		0			0
$181$	219.562			1.21305			0.606525	−	0.795064i	$-0.292563\pi$
$181$	219.562			1.21305			0.606525	+	0.795064i	$0.292563\pi$
$182$		0			0
$183$	119.485	−	62.2832i	0.652922	−	0.340345i
$184$		0			0
$185$	4.92692	+	2.84456i	0.0266320	+	0.0153760i
$186$		0			0
$187$	135.696	+	235.032i	0.725647	+	1.25686i
$188$		0			0
$189$	165.320	−	68.7968i	0.874707	−	0.364004i
$190$		0			0
$191$	279.710	−	161.491i	1.46445	−	0.845501i	0.465239	−	0.885185i	$-0.345968\pi$
$191$	279.710	−	161.491i	1.46445	−	0.845501i	0.999212	+	0.0396836i	$0.0126350\pi$
$192$		0			0
$193$	86.3918	−	149.635i	0.447626	−	0.775311i	−0.550605	−	0.834766i	$-0.685603\pi$
$193$	86.3918	−	149.635i	0.447626	−	0.775311i	0.998231	+	0.0594550i	$0.0189363\pi$
$194$		0			0
$195$	−30.3332	−	58.1915i	−0.155555	−	0.298418i
$196$		0			0
$197$		−	71.7321i		−	0.364123i	−0.983287	−	0.182061i	$-0.941723\pi$
$197$		−	71.7321i		−	0.364123i	0.983287	−	0.182061i	$-0.0582769\pi$
$198$		0			0
$199$	−133.225			−0.669472			−0.334736	−	0.942312i	$-0.608647\pi$
$199$	−133.225			−0.669472			−0.334736	+	0.942312i	$0.608647\pi$
$200$		0			0
$201$	8.45714	+	5.38127i	0.0420753	+	0.0267725i
$202$		0			0
$203$	−287.512	−	165.995i	−1.41632	−	0.817711i
$204$		0			0
$205$	−60.1109	−	104.115i	−0.293224	−	0.507879i
$206$		0			0
$207$	124.958	+	87.2920i	0.603660	+	0.421701i
$208$		0			0
$209$	−294.793	+	170.199i	−1.41049	+	0.814349i
$210$		0			0
$211$	−188.164	+	325.909i	−0.891771	+	1.54459i	−0.0540209	+	0.998540i	$0.517204\pi$
$211$	−188.164	+	325.909i	−0.891771	+	1.54459i	−0.837750	+	0.546053i	$0.816130\pi$
$212$		0			0
$213$	−115.294	−	4.97043i	−0.541285	−	0.0233354i
$214$		0			0
$215$		−	167.336i		−	0.778307i
$216$		0			0
$217$	66.7457			0.307584
$218$		0			0
$219$	−11.4896	+	266.513i	−0.0524641	+	1.21695i
$220$		0			0
$221$	109.301	+	63.1051i	0.494576	+	0.285543i
$222$		0			0
$223$	29.5885	+	51.2488i	0.132684	+	0.229815i	0.924710	−	0.380672i	$-0.124307\pi$
$223$	29.5885	+	51.2488i	0.132684	+	0.229815i	−0.792026	+	0.610487i	$0.790974\pi$
$224$		0			0
$225$	−19.0626	−	40.7629i	−0.0847226	−	0.181169i
$226$		0			0
$227$	−129.764	+	74.9193i	−0.571647	+	0.330041i	−0.757807	−	0.652479i	$-0.773729\pi$
$227$	−129.764	+	74.9193i	−0.571647	+	0.330041i	0.186160	+	0.982520i	$0.440396\pi$
$228$		0			0
$229$	85.4319	−	147.972i	0.373065	−	0.646167i	−0.616970	−	0.786986i	$-0.711640\pi$
$229$	85.4319	−	147.972i	0.373065	−	0.646167i	0.990035	+	0.140819i	$0.0449736\pi$
$230$		0			0
$231$	−224.676	+	353.099i	−0.972625	+	1.52857i
$232$		0			0
$233$		−	448.983i		−	1.92697i	−0.267770	−	0.963483i	$-0.586287\pi$
$233$		−	448.983i		−	1.92697i	0.267770	−	0.963483i	$-0.413713\pi$
$234$		0			0
$235$	−105.543			−0.449119
$236$		0			0
$237$	312.973	−	163.142i	1.32056	−	0.688363i
$238$		0			0
$239$	200.845	+	115.958i	0.840356	+	0.485180i	0.857385	−	0.514675i	$-0.172087\pi$
$239$	200.845	+	115.958i	0.840356	+	0.485180i	−0.0170289	+	0.999855i	$0.505421\pi$
$240$		0			0
$241$	198.671	+	344.108i	0.824359	+	1.42783i	0.902408	+	0.430882i	$0.141798\pi$
$241$	198.671	+	344.108i	0.824359	+	1.42783i	−0.0780488	+	0.996950i	$0.524869\pi$
$242$		0			0
$243$	51.9436	−	237.383i	0.213759	−	0.976886i
$244$		0			0
$245$	9.71538	−	5.60918i	0.0396546	−	0.0228946i
$246$		0			0
$247$	−79.1506	+	137.093i	−0.320448	+	0.555032i
$248$		0			0
$249$	204.016	+	391.387i	0.819342	+	1.57183i
$250$		0			0
$251$			193.179i			0.769636i	0.922992	+	0.384818i	$0.125736\pi$
$251$			193.179i			0.769636i	−0.922992	+	0.384818i	$0.874264\pi$
$252$		0			0
$253$	−356.266			−1.40816
$254$		0			0
$255$	73.0185	+	46.4616i	0.286347	+	0.182202i
$256$		0			0
$257$	104.673	+	60.4331i	0.407289	+	0.235148i	0.689624	−	0.724167i	$-0.257776\pi$
$257$	104.673	+	60.4331i	0.407289	+	0.235148i	−0.282335	+	0.959316i	$0.591109\pi$
$258$		0			0
$259$	−8.43669	−	14.6128i	−0.0325741	−	0.0564200i
$260$		0			0
$261$	−408.112	+	190.851i	−1.56365	+	0.731231i
$262$		0			0
$263$	260.705	−	150.518i	0.991273	−	0.572312i	0.0856183	−	0.996328i	$-0.472713\pi$
$263$	260.705	−	150.518i	0.991273	−	0.572312i	0.905655	+	0.424016i	$0.139380\pi$
$264$		0			0
$265$	−1.21656	+	2.10715i	−0.00459081	+	0.00795151i
$266$		0			0
$267$	−435.587	−	18.7786i	−1.63141	−	0.0703319i
$268$		0			0
$269$		−	128.065i		−	0.476077i	−0.971256	−	0.238038i	$-0.923496\pi$
$269$		−	128.065i		−	0.476077i	0.971256	−	0.238038i	$-0.0765044\pi$
$270$		0			0
$271$	512.831			1.89236			0.946182	−	0.323635i	$-0.104905\pi$
$271$	512.831			1.89236			0.946182	+	0.323635i	$0.104905\pi$
$272$		0			0
$273$	−8.38297	+	194.451i	−0.0307068	+	0.712273i
$274$		0			0
$275$	91.0861	+	52.5886i	0.331222	+	0.191231i
$276$		0			0
$277$	138.761	+	240.341i	0.500942	+	0.867658i	0.999999	+	0.00108844i	$0.000346460\pi$
$277$	138.761	+	240.341i	0.500942	+	0.867658i	−0.499057	+	0.866569i	$0.666320\pi$
$278$		0			0
$279$	51.8720	−	74.2542i	0.185921	−	0.266144i
$280$		0			0
$281$	−89.3698	+	51.5977i	−0.318042	+	0.183622i	−0.650519	−	0.759490i	$-0.725449\pi$
$281$	−89.3698	+	51.5977i	−0.318042	+	0.183622i	0.332478	+	0.943111i	$0.392115\pi$
$282$		0			0
$283$	−82.0340	+	142.087i	−0.289873	+	0.502075i	−0.973779	−	0.227495i	$-0.926946\pi$
$283$	−82.0340	+	142.087i	−0.289873	+	0.502075i	0.683906	+	0.729570i	$0.260280\pi$
$284$		0			0
$285$	−58.2752	+	91.5846i	−0.204474	+	0.321350i
$286$		0			0
$287$			356.567i			1.24239i
$288$		0			0
$289$	122.547			0.424039
$290$		0			0
$291$	125.175	−	65.2492i	0.430154	−	0.224224i
$292$		0			0
$293$	−253.735	−	146.494i	−0.865988	−	0.499979i	2.47977e−5	−	1.00000i	$-0.499992\pi$
$293$	−253.735	−	146.494i	−0.865988	−	0.499979i	−0.866013	+	0.500021i	$0.833325\pi$
$294$		0			0
$295$	−10.7773	−	18.6668i	−0.0365333	−	0.0632774i
$296$		0			0
$297$	218.211	+	524.365i	0.734719	+	1.76554i
$298$		0			0
$299$	−143.484	+	82.8402i	−0.479878	+	0.277058i
$300$		0			0
$301$	−248.151	+	429.811i	−0.824423	+	1.42794i
$302$		0			0
$303$	30.9998	+	59.4704i	0.102310	+	0.196272i
$304$		0			0
$305$			100.432i			0.329285i
$306$		0			0
$307$	467.606			1.52315			0.761573	−	0.648079i	$-0.224427\pi$
$307$	467.606			1.52315			0.761573	+	0.648079i	$0.224427\pi$
$308$		0			0
$309$	−313.596	−	199.541i	−1.01487	−	0.645763i
$310$		0			0
$311$	−465.753	−	268.902i	−1.49760	−	0.864638i	−0.497601	−	0.867406i	$-0.665786\pi$
$311$	−465.753	−	268.902i	−1.49760	−	0.864638i	−0.999996	+	0.00276786i	$0.999119\pi$
$312$		0			0
$313$	133.129	+	230.586i	0.425332	+	0.736697i	0.996451	−	0.0841703i	$-0.0268240\pi$
$313$	133.129	+	230.586i	0.425332	+	0.736697i	−0.571119	+	0.820867i	$0.693491\pi$
$314$		0			0
$315$	−11.4863	+	132.971i	−0.0364646	+	0.422129i
$316$		0			0
$317$	412.986	−	238.437i	1.30279	−	0.752168i	0.321911	−	0.946770i	$-0.395675\pi$
$317$	412.986	−	238.437i	1.30279	−	0.752168i	0.980882	+	0.194602i	$0.0623414\pi$
$318$		0			0
$319$	526.508	−	911.939i	1.65050	−	2.85874i
$320$		0			0
$321$	−141.975	−	6.12070i	−0.442290	−	0.0190676i
$322$		0			0
$323$		−	208.776i		−	0.646366i
$324$		0			0
$325$	48.9124			0.150500
$326$		0			0
$327$	−3.47254	+	80.5488i	−0.0106194	+	0.246326i
$328$		0			0
$329$	271.093	+	156.515i	0.823990	+	0.475731i
$330$		0			0
$331$	17.6720	+	30.6088i	0.0533898	+	0.0924738i	0.891485	−	0.453050i	$-0.149664\pi$
$331$	17.6720	+	30.6088i	0.0533898	+	0.0924738i	−0.838095	+	0.545524i	$0.816331\pi$
$332$		0			0
$333$	−22.8133	−	1.97067i	−0.0685084	−	0.00591793i
$334$		0			0
$335$	−6.47049	+	3.73574i	−0.0193149	+	0.0111515i
$336$		0			0
$337$	124.246	−	215.201i	0.368684	−	0.638579i	−0.620676	−	0.784067i	$-0.713142\pi$
$337$	124.246	−	215.201i	0.368684	−	0.638579i	0.989360	+	0.145488i	$0.0464752\pi$
$338$		0			0
$339$	−30.2935	+	47.6090i	−0.0893615	+	0.140439i
$340$		0			0
$341$			211.706i			0.620838i
$342$		0			0
$343$	−358.239			−1.04443
$344$		0			0
$345$	−100.747	+	52.5160i	−0.292021	+	0.152220i
$346$		0			0
$347$	2.33212	+	1.34645i	0.00672082	+	0.00388026i	0.503357	−	0.864079i	$-0.332098\pi$
$347$	2.33212	+	1.34645i	0.00672082	+	0.00388026i	−0.496636	+	0.867959i	$0.665432\pi$
$348$		0			0
$349$	−196.192	−	339.815i	−0.562156	−	0.973682i	−0.997308	−	0.0733253i	$-0.976639\pi$
$349$	−196.192	−	339.815i	−0.562156	−	0.973682i	0.435152	−	0.900357i	$-0.356694\pi$
$350$		0			0
$351$	209.810	+	160.445i	0.597751	+	0.457108i
$352$		0			0
$353$	17.1321	−	9.89124i	0.0485329	−	0.0280205i	−0.475537	−	0.879696i	$-0.657746\pi$
$353$	17.1321	−	9.89124i	0.0485329	−	0.0280205i	0.524070	+	0.851675i	$0.324413\pi$
$354$		0			0
$355$	43.0074	−	74.4909i	0.121148	−	0.209834i
$356$		0			0
$357$	−118.651	−	227.622i	−0.332356	−	0.637596i
$358$		0			0
$359$			415.325i			1.15689i	0.815720	+	0.578447i	$0.196341\pi$
$359$			415.325i			1.15689i	−0.815720	+	0.578447i	$0.803659\pi$
$360$		0			0
$361$	−99.1389			−0.274623
$362$		0			0
$363$	−813.709	−	517.762i	−2.24162	−	1.42634i
$364$		0			0
$365$	−172.193	−	99.4157i	−0.471762	−	0.272372i
$366$		0			0
$367$	−266.694	−	461.927i	−0.726685	−	1.25866i	−0.958276	−	0.285843i	$-0.907726\pi$
$367$	−266.694	−	461.927i	−0.726685	−	1.25866i	0.231591	−	0.972813i	$-0.425607\pi$
$368$		0			0
$369$	396.678	+	277.109i	1.07501	+	0.750972i
$370$		0			0
$371$	6.24961	−	3.60821i	0.0168453	−	0.00972564i
$372$		0			0
$373$	107.790	−	186.697i	0.288981	−	0.500529i	−0.684586	−	0.728932i	$-0.740017\pi$
$373$	107.790	−	186.697i	0.288981	−	0.500529i	0.973567	+	0.228403i	$0.0733503\pi$
$374$		0			0
$375$	33.5099	+	1.44465i	0.0893597	+	0.00385239i
$376$		0			0
$377$		−	489.702i		−	1.29895i
$378$		0			0
$379$	−176.846			−0.466612			−0.233306	−	0.972403i	$-0.574954\pi$
$379$	−176.846			−0.466612			−0.233306	+	0.972403i	$0.574954\pi$
$380$		0			0
$381$	16.6452	−	386.102i	0.0436883	−	1.01339i
$382$		0			0
$383$	−14.8980	−	8.60134i	−0.0388980	−	0.0224578i	0.480425	−	0.877036i	$-0.340482\pi$
$383$	−14.8980	−	8.60134i	−0.0388980	−	0.0224578i	−0.519323	+	0.854578i	$0.673816\pi$
$384$		0			0
$385$	−155.973	−	270.153i	−0.405124	−	0.701696i
$386$		0			0
$387$	285.309	+	610.098i	0.737233	+	1.57648i
$388$		0			0
$389$	298.375	−	172.267i	0.767030	−	0.442845i	−0.0647844	−	0.997899i	$-0.520636\pi$
$389$	298.375	−	172.267i	0.767030	−	0.442845i	0.831814	+	0.555055i	$0.187303\pi$
$390$		0			0
$391$	109.254	−	189.234i	0.279422	−	0.483974i
$392$		0			0
$393$	49.6223	−	77.9858i	0.126265	−	0.198437i
$394$		0			0
$395$			263.067i			0.665992i
$396$		0			0
$397$	68.9955			0.173792			0.0868960	−	0.996217i	$-0.472305\pi$
$397$	68.9955			0.173792			0.0868960	+	0.996217i	$0.472305\pi$
$398$		0			0
$399$	285.499	−	148.820i	0.715535	−	0.372983i
$400$		0			0
$401$	−154.315	−	89.0938i	−0.384825	−	0.222179i	0.295090	−	0.955469i	$-0.404650\pi$
$401$	−154.315	−	89.0938i	−0.384825	−	0.222179i	−0.679916	+	0.733290i	$0.737984\pi$
$402$		0			0
$403$	49.2266	+	85.2629i	0.122150	+	0.211571i
$404$		0			0
$405$	139.002	+	116.118i	0.343216	+	0.286711i
$406$		0			0
$407$	46.3492	−	26.7597i	0.113880	−	0.0657487i
$408$		0			0
$409$	−5.64530	+	9.77795i	−0.0138027	+	0.0239070i	−0.872844	−	0.487999i	$-0.837727\pi$
$409$	−5.64530	+	9.77795i	−0.0138027	+	0.0239070i	0.859042	+	0.511906i	$0.171060\pi$
$410$		0			0
$411$	147.746	+	283.437i	0.359479	+	0.689629i
$412$		0			0
$413$			63.9290i			0.154792i
$414$		0			0
$415$	−328.977			−0.792715
$416$		0			0
$417$	−289.139	−	183.979i	−0.693380	−	0.441197i
$418$		0			0
$419$	56.3602	+	32.5396i	0.134511	+	0.0776601i	0.565746	−	0.824580i	$-0.308588\pi$
$419$	56.3602	+	32.5396i	0.134511	+	0.0776601i	−0.431234	+	0.902240i	$0.641922\pi$
$420$		0			0
$421$	115.044	+	199.262i	0.273263	+	0.473306i	0.969696	−	0.244317i	$-0.0785636\pi$
$421$	115.044	+	199.262i	0.273263	+	0.473306i	−0.696432	+	0.717623i	$0.745230\pi$
$422$		0			0
$423$	384.805	−	179.952i	0.909703	−	0.425418i
$424$		0			0
$425$	−55.8658	+	32.2541i	−0.131449	+	0.0758921i
$426$		0			0
$427$	148.936	−	257.964i	0.348796	−	0.604132i
$428$		0			0
$429$	−616.763	−	26.5893i	−1.43768	−	0.0619797i
$430$		0			0
$431$			67.4877i			0.156584i	0.996930	+	0.0782920i	$0.0249467\pi$
$431$			67.4877i			0.156584i	−0.996930	+	0.0782920i	$0.975053\pi$
$432$		0			0
$433$	132.060			0.304989			0.152495	−	0.988304i	$-0.451269\pi$
$433$	132.060			0.304989			0.152495	+	0.988304i	$0.451269\pi$
$434$		0			0
$435$	14.4635	−	335.495i	0.0332495	−	0.771253i
$436$		0			0
$437$	237.350	+	137.034i	0.543134	+	0.313579i
$438$		0			0
$439$	344.511	+	596.711i	0.784764	+	1.35925i	0.929140	+	0.369728i	$0.120549\pi$
$439$	344.511	+	596.711i	0.784764	+	1.35925i	−0.144376	+	0.989523i	$0.546118\pi$
$440$		0			0
$441$	−25.8581	+	37.0156i	−0.0586351	+	0.0839356i
$442$		0			0
$443$	−58.9612	+	34.0413i	−0.133095	+	0.0768426i	−0.565069	−	0.825043i	$-0.691151\pi$
$443$	−58.9612	+	34.0413i	−0.133095	+	0.0768426i	0.431974	+	0.901886i	$0.357817\pi$
$444$		0			0
$445$	162.485	−	281.432i	0.365134	−	0.632431i
$446$		0			0
$447$	194.685	−	305.964i	0.435536	−	0.684484i
$448$		0			0
$449$			685.554i			1.52685i	0.645898	+	0.763423i	$0.276483\pi$
$449$			685.554i			1.52685i	−0.645898	+	0.763423i	$0.723517\pi$
$450$		0			0
$451$	−1130.97			−2.50769
$452$		0			0
$453$	337.822	−	176.095i	0.745743	−	0.388730i
$454$		0			0
$455$	−125.634	−	72.5348i	−0.276119	−	0.159417i
$456$		0			0
$457$	−259.698	−	449.810i	−0.568266	−	0.984266i	−0.996738	−	0.0807109i	$-0.974281\pi$
$457$	−259.698	−	449.810i	−0.568266	−	0.984266i	0.428471	−	0.903555i	$-0.359052\pi$
$458$		0			0
$459$	−345.439	−	44.8994i	−0.752590	−	0.0978200i
$460$		0			0
$461$	77.5379	−	44.7665i	0.168195	−	0.0971074i	−0.413539	−	0.910486i	$-0.635708\pi$
$461$	77.5379	−	44.7665i	0.168195	−	0.0971074i	0.581734	+	0.813379i	$0.302374\pi$
$462$		0			0
$463$	−254.981	+	441.640i	−0.550714	+	0.953865i	0.447509	+	0.894279i	$0.352311\pi$
$463$	−254.981	+	441.640i	−0.550714	+	0.953865i	−0.998223	+	0.0595857i	$0.981022\pi$
$464$		0			0
$465$	31.2069	+	59.8676i	0.0671116	+	0.128748i
$466$		0			0
$467$		−	539.803i		−	1.15590i	−0.816074	−	0.577948i	$-0.803854\pi$
$467$		−	539.803i		−	1.15590i	0.816074	−	0.577948i	$-0.196146\pi$
$468$		0			0
$469$	22.1597			0.0472488
$470$		0			0
$471$	263.769	+	167.836i	0.560019	+	0.356339i
$472$		0			0
$473$	−1363.28	−	787.093i	−2.88221	−	1.66404i
$474$		0			0
$475$	−40.4553	−	70.0706i	−0.0851691	−	0.147517i
$476$		0			0
$477$	0.842819	−	9.75681i	0.00176692	−	0.0204545i
$478$		0			0
$479$	−94.2261	+	54.4015i	−0.196714	+	0.113573i	−0.595122	−	0.803635i	$-0.702896\pi$
$479$	−94.2261	+	54.4015i	−0.196714	+	0.113573i	0.398408	+	0.917208i	$0.369563\pi$
$480$		0			0
$481$	12.4445	−	21.5546i	0.0258722	−	0.0448120i
$482$		0			0
$483$	336.653	+	14.5135i	0.697005	+	0.0300486i
$484$		0			0
$485$			105.215i			0.216937i
$486$		0			0
$487$	−342.524			−0.703334			−0.351667	−	0.936125i	$-0.614385\pi$
$487$	−342.524			−0.703334			−0.351667	+	0.936125i	$0.614385\pi$
$488$		0			0
$489$	24.3609	−	565.073i	0.0498178	−	1.15557i
$490$		0			0
$491$	−430.657	−	248.640i	−0.877102	−	0.506395i	−0.00740027	−	0.999973i	$-0.502356\pi$
$491$	−430.657	−	248.640i	−0.877102	−	0.506395i	−0.869702	+	0.493577i	$0.835689\pi$
$492$		0			0
$493$	322.923	+	559.319i	0.655016	+	1.13452i
$494$		0			0
$495$	−421.759	−	36.4327i	−0.852039	−	0.0736014i
$496$		0			0
$497$	−220.933	+	127.556i	−0.444533	+	0.256652i
$498$		0			0
$499$	77.5164	−	134.262i	0.155343	−	0.269063i	−0.777841	−	0.628462i	$-0.783685\pi$
$499$	77.5164	−	134.262i	0.155343	−	0.269063i	0.933184	+	0.359399i	$0.117018\pi$
$500$		0			0
$501$	109.380	−	171.900i	0.218323	−	0.343114i
$502$		0			0
$503$		−	580.438i		−	1.15395i	−0.816761	−	0.576976i	$-0.804233\pi$
$503$		−	580.438i		−	1.15395i	0.816761	−	0.576976i	$-0.195767\pi$
$504$		0			0
$505$	−49.9873			−0.0989848
$506$		0			0
$507$	195.006	−	101.650i	0.384628	−	0.200493i
$508$		0			0
$509$	158.209	+	91.3419i	0.310823	+	0.179454i	0.647295	−	0.762240i	$-0.275900\pi$
$509$	158.209	+	91.3419i	0.310823	+	0.179454i	−0.336472	+	0.941694i	$0.609234\pi$
$510$		0			0
$511$	294.858	+	510.709i	0.577021	+	0.999430i
$512$		0			0
$513$	56.3158	−	433.273i	0.109777	−	0.844586i
$514$		0			0
$515$	239.929	−	138.523i	0.465882	−	0.268977i
$516$		0			0
$517$	−496.439	+	859.858i	−0.960231	+	1.66317i
$518$		0			0
$519$	−169.723	−	325.598i	−0.327019	−	0.627356i
$520$		0			0
$521$			47.7611i			0.0916720i	0.998949	+	0.0458360i	$0.0145952\pi$
$521$			47.7611i			0.0916720i	−0.998949	+	0.0458360i	$0.985405\pi$
$522$		0			0
$523$	−266.851			−0.510230			−0.255115	−	0.966911i	$-0.582113\pi$
$523$	−266.851			−0.510230			−0.255115	+	0.966911i	$0.582113\pi$
$524$		0			0
$525$	−83.9295	−	53.4042i	−0.159866	−	0.101722i
$526$		0			0
$527$	−112.449	−	64.9227i	−0.213376	−	0.123193i
$528$		0			0
$529$	−121.078	−	209.714i	−0.228881	−	0.396434i
$530$		0			0
$531$	71.1207	+	49.6830i	0.133937	+	0.0935649i
$532$		0			0
$533$	−455.489	+	262.977i	−0.854576	+	0.493389i
$534$		0			0
$535$	52.9602	−	91.7297i	0.0989910	−	0.171457i
$536$		0			0
$537$	−235.059	−	10.1337i	−0.437727	−	0.0188709i
$538$		0			0
$539$		−	105.535i		−	0.195798i
$540$		0			0
$541$	−707.266			−1.30733			−0.653666	−	0.756783i	$-0.726770\pi$
$541$	−707.266			−1.30733			−0.653666	+	0.756783i	$0.726770\pi$
$542$		0			0
$543$	28.3703	−	658.075i	0.0522474	−	1.21193i
$544$		0			0
$545$	−52.0423	−	30.0466i	−0.0954904	−	0.0551314i
$546$		0			0
$547$	103.164	+	178.686i	0.188600	+	0.326665i	0.944784	−	0.327695i	$-0.106272\pi$
$547$	103.164	+	178.686i	0.188600	+	0.326665i	−0.756184	+	0.654359i	$0.772938\pi$
$548$		0			0
$549$	−171.237	−	366.170i	−0.311908	−	0.666975i
$550$		0			0
$551$	−701.535	+	405.032i	−1.27320	+	0.735084i
$552$		0			0
$553$	390.116	−	675.700i	0.705454	−	1.22188i
$554$		0			0
$555$	9.16238	−	14.3995i	0.0165088	−	0.0259450i
$556$		0			0
$557$			643.753i			1.15575i	0.816125	+	0.577876i	$0.196118\pi$
$557$			643.753i			1.15575i	−0.816125	+	0.577876i	$0.803882\pi$
$558$		0			0
$559$	−732.071			−1.30961
$560$		0			0
$561$	721.977	−	376.341i	1.28695	−	0.670840i
$562$		0			0
$563$	626.694	+	361.822i	1.11313	+	0.642668i	0.939639	−	0.342167i	$-0.111161\pi$
$563$	626.694	+	361.822i	1.11313	+	0.642668i	0.173494	+	0.984835i	$0.444494\pi$
$564$		0			0
$565$	−21.0301	−	36.4252i	−0.0372214	−	0.0644694i
$566$		0			0
$567$	−184.837	−	504.388i	−0.325992	−	0.889574i
$568$		0			0
$569$	329.204	−	190.066i	0.578566	−	0.334035i	−0.181997	−	0.983299i	$-0.558256\pi$
$569$	329.204	−	190.066i	0.578566	−	0.334035i	0.760563	+	0.649264i	$0.224923\pi$
$570$		0			0
$571$	20.7292	−	35.9040i	0.0363033	−	0.0628791i	−0.847303	−	0.531110i	$-0.821775\pi$
$571$	20.7292	−	35.9040i	0.0363033	−	0.0628791i	0.883606	+	0.468231i	$0.155108\pi$
$572$		0			0
$573$	−447.881	−	859.219i	−0.781641	−	1.49951i
$574$		0			0
$575$		−	84.6823i		−	0.147274i
$576$		0			0
$577$	−601.252			−1.04203			−0.521016	−	0.853547i	$-0.674447\pi$
$577$	−601.252			−1.04203			−0.521016	+	0.853547i	$0.674447\pi$
$578$		0			0
$579$	−437.325	−	278.270i	−0.755312	−	0.480604i
$580$		0			0
$581$	844.993	+	487.857i	1.45438	+	0.839685i
$582$		0			0
$583$	11.4446	+	19.8227i	0.0196306	+	0.0340011i
$584$		0			0
$585$	−178.332	+	83.3961i	−0.304841	+	0.142557i
$586$		0			0
$587$	630.446	−	363.988i	1.07401	−	0.620082i	0.144738	−	0.989470i	$-0.453766\pi$
$587$	630.446	−	363.988i	1.07401	−	0.620082i	0.929275	+	0.369388i	$0.120433\pi$
$588$		0			0
$589$	81.4303	−	141.041i	0.138252	−	0.239459i
$590$		0			0
$591$	−214.997	−	9.26873i	−0.363785	−	0.0156831i
$592$		0			0
$593$			418.998i			0.706573i	0.935515	+	0.353286i	$0.114936\pi$
$593$			418.998i			0.706573i	−0.935515	+	0.353286i	$0.885064\pi$
$594$		0			0
$595$	191.326			0.321555
$596$		0			0
$597$	−17.2144	+	399.304i	−0.0288348	+	0.668851i
$598$		0			0
$599$	760.433	+	439.036i	1.26950	+	0.732948i	0.974894	−	0.222669i	$-0.0714771\pi$
$599$	760.433	+	439.036i	1.26950	+	0.732948i	0.294610	+	0.955618i	$0.404810\pi$
$600$		0			0
$601$	266.229	+	461.122i	0.442977	+	0.767259i	0.997909	−	0.0646372i	$-0.0205890\pi$
$601$	266.229	+	461.122i	0.442977	+	0.767259i	−0.554932	+	0.831896i	$0.687256\pi$
$602$		0			0
$603$	17.2216	−	24.6526i	0.0285599	−	0.0408832i
$604$		0			0
$605$	622.562	−	359.436i	1.02903	−	0.594110i
$606$		0			0
$607$	47.2643	−	81.8641i	0.0778653	−	0.134867i	−0.824463	−	0.565915i	$-0.808523\pi$
$607$	47.2643	−	81.8641i	0.0778653	−	0.134867i	0.902329	+	0.431049i	$0.141856\pi$
$608$		0			0
$609$	−534.674	+	840.288i	−0.877954	+	1.37978i
$610$		0			0
$611$			461.736i			0.755705i
$612$		0			0
$613$	−816.657			−1.33223			−0.666115	−	0.745849i	$-0.732044\pi$
$613$	−816.657			−1.33223			−0.666115	+	0.745849i	$0.732044\pi$
$614$		0			0
$615$	−319.823	+	166.712i	−0.520037	+	0.271077i
$616$		0			0
$617$	164.232	+	94.8195i	0.266179	+	0.153678i	0.627150	−	0.778899i	$-0.284221\pi$
$617$	164.232	+	94.8195i	0.266179	+	0.153678i	−0.360971	+	0.932577i	$0.617555\pi$
$618$		0			0
$619$	−47.7312	−	82.6728i	−0.0771101	−	0.133559i	0.824892	−	0.565291i	$-0.191236\pi$
$619$	−47.7312	−	82.6728i	−0.0771101	−	0.133559i	−0.902002	+	0.431732i	$0.857903\pi$
$620$		0			0
$621$	277.779	−	363.246i	0.447310	−	0.584937i
$622$		0			0
$623$	−834.700	+	481.914i	−1.33981	+	0.773538i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	472.032	+	905.551i	0.752842	+	1.44426i
$628$		0			0
$629$			32.8250i			0.0521861i
$630$		0			0
$631$	192.912			0.305724			0.152862	−	0.988248i	$-0.451151\pi$
$631$	192.912			0.305724			0.152862	+	0.988248i	$0.451151\pi$
$632$		0			0
$633$	952.507	+	606.079i	1.50475	+	0.957471i
$634$		0			0
$635$	249.459	+	144.025i	0.392849	+	0.226811i
$636$		0			0
$637$	−24.5394	−	42.5034i	−0.0385233	−	0.0667244i
$638$		0			0
$639$	−29.7949	+	344.918i	−0.0466274	+	0.539778i
$640$		0			0
$641$	−277.039	+	159.949i	−0.432198	+	0.249530i	−0.700283	−	0.713866i	$-0.746943\pi$
$641$	−277.039	+	159.949i	−0.432198	+	0.249530i	0.268084	+	0.963395i	$0.413609\pi$
$642$		0			0
$643$	76.1741	−	131.937i	0.118467	−	0.205190i	−0.800693	−	0.599074i	$-0.795535\pi$
$643$	76.1741	−	131.937i	0.118467	−	0.205190i	0.919160	+	0.393884i	$0.128869\pi$
$644$		0			0
$645$	−501.542	−	21.6220i	−0.777584	−	0.0335225i
$646$		0			0
$647$			632.862i			0.978148i	0.872242	+	0.489074i	$0.162665\pi$
$647$			632.862i			0.978148i	−0.872242	+	0.489074i	$0.837335\pi$
$648$		0			0
$649$	−202.772			−0.312437
$650$		0			0
$651$	8.62442	−	200.051i	0.0132480	−	0.307298i
$652$		0			0
$653$	708.299	+	408.937i	1.08468	+	0.626243i	0.932156	−	0.362056i	$-0.117925\pi$
$653$	708.299	+	408.937i	1.08468	+	0.626243i	0.152529	+	0.988299i	$0.451258\pi$
$654$		0			0
$655$	34.4484	+	59.6663i	0.0525929	+	0.0910936i
$656$		0			0
$657$	797.312	+	68.8739i	1.21356	+	0.104831i
$658$		0			0
$659$	−368.474	+	212.738i	−0.559141	+	0.322820i	−0.752800	−	0.658249i	$-0.771297\pi$
$659$	−368.474	+	212.738i	−0.559141	+	0.322820i	0.193660	+	0.981069i	$0.437964\pi$
$660$		0			0
$661$	−142.986	+	247.659i	−0.216318	+	0.374673i	−0.953679	−	0.300825i	$-0.902738\pi$
$661$	−142.986	+	247.659i	−0.216318	+	0.374673i	0.737362	+	0.675498i	$0.236071\pi$
$662$		0			0
$663$	203.263	−	319.445i	0.306580	−	0.481818i
$664$		0			0
$665$			239.973i			0.360862i
$666$		0			0
$667$	−847.824			−1.27110
$668$		0			0
$669$	157.427	−	82.0611i	0.235317	−	0.122662i
$670$		0			0
$671$	818.218	+	472.398i	1.21940	+	0.704021i
$672$		0			0
$673$	−598.709	−	1036.99i	−0.889612	−	1.54085i	−0.840335	−	0.542068i	$-0.817642\pi$
$673$	−598.709	−	1036.99i	−0.889612	−	1.54085i	−0.0492769	−	0.998785i	$-0.515692\pi$
$674$		0			0
$675$	−124.638	+	51.8676i	−0.184650	+	0.0768408i
$676$		0			0
$677$	−784.232	+	452.777i	−1.15839	+	0.668799i	−0.950918	−	0.309442i	$-0.899858\pi$
$677$	−784.232	+	452.777i	−1.15839	+	0.668799i	−0.207475	+	0.978240i	$0.566525\pi$
$678$		0			0
$679$	156.028	−	270.249i	0.229791	−	0.398010i
$680$		0			0
$681$	207.782	+	398.611i	0.305113	+	0.585332i
$682$		0			0
$683$			31.1970i			0.0456764i	0.999739	+	0.0228382i	$0.00727026\pi$
$683$			31.1970i			0.0456764i	−0.999739	+	0.0228382i	$0.992730\pi$
$684$		0			0
$685$	−238.241			−0.347797
$686$		0			0
$687$	−432.466	−	275.178i	−0.629499	−	0.400550i
$688$		0			0
$689$	9.21848	+	5.32229i	0.0133795	+	0.00772466i
$690$		0			0
$691$	−101.532	−	175.858i	−0.146935	−	0.254498i	0.783158	−	0.621822i	$-0.213607\pi$
$691$	−101.532	−	175.858i	−0.146935	−	0.254498i	−0.930093	+	0.367324i	$0.880274\pi$
$692$		0			0
$693$	1029.28	+	719.029i	1.48526	+	1.03756i
$694$		0			0
$695$	221.218	−	127.720i	0.318299	−	0.183770i
$696$		0			0
$697$	346.828	−	600.723i	0.497601	−	0.861870i
$698$		0			0
$699$	−1345.70	−	58.0145i	−1.92518	−	0.0829964i
$700$		0			0
$701$		−	633.699i		−	0.903993i	−0.892020	−	0.451997i	$-0.850712\pi$
$701$		−	633.699i		−	0.903993i	0.892020	−	0.451997i	$-0.149288\pi$
$702$		0			0
$703$	−41.1714			−0.0585652
$704$		0			0
$705$	−13.6375	+	316.335i	−0.0193440	+	0.448703i
$706$		0			0
$707$	128.395	+	74.1289i	0.181605	+	0.104850i
$708$		0			0
$709$	74.6901	+	129.367i	0.105346	+	0.182464i	0.913879	−	0.405986i	$-0.133072\pi$
$709$	74.6901	+	129.367i	0.105346	+	0.182464i	−0.808534	+	0.588450i	$0.799738\pi$
$710$		0			0
$711$	−448.531	−	959.128i	−0.630846	−	1.34899i
$712$		0			0
$713$	147.616	−	85.2262i	0.207035	−	0.119532i
$714$		0			0
$715$	230.068	−	398.489i	0.321773	−	0.557327i
$716$		0			0
$717$	373.503	−	586.993i	0.520925	−	0.818679i
$718$		0			0
$719$		−	257.590i		−	0.358262i	−0.983825	−	0.179131i	$-0.942671\pi$
$719$		−	257.590i		−	0.358262i	0.983825	−	0.179131i	$-0.0573285\pi$
$720$		0			0
$721$	−821.694			−1.13966
$722$		0			0
$723$	1057.04	−	550.995i	1.46201	−	0.762096i
$724$		0			0
$725$	216.762	+	125.148i	0.298983	+	0.172618i
$726$		0			0
$727$	303.691	+	526.008i	0.417731	+	0.723532i	0.995711	−	0.0925193i	$-0.0294920\pi$
$727$	303.691	+	526.008i	0.417731	+	0.723532i	−0.577980	+	0.816051i	$0.696159\pi$
$728$		0			0
$729$	−704.777	−	186.359i	−0.966773	−	0.255637i
$730$		0			0
$731$	836.143	−	482.747i	1.14383	−	0.660393i
$732$		0			0
$733$	−443.643	+	768.411i	−0.605242	+	1.04831i	0.386771	+	0.922176i	$0.373590\pi$
$733$	−443.643	+	768.411i	−0.605242	+	1.04831i	−0.992013	+	0.126134i	$0.959743\pi$
$734$		0			0
$735$	−15.5566	−	29.8439i	−0.0211654	−	0.0406039i
$736$		0			0
$737$			70.2867i			0.0953686i
$738$		0			0
$739$	30.1955			0.0408599			0.0204300	−	0.999791i	$-0.493496\pi$
$739$	30.1955			0.0408599			0.0204300	+	0.999791i	$0.493496\pi$
$740$		0			0
$741$	400.670	+	254.946i	0.540715	+	0.344056i
$742$		0			0
$743$	−493.648	−	285.008i	−0.664399	−	0.383591i	0.129552	−	0.991573i	$-0.458646\pi$
$743$	−493.648	−	285.008i	−0.664399	−	0.383591i	−0.793951	+	0.607982i	$0.791979\pi$
$744$		0			0
$745$	135.152	+	234.091i	0.181412	+	0.314216i
$746$		0			0
$747$	1199.43	−	560.908i	1.60567	−	0.750881i
$748$		0			0
$749$	−272.062	+	157.075i	−0.363233	+	0.209713i
$750$		0			0
$751$	213.747	−	370.221i	0.284617	−	0.492970i	−0.687900	−	0.725806i	$-0.741467\pi$
$751$	213.747	−	370.221i	0.284617	−	0.492970i	0.972516	+	0.232836i	$0.0748004\pi$
$752$		0			0
$753$	578.998	+	24.9612i	0.768922	+	0.0331490i
$754$		0			0
$755$			283.953i			0.376097i
$756$		0			0
$757$	−587.791			−0.776474			−0.388237	−	0.921560i	$-0.626916\pi$
$757$	−587.791			−0.776474			−0.388237	+	0.921560i	$0.626916\pi$
$758$		0			0
$759$	−46.0342	+	1067.81i	−0.0606511	+	1.40686i
$760$		0			0
$761$	−1135.73	−	655.716i	−1.49242	−	0.861651i	−0.492461	−	0.870335i	$-0.663903\pi$
$761$	−1135.73	−	655.716i	−1.49242	−	0.861651i	−0.999962	+	0.00868376i	$0.997236\pi$
$762$		0			0
$763$	89.1155	+	154.353i	0.116796	+	0.202297i
$764$		0			0
$765$	148.690	−	212.849i	0.194366	−	0.278234i
$766$		0			0
$767$	−81.6648	+	47.1492i	−0.106473	+	0.0614722i
$768$		0			0
$769$	595.762	−	1031.89i	0.774724	−	1.34186i	−0.160226	−	0.987080i	$-0.551222\pi$
$769$	595.762	−	1031.89i	0.774724	−	1.34186i	0.934950	−	0.354780i	$-0.115444\pi$
$770$		0			0
$771$	194.656	−	305.920i	0.252473	−	0.396783i
$772$		0			0
$773$			204.848i			0.265003i	0.991183	+	0.132502i	$0.0423010\pi$
$773$			204.848i			0.265003i	−0.991183	+	0.132502i	$0.957699\pi$
$774$		0			0
$775$	−50.3212			−0.0649306
$776$		0			0
$777$	−44.8878	+	23.3984i	−0.0577706	+	0.0301138i
$778$		0			0
$779$	753.467	+	435.014i	0.967223	+	0.558427i
$780$		0			0
$781$	−404.585	−	700.761i	−0.518034	−	0.897261i
$782$		0			0
$783$	519.289	+	1247.86i	0.663204	+	1.59369i
$784$		0			0
$785$	−201.807	+	116.514i	−0.257079	+	0.148425i
$786$		0			0
$787$	66.6137	−	115.378i	0.0846426	−	0.146605i	−0.820596	−	0.571508i	$-0.806358\pi$
$787$	66.6137	−	115.378i	0.0846426	−	0.146605i	0.905239	+	0.424903i	$0.139692\pi$
$788$		0			0
$789$	−417.448	−	800.837i	−0.529085	−	1.01500i
$790$		0			0
$791$			124.747i			0.157708i
$792$		0			0
$793$	439.375			0.554067
$794$		0			0
$795$	6.15839	+	3.91858i	0.00774640	+	0.00492903i
$796$		0			0
$797$	527.341	+	304.460i	0.661657	+	0.382008i	0.792908	−	0.609341i	$-0.208566\pi$
$797$	527.341	+	304.460i	0.661657	+	0.382008i	−0.131251	+	0.991349i	$0.541899\pi$
$798$		0			0
$799$	−304.481	−	527.376i	−0.381077	−	0.660046i
$800$		0			0
$801$	−112.567	+	1303.12i	−0.140533	+	1.62687i
$802$		0			0
$803$	−1619.88	+	935.237i	−2.01728	+	1.16468i
$804$		0			0
$805$	−125.580	+	217.511i	−0.156000	+	0.270200i
$806$		0			0
$807$	−383.838	−	16.5476i	−0.475635	−	0.0205051i
$808$		0			0
$809$		−	164.342i		−	0.203142i	−0.994828	−	0.101571i	$-0.967613\pi$
$809$		−	164.342i		−	0.203142i	0.994828	−	0.101571i	$-0.0323869\pi$
$810$		0			0
$811$	1026.77			1.26606			0.633028	−	0.774129i	$-0.281812\pi$
$811$	1026.77			1.26606			0.633028	+	0.774129i	$0.281812\pi$
$812$		0			0
$813$	66.2644	−	1537.06i	0.0815061	−	1.89061i
$814$		0			0
$815$	365.092	+	210.786i	0.447965	+	0.258633i
$816$		0			0
$817$	605.494	+	1048.75i	0.741118	+	1.28365i
$818$		0			0
$819$	581.727	+	50.2511i	0.710290	+	0.0613567i
$820$		0			0
$821$	262.140	−	151.347i	0.319293	−	0.184344i	−0.331784	−	0.943355i	$-0.607651\pi$
$821$	262.140	−	151.347i	0.319293	−	0.184344i	0.651078	+	0.759011i	$0.274317\pi$
$822$		0			0
$823$	−348.559	+	603.723i	−0.423523	+	0.733563i	−0.996281	−	0.0861609i	$-0.972540\pi$
$823$	−348.559	+	603.723i	−0.423523	+	0.733563i	0.572758	+	0.819724i	$0.305873\pi$
$824$		0			0
$825$	169.389	−	266.210i	0.205320	−	0.322678i
$826$		0			0
$827$			454.516i			0.549596i	0.961502	+	0.274798i	$0.0886110\pi$
$827$			454.516i			0.549596i	−0.961502	+	0.274798i	$0.911389\pi$
$828$		0			0
$829$	591.488			0.713496			0.356748	−	0.934201i	$-0.383885\pi$
$829$	591.488			0.713496			0.356748	+	0.934201i	$0.383885\pi$
$830$		0			0
$831$	738.284	−	384.842i	0.888428	−	0.463107i
$832$		0			0
$833$	56.0558	+	32.3638i	0.0672939	+	0.0388521i
$834$		0			0
$835$	75.9327	+	131.519i	0.0909374	+	0.157508i
$836$		0			0
$837$	−215.853	−	165.066i	−0.257889	−	0.197212i
$838$		0			0
$839$	1342.11	−	774.866i	1.59965	−	0.923559i	0.608097	−	0.793863i	$-0.291933\pi$
$839$	1342.11	−	774.866i	1.59965	−	0.923559i	0.991554	−	0.129696i	$-0.0414001\pi$
$840$		0			0
$841$	832.459	−	1441.86i	0.989844	−	1.71446i
$842$		0			0
$843$	143.102	+	274.528i	0.169753	+	0.325655i
$844$		0			0
$845$			163.911i			0.193977i
$846$		0			0
$847$	−2132.11			−2.51725
$848$		0			0
$849$	415.266	+	264.233i	0.489124	+	0.311229i
$850$		0			0
$851$	−37.3175	−	21.5453i	−0.0438514	−	0.0253176i
$852$		0			0
$853$	820.773	+	1421.62i	0.962219	+	1.66661i	0.716907	+	0.697169i	$0.245557\pi$
$853$	820.773	+	1421.62i	0.962219	+	1.66661i	0.245312	+	0.969444i	$0.421110\pi$
$854$		0			0
$855$	266.969	+	186.497i	0.312245	+	0.218126i
$856$		0			0
$857$	275.953	−	159.321i	0.321998	−	0.185906i	−0.330285	−	0.943881i	$-0.607145\pi$
$857$	275.953	−	159.321i	0.321998	−	0.185906i	0.652283	+	0.757976i	$0.273811\pi$
$858$		0			0
$859$	−314.166	+	544.152i	−0.365735	+	0.633471i	−0.988894	−	0.148624i	$-0.952516\pi$
$859$	−314.166	+	544.152i	−0.365735	+	0.633471i	0.623159	+	0.782095i	$0.285849\pi$
$860$		0			0
$861$	1068.71	+	46.0731i	1.24124	+	0.0535111i
$862$		0			0
$863$		−	183.620i		−	0.212770i	−0.994325	−	0.106385i	$-0.966072\pi$
$863$		−	183.620i		−	0.212770i	0.994325	−	0.106385i	$-0.0339276\pi$
$864$		0			0
$865$	273.678			0.316391
$866$		0			0
$867$	15.8347	−	367.301i	0.0182638	−	0.423645i
$868$		0			0
$869$	2143.20	+	1237.38i	2.46629	+	1.42391i
$870$		0			0
$871$	16.3433	+	28.3075i	0.0187639	+	0.0325000i
$872$		0			0
$873$	−179.392	−	383.607i	−0.205489	−	0.439412i
$874$		0			0
$875$	64.2138	−	37.0738i	0.0733871	−	0.0423701i
$876$		0			0
$877$	722.647	−	1251.66i	0.823999	−	1.42721i	−0.0786834	−	0.996900i	$-0.525072\pi$
$877$	722.647	−	1251.66i	0.823999	−	1.42721i	0.902682	−	0.430308i	$-0.141595\pi$
$878$		0			0
$879$	−471.859	+	741.568i	−0.536814	+	0.843650i
$880$		0			0
$881$		−	608.977i		−	0.691234i	−0.938376	−	0.345617i	$-0.887670\pi$
$881$		−	608.977i		−	0.691234i	0.938376	−	0.345617i	$-0.112330\pi$
$882$		0			0
$883$	120.519			0.136488			0.0682440	−	0.997669i	$-0.478260\pi$
$883$	120.519			0.136488			0.0682440	+	0.997669i	$0.478260\pi$
$884$		0			0
$885$	−57.3411	+	29.8899i	−0.0647923	+	0.0337739i
$886$		0			0
$887$	−1392.07	−	803.710i	−1.56941	−	0.906100i	−0.996237	−	0.0866653i	$-0.972379\pi$
$887$	−1392.07	−	803.710i	−1.56941	−	0.906100i	−0.573173	−	0.819434i	$-0.694288\pi$
$888$		0			0
$889$	−427.165	−	739.872i	−0.480501	−	0.832252i
$890$		0			0
$891$	1599.83	−	586.272i	1.79555	−	0.657993i
$892$		0			0
$893$	661.471	−	381.900i	0.740729	−	0.427660i
$894$		0			0
$895$	87.6828	−	151.871i	0.0979697	−	0.169688i
$896$		0			0
$897$	229.750	+	440.755i	0.256132	+	0.491366i
$898$		0			0
$899$			503.807i			0.560408i
$900$		0			0
$901$	−14.0386			−0.0155812
$902$		0			0
$903$	1256.17	+	799.300i	1.39111	+	0.885161i
$904$		0			0
$905$	425.180	+	245.478i	0.469813	+	0.271246i
$906$		0			0
$907$	323.994	+	561.175i	0.357215	+	0.618715i	0.987495	−	0.157653i	$-0.0503929\pi$
$907$	323.994	+	561.175i	0.357215	+	0.618715i	−0.630279	+	0.776369i	$0.717060\pi$
$908$		0			0
$909$	182.251	−	85.2289i	0.200496	−	0.0937611i
$910$		0			0
$911$	173.671	−	100.269i	0.190638	−	0.110065i	−0.401643	−	0.915796i	$-0.631561\pi$
$911$	173.671	−	100.269i	0.190638	−	0.110065i	0.592281	+	0.805731i	$0.298227\pi$
$912$		0			0
$913$	−1547.40	+	2680.17i	−1.69485	+	2.93556i
$914$		0			0
$915$	301.016	+	12.9771i	0.328979	+	0.0141826i
$916$		0			0
$917$		−	204.341i		−	0.222837i
$918$		0			0
$919$	619.581			0.674191			0.337095	−	0.941471i	$-0.390556\pi$
$919$	619.581			0.674191			0.337095	+	0.941471i	$0.390556\pi$
$920$		0			0
$921$	60.4208	−	1401.52i	0.0656035	−	1.52173i
$922$		0			0
$923$	−325.887	−	188.151i	−0.353074	−	0.203847i
$924$		0			0
$925$	6.36062	+	11.0169i	0.00687635	+	0.0119102i
$926$		0			0
$927$	−638.587	+	914.131i	−0.688875	+	0.986117i
$928$		0			0
$929$	−615.591	+	355.411i	−0.662638	+	0.382574i	−0.793281	−	0.608855i	$-0.791629\pi$
$929$	−615.591	+	355.411i	−0.662638	+	0.382574i	0.130643	+	0.991429i	$0.458296\pi$
$930$		0			0
$931$	−40.5929	+	70.3089i	−0.0436014	+	0.0755198i
$932$		0			0
$933$	−866.140	+	1361.22i	−0.928339	+	1.45897i
$934$		0			0
$935$			606.851i			0.649039i
$936$		0			0
$937$	435.674			0.464967			0.232483	−	0.972600i	$-0.425315\pi$
$937$	435.674			0.464967			0.232483	+	0.972600i	$0.425315\pi$
$938$		0			0
$939$	708.318	−	369.221i	0.754333	−	0.393207i
$940$		0			0
$941$	109.205	+	63.0496i	0.116052	+	0.0670027i	0.556902	−	0.830578i	$-0.311990\pi$
$941$	109.205	+	63.0496i	0.116052	+	0.0670027i	−0.440850	+	0.897581i	$0.645323\pi$
$942$		0			0
$943$	455.293	+	788.590i	0.482813	+	0.836257i
$944$		0			0
$945$	397.057	+	51.6086i	0.420167	+	0.0546123i
$946$		0			0
$947$	491.359	−	283.686i	0.518858	−	0.299563i	−0.217609	−	0.976036i	$-0.569826\pi$
$947$	491.359	−	283.686i	0.518858	−	0.299563i	0.736467	+	0.676473i	$0.236493\pi$
$948$		0			0
$949$	−434.930	+	753.320i	−0.458303	+	0.793804i
$950$		0			0
$951$	−661.285	−	1268.62i	−0.695358	−	1.33398i
$952$		0			0
$953$			873.128i			0.916189i	0.888903	+	0.458095i	$0.151468\pi$
$953$			873.128i			0.916189i	−0.888903	+	0.458095i	$0.848532\pi$
$954$		0			0
$955$	722.209			0.756239
$956$		0			0
$957$	−2665.25	−	1695.89i	−2.78500	−	1.77209i
$958$		0			0
$959$	611.934	+	353.300i	0.638095	+	0.368405i
$960$		0			0
$961$	429.856	+	744.532i	0.447300	+	0.774747i
$962$		0			0
$963$	−36.6901	+	424.739i	−0.0380998	+	0.441059i
$964$		0			0
$965$	334.594	−	193.178i	0.346730	−	0.200184i
$966$		0			0
$967$	−420.374	+	728.109i	−0.434720	+	0.752957i	−0.997273	−	0.0738046i	$-0.976486\pi$
$967$	−420.374	+	728.109i	−0.434720	+	0.752957i	0.562553	+	0.826761i	$0.309819\pi$
$968$		0			0
$969$	−625.747	−	26.9766i	−0.645766	−	0.0278396i
$970$		0			0
$971$		−	258.099i		−	0.265807i	−0.991129	−	0.132903i	$-0.957570\pi$
$971$		−	258.099i		−	0.265807i	0.991129	−	0.132903i	$-0.0424300\pi$
$972$		0			0
$973$	−757.613			−0.778636
$974$		0			0
$975$	6.32012	−	146.601i	0.00648218	−	0.150360i
$976$		0			0
$977$	−997.653	−	575.995i	−1.02114	−	0.589555i	−0.106706	−	0.994291i	$-0.534030\pi$
$977$	−997.653	−	575.995i	−1.02114	−	0.589555i	−0.914434	+	0.404736i	$0.867364\pi$
$978$		0			0
$979$	−1528.55	−	2647.52i	−1.56134	−	2.70431i
$980$		0			0
$981$	240.973	+	20.8159i	0.245641	+	0.0212191i
$982$		0			0
$983$	553.718	−	319.689i	0.563294	−	0.325218i	−0.191172	−	0.981556i	$-0.561229\pi$
$983$	553.718	−	319.689i	0.563294	−	0.325218i	0.754467	+	0.656338i	$0.227896\pi$
$984$		0			0
$985$	80.1990	−	138.909i	0.0814203	−	0.141024i
$986$		0			0
$987$	504.139	−	792.299i	0.510779	−	0.802735i
$988$		0			0
$989$			1267.44i			1.28153i
$990$		0			0
$991$	−1875.09			−1.89212			−0.946060	−	0.323992i	$-0.894975\pi$
$991$	−1875.09			−1.89212			−0.946060	+	0.323992i	$0.894975\pi$
$992$		0			0
$993$	94.0248	−	49.0118i	0.0946876	−	0.0493573i
$994$		0			0
$995$	−257.989	−	148.950i	−0.259285	−	0.149698i
$996$		0			0
$997$	472.697	+	818.736i	0.474120	+	0.821199i	0.999561	−	0.0296306i	$-0.00943309\pi$
$997$	472.697	+	818.736i	0.474120	+	0.821199i	−0.525441	+	0.850830i	$0.676100\pi$
$998$		0			0
$999$	−8.85430	+	68.1217i	−0.00886317	+	0.0681899i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.3.bs.d.401.5		16
3.2	odd	2		2160.3.bs.d.881.1		16
4.3	odd	2		90.3.h.a.41.3	yes	16
9.2	odd	6	inner	720.3.bs.d.641.5		16
9.7	even	3		2160.3.bs.d.1601.1		16
12.11	even	2		270.3.h.a.71.6		16
20.3	even	4		450.3.k.c.149.14		32
20.7	even	4		450.3.k.c.149.3		32
20.19	odd	2		450.3.i.g.401.6		16
36.7	odd	6		270.3.h.a.251.6		16
36.11	even	6		90.3.h.a.11.3	✓	16
36.23	even	6		810.3.d.c.161.13		16
36.31	odd	6		810.3.d.c.161.1		16
60.23	odd	4		1350.3.k.b.449.3		32
60.47	odd	4		1350.3.k.b.449.14		32
60.59	even	2		1350.3.i.g.1151.2		16
180.7	even	12		1350.3.k.b.899.3		32
180.43	even	12		1350.3.k.b.899.14		32
180.47	odd	12		450.3.k.c.299.14		32
180.79	odd	6		1350.3.i.g.251.2		16
180.83	odd	12		450.3.k.c.299.3		32
180.119	even	6		450.3.i.g.101.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.h.a.11.3	✓	16	36.11	even	6
90.3.h.a.41.3	yes	16	4.3	odd	2
270.3.h.a.71.6		16	12.11	even	2
270.3.h.a.251.6		16	36.7	odd	6
450.3.i.g.101.6		16	180.119	even	6
450.3.i.g.401.6		16	20.19	odd	2
450.3.k.c.149.3		32	20.7	even	4
450.3.k.c.149.14		32	20.3	even	4
450.3.k.c.299.3		32	180.83	odd	12
450.3.k.c.299.14		32	180.47	odd	12
720.3.bs.d.401.5		16	1.1	even	1	trivial
720.3.bs.d.641.5		16	9.2	odd	6	inner
810.3.d.c.161.1		16	36.31	odd	6
810.3.d.c.161.13		16	36.23	even	6
1350.3.i.g.251.2		16	180.79	odd	6
1350.3.i.g.1151.2		16	60.59	even	2
1350.3.k.b.449.3		32	60.23	odd	4
1350.3.k.b.449.14		32	60.47	odd	4
1350.3.k.b.899.3		32	180.7	even	12
1350.3.k.b.899.14		32	180.43	even	12
2160.3.bs.d.881.1		16	3.2	odd	2
2160.3.bs.d.1601.1		16	9.7	even	3

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	720.3.bs.d.401.5

Level	$720$
Weight	$3$
Character	720.401
Analytic conductor	$19.619$
Analytic rank	$0$
Dimension	$16$
Inner twists	$2$