LMFDB - Embedded newform 720.3.bs.d.641.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,3,Mod(401,720)]

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

lf = mfeigenbasis(mf)

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")

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

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			641.5
Root			$-2.11536 - 0.410927i$ of defining polynomial
Character	$\chi$	$=$	720.641
Dual form			720.3.bs.d.401.5

$q$-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 $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			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	−0.999547	−	0.0300933i	$-0.990420\pi$
$7$	−3.31598	+	5.74345i	−0.473712	+	0.820493i	0.525835	+	0.850587i	$0.323753\pi$
$8$		0			0
$9$	−8.96661	+	0.774559i	−0.996290	+	0.0860621i
$10$		0			0
$11$	18.2172	+	10.5177i	1.65611	+	0.956156i	0.974484	+	0.224457i	$0.0720608\pi$
$11$	18.2172	+	10.5177i	1.65611	+	0.956156i	0.681627	+	0.731699i	$0.261273\pi$
$12$		0			0
$13$	4.89124	+	8.47187i	0.376249	+	0.651683i	0.990513	−	0.137418i	$-0.0438803\pi$
$13$	4.89124	+	8.47187i	0.376249	+	0.651683i	−0.614264	+	0.789101i	$0.710547\pi$
$14$		0			0
$15$	3.60121	+	5.65962i	0.240081	+	0.377308i
$16$		0			0
$17$		−	12.9017i		−	0.758921i	−0.925208	−	0.379460i	$-0.876110\pi$
$17$		−	12.9017i		−	0.758921i	0.925208	−	0.379460i	$-0.123890\pi$
$18$		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	−0.783733	−	0.621098i	$-0.786687\pi$
$23$	−14.6674	+	8.46823i	−0.637713	+	0.368184i	0.146020	+	0.989282i	$0.453354\pi$
$24$		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	0.999983	−	0.00584415i	$-0.00186026\pi$
$29$	43.3525	+	25.0296i	1.49491	+	0.863089i	0.494930	+	0.868933i	$0.335194\pi$
$30$		0			0
$31$	−5.03212	−	8.71588i	−0.162326	−	0.281158i	0.773376	−	0.633947i	$-0.218566\pi$
$31$	−5.03212	−	8.71588i	−0.162326	−	0.281158i	−0.935703	+	0.352790i	$0.885233\pi$
$32$		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	−0.945350	−	0.326057i	$-0.894280\pi$
$41$	−46.5617	+	26.8824i	−1.13565	+	0.655669i	−0.190301	+	0.981726i	$0.560946\pi$
$42$		0			0
$43$	−37.4175	+	64.8089i	−0.870173	+	1.50718i	−0.00835640	+	0.999965i	$0.502660\pi$
$43$	−37.4175	+	64.8089i	−0.870173	+	1.50718i	−0.861817	+	0.507219i	$0.830673\pi$
$44$		0			0
$45$	−16.4978	+	11.5249i	−0.366617	+	0.256109i
$46$		0			0
$47$	−40.8766	−	23.6001i	−0.869716	−	0.502131i	−0.00246200	−	0.999997i	$-0.500784\pi$
$47$	−40.8766	−	23.6001i	−0.869716	−	0.502131i	−0.867254	+	0.497866i	$0.834117\pi$
$48$		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	$-0.996732\pi$
$53$		−	1.08813i		−	0.0205307i	0.999947	−	0.0102654i	$-0.00326762\pi$
$54$		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	−0.569075	−	0.822285i	$-0.692699\pi$
$59$	−8.34807	+	4.81976i	−0.141493	+	0.0816908i	0.427583	+	0.903976i	$0.359365\pi$
$60$		0			0
$61$	22.4573	−	38.8971i	0.368152	−	0.637657i	−0.621125	−	0.783712i	$-0.713324\pi$
$61$	22.4573	−	38.8971i	0.368152	−	0.637657i	0.989277	+	0.146054i	$0.0466574\pi$
$62$		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	0.853288	−	0.521439i	$-0.174605\pi$
$67$	−1.67067	−	2.89369i	−0.0249354	−	0.0431894i	−0.878224	+	0.478250i	$0.841271\pi$
$68$		0			0
$69$	−27.2763	−	42.8672i	−0.395309	−	0.621263i
$70$		0			0
$71$			38.4670i			0.541788i	0.962609	+	0.270894i	$0.0873193\pi$
$71$			38.4670i			0.541788i	−0.962609	+	0.270894i	$0.912681\pi$
$72$		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	−0.205779	−	0.978599i	$-0.565973\pi$
$79$	58.8235	−	101.885i	0.744602	−	1.28969i	0.950381	−	0.311090i	$-0.100694\pi$
$80$		0			0
$81$	79.8001	−	13.8903i	0.985187	−	0.171486i
$82$		0			0
$83$	−127.412	−	73.5614i	−1.53509	−	0.886282i	−0.999116	−	0.0420449i	$-0.986613\pi$
$83$	−127.412	−	73.5614i	−1.53509	−	0.886282i	−0.535970	−	0.844237i	$-0.680054\pi$
$84$		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	$0.304069\pi$
$89$			145.331i			1.63293i	−0.577396	+	0.816464i	$0.695931\pi$
$90$		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	−0.718895	−	0.695119i	$-0.755352\pi$
$97$	23.5267	−	40.7494i	0.242543	−	0.420097i	0.961438	+	0.275022i	$0.0886851\pi$
$98$		0			0
$99$	−171.493	−	80.1980i	−1.73226	−	0.810080i
$100$		0			0
$101$	−19.3600	−	11.1775i	−0.191683	−	0.110668i	0.401087	−	0.916040i	$-0.368632\pi$
$101$	−19.3600	−	11.1775i	−0.191683	−	0.110668i	−0.592770	+	0.805372i	$0.701966\pi$
$102$		0			0
$103$	61.9495	+	107.300i	0.601452	+	1.04174i	0.992601	+	0.121418i	$0.0387441\pi$
$103$	61.9495	+	107.300i	0.601452	+	1.04174i	−0.391150	+	0.920327i	$0.627923\pi$
$104$		0			0
$105$	−44.4473	+	1.91617i	−0.423308	+	0.0182492i
$106$		0			0
$107$			47.3690i			0.442701i	0.975194	+	0.221351i	$0.0710465\pi$
$107$			47.3690i			0.442701i	−0.975194	+	0.221351i	$0.928954\pi$
$108$		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	−0.570344	−	0.821406i	$-0.693190\pi$
$113$	−16.2899	+	9.40495i	−0.144158	+	0.0832297i	0.426186	+	0.904635i	$0.359857\pi$
$114$		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	−0.394685	−	0.918817i	$-0.629146\pi$
$131$	26.6836	−	15.4058i	0.203692	−	0.117601i	0.598376	+	0.801215i	$0.295813\pi$
$132$		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	0.123898	−	0.992295i	$-0.460460\pi$
$137$	−92.2703	−	53.2723i	−0.673506	−	0.388849i	−0.797404	+	0.603446i	$0.793794\pi$
$138$		0			0
$139$	57.1183	+	98.9317i	0.410923	+	0.711739i	0.994991	−	0.0999656i	$-0.0318733\pi$
$139$	57.1183	+	98.9317i	0.410923	+	0.711739i	−0.584068	+	0.811705i	$0.698540\pi$
$140$		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	−0.105710	−	0.994397i	$-0.533712\pi$
$149$	104.689	−	60.4419i	0.702607	−	0.405651i	0.808318	+	0.588746i	$0.200378\pi$
$150$		0			0
$151$	63.4938	−	109.975i	0.420489	−	0.728308i	−0.575498	−	0.817803i	$-0.695192\pi$
$151$	63.4938	−	109.975i	0.420489	−	0.728308i	0.995987	+	0.0894947i	$0.0285252\pi$
$152$		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	0.650994	−	0.759083i	$-0.274352\pi$
$157$	−52.1064	−	90.2510i	−0.331888	−	0.574847i	−0.982882	+	0.184236i	$0.941019\pi$
$158$		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	−0.313454	−	0.949603i	$-0.601486\pi$
$167$	58.8172	−	33.9581i	0.352199	−	0.203342i	0.665653	+	0.746261i	$0.268153\pi$
$168$		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	0.774017	−	0.633165i	$-0.218244\pi$
$173$	105.995	+	61.1963i	0.612689	+	0.353736i	−0.161328	+	0.986901i	$0.551578\pi$
$174$		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	$0.0703013\pi$
$179$			78.4259i			0.438134i	−0.975710	+	0.219067i	$0.929699\pi$
$180$		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	0.999212	−	0.0396836i	$-0.0126350\pi$
$191$	279.710	+	161.491i	1.46445	+	0.845501i	0.465239	+	0.885185i	$0.345968\pi$
$192$		0			0
$193$	86.3918	+	149.635i	0.447626	+	0.775311i	0.998231	−	0.0594550i	$-0.0189363\pi$
$193$	86.3918	+	149.635i	0.447626	+	0.775311i	−0.550605	+	0.834766i	$0.685603\pi$
$194$		0			0
$195$	−30.3332	+	58.1915i	−0.155555	+	0.298418i
$196$		0			0
$197$			71.7321i			0.364123i	0.983287	+	0.182061i	$0.0582769\pi$
$197$			71.7321i			0.364123i	−0.983287	+	0.182061i	$0.941723\pi$
$198$		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	−0.837750	−	0.546053i	$-0.816130\pi$
$211$	−188.164	−	325.909i	−0.891771	−	1.54459i	−0.0540209	−	0.998540i	$-0.517204\pi$
$212$		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	−0.792026	−	0.610487i	$-0.790974\pi$
$223$	29.5885	−	51.2488i	0.132684	−	0.229815i	0.924710	+	0.380672i	$0.124307\pi$
$224$		0			0
$225$	−19.0626	+	40.7629i	−0.0847226	+	0.181169i
$226$		0			0
$227$	−129.764	−	74.9193i	−0.571647	−	0.330041i	0.186160	−	0.982520i	$-0.440396\pi$
$227$	−129.764	−	74.9193i	−0.571647	−	0.330041i	−0.757807	+	0.652479i	$0.773729\pi$
$228$		0			0
$229$	85.4319	+	147.972i	0.373065	+	0.646167i	0.990035	−	0.140819i	$-0.0449736\pi$
$229$	85.4319	+	147.972i	0.373065	+	0.646167i	−0.616970	+	0.786986i	$0.711640\pi$
$230$		0			0
$231$	−224.676	−	353.099i	−0.972625	−	1.52857i
$232$		0			0
$233$			448.983i			1.92697i	0.267770	+	0.963483i	$0.413713\pi$
$233$			448.983i			1.92697i	−0.267770	+	0.963483i	$0.586287\pi$
$234$		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	−0.0170289	−	0.999855i	$-0.505421\pi$
$239$	200.845	−	115.958i	0.840356	−	0.485180i	0.857385	+	0.514675i	$0.172087\pi$
$240$		0			0
$241$	198.671	−	344.108i	0.824359	−	1.42783i	−0.0780488	−	0.996950i	$-0.524869\pi$
$241$	198.671	−	344.108i	0.824359	−	1.42783i	0.902408	−	0.430882i	$-0.141798\pi$
$242$		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	$-0.874264\pi$
$251$		−	193.179i		−	0.769636i	0.922992	−	0.384818i	$-0.125736\pi$
$252$		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	−0.282335	−	0.959316i	$-0.591109\pi$
$257$	104.673	−	60.4331i	0.407289	−	0.235148i	0.689624	+	0.724167i	$0.257776\pi$
$258$		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	0.905655	−	0.424016i	$-0.139380\pi$
$263$	260.705	+	150.518i	0.991273	+	0.572312i	0.0856183	+	0.996328i	$0.472713\pi$
$264$		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	$0.0765044\pi$
$269$			128.065i			0.476077i	−0.971256	+	0.238038i	$0.923496\pi$
$270$		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	−0.499057	−	0.866569i	$-0.666320\pi$
$277$	138.761	−	240.341i	0.500942	−	0.867658i	0.999999	−	0.00108844i	$-0.000346460\pi$
$278$		0			0
$279$	51.8720	+	74.2542i	0.185921	+	0.266144i
$280$		0			0
$281$	−89.3698	−	51.5977i	−0.318042	−	0.183622i	0.332478	−	0.943111i	$-0.392115\pi$
$281$	−89.3698	−	51.5977i	−0.318042	−	0.183622i	−0.650519	+	0.759490i	$0.725449\pi$
$282$		0			0
$283$	−82.0340	−	142.087i	−0.289873	−	0.502075i	0.683906	−	0.729570i	$-0.260280\pi$
$283$	−82.0340	−	142.087i	−0.289873	−	0.502075i	−0.973779	+	0.227495i	$0.926946\pi$
$284$		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	−0.866013	−	0.500021i	$-0.833325\pi$
$293$	−253.735	+	146.494i	−0.865988	+	0.499979i	2.47977e−5		1.00000i	$0.499992\pi$
$294$		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	−0.999996	−	0.00276786i	$-0.999119\pi$
$311$	−465.753	+	268.902i	−1.49760	+	0.864638i	−0.497601	+	0.867406i	$0.665786\pi$
$312$		0			0
$313$	133.129	−	230.586i	0.425332	−	0.736697i	−0.571119	−	0.820867i	$-0.693491\pi$
$313$	133.129	−	230.586i	0.425332	−	0.736697i	0.996451	+	0.0841703i	$0.0268240\pi$
$314$		0			0
$315$	−11.4863	−	132.971i	−0.0364646	−	0.422129i
$316$		0			0
$317$	412.986	+	238.437i	1.30279	+	0.752168i	0.980882	−	0.194602i	$-0.0623414\pi$
$317$	412.986	+	238.437i	1.30279	+	0.752168i	0.321911	+	0.946770i	$0.395675\pi$
$318$		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	−0.838095	−	0.545524i	$-0.816331\pi$
$331$	17.6720	−	30.6088i	0.0533898	−	0.0924738i	0.891485	+	0.453050i	$0.149664\pi$
$332$		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	0.989360	−	0.145488i	$-0.0464752\pi$
$337$	124.246	+	215.201i	0.368684	+	0.638579i	−0.620676	+	0.784067i	$0.713142\pi$
$338$		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	−0.496636	−	0.867959i	$-0.665432\pi$
$347$	2.33212	−	1.34645i	0.00672082	−	0.00388026i	0.503357	+	0.864079i	$0.332098\pi$
$348$		0			0
$349$	−196.192	+	339.815i	−0.562156	+	0.973682i	0.435152	+	0.900357i	$0.356694\pi$
$349$	−196.192	+	339.815i	−0.562156	+	0.973682i	−0.997308	+	0.0733253i	$0.976639\pi$
$350$		0			0
$351$	209.810	−	160.445i	0.597751	−	0.457108i
$352$		0			0
$353$	17.1321	+	9.89124i	0.0485329	+	0.0280205i	0.524070	−	0.851675i	$-0.324413\pi$
$353$	17.1321	+	9.89124i	0.0485329	+	0.0280205i	−0.475537	+	0.879696i	$0.657746\pi$
$354$		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	$-0.803659\pi$
$359$		−	415.325i		−	1.15689i	0.815720	−	0.578447i	$-0.196341\pi$
$360$		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	0.231591	+	0.972813i	$0.425607\pi$
$367$	−266.694	+	461.927i	−0.726685	+	1.25866i	−0.958276	+	0.285843i	$0.907726\pi$
$368$		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	0.973567	−	0.228403i	$-0.0733503\pi$
$373$	107.790	+	186.697i	0.288981	+	0.500529i	−0.684586	+	0.728932i	$0.740017\pi$
$374$		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	−0.519323	−	0.854578i	$-0.673816\pi$
$383$	−14.8980	+	8.60134i	−0.0388980	+	0.0224578i	0.480425	+	0.877036i	$0.340482\pi$
$384$		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	0.831814	−	0.555055i	$-0.187303\pi$
$389$	298.375	+	172.267i	0.767030	+	0.442845i	−0.0647844	+	0.997899i	$0.520636\pi$
$390$		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	−0.679916	−	0.733290i	$-0.737984\pi$
$401$	−154.315	+	89.0938i	−0.384825	+	0.222179i	0.295090	+	0.955469i	$0.404650\pi$
$402$		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	0.859042	−	0.511906i	$-0.171060\pi$
$409$	−5.64530	−	9.77795i	−0.0138027	−	0.0239070i	−0.872844	+	0.487999i	$0.837727\pi$
$410$		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	−0.431234	−	0.902240i	$-0.641922\pi$
$419$	56.3602	−	32.5396i	0.134511	−	0.0776601i	0.565746	+	0.824580i	$0.308588\pi$
$420$		0			0
$421$	115.044	−	199.262i	0.273263	−	0.473306i	−0.696432	−	0.717623i	$-0.745230\pi$
$421$	115.044	−	199.262i	0.273263	−	0.473306i	0.969696	+	0.244317i	$0.0785636\pi$
$422$		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	$-0.975053\pi$
$431$		−	67.4877i		−	0.156584i	0.996930	−	0.0782920i	$-0.0249467\pi$
$432$		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	−0.144376	−	0.989523i	$-0.546118\pi$
$439$	344.511	−	596.711i	0.784764	−	1.35925i	0.929140	−	0.369728i	$-0.120549\pi$
$440$		0			0
$441$	−25.8581	−	37.0156i	−0.0586351	−	0.0839356i
$442$		0			0
$443$	−58.9612	−	34.0413i	−0.133095	−	0.0768426i	0.431974	−	0.901886i	$-0.357817\pi$
$443$	−58.9612	−	34.0413i	−0.133095	−	0.0768426i	−0.565069	+	0.825043i	$0.691151\pi$
$444$		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	$-0.723517\pi$
$449$		−	685.554i		−	1.52685i	0.645898	−	0.763423i	$-0.276483\pi$
$450$		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	0.428471	+	0.903555i	$0.359052\pi$
$457$	−259.698	+	449.810i	−0.568266	+	0.984266i	−0.996738	+	0.0807109i	$0.974281\pi$
$458$		0			0
$459$	−345.439	+	44.8994i	−0.752590	+	0.0978200i
$460$		0			0
$461$	77.5379	+	44.7665i	0.168195	+	0.0971074i	0.581734	−	0.813379i	$-0.302374\pi$
$461$	77.5379	+	44.7665i	0.168195	+	0.0971074i	−0.413539	+	0.910486i	$0.635708\pi$
$462$		0			0
$463$	−254.981	−	441.640i	−0.550714	−	0.953865i	−0.998223	−	0.0595857i	$-0.981022\pi$
$463$	−254.981	−	441.640i	−0.550714	−	0.953865i	0.447509	−	0.894279i	$-0.352311\pi$
$464$		0			0
$465$	31.2069	−	59.8676i	0.0671116	−	0.128748i
$466$		0			0
$467$			539.803i			1.15590i	0.816074	+	0.577948i	$0.196146\pi$
$467$			539.803i			1.15590i	−0.816074	+	0.577948i	$0.803854\pi$
$468$		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	0.398408	−	0.917208i	$-0.369563\pi$
$479$	−94.2261	−	54.4015i	−0.196714	−	0.113573i	−0.595122	+	0.803635i	$0.702896\pi$
$480$		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	−0.869702	−	0.493577i	$-0.835689\pi$
$491$	−430.657	+	248.640i	−0.877102	+	0.506395i	−0.00740027	+	0.999973i	$0.502356\pi$
$492$		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	0.933184	−	0.359399i	$-0.117018\pi$
$499$	77.5164	+	134.262i	0.155343	+	0.269063i	−0.777841	+	0.628462i	$0.783685\pi$
$500$		0			0
$501$	109.380	+	171.900i	0.218323	+	0.343114i
$502$		0			0
$503$			580.438i			1.15395i	0.816761	+	0.576976i	$0.195767\pi$
$503$			580.438i			1.15395i	−0.816761	+	0.576976i	$0.804233\pi$
$504$		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	−0.336472	−	0.941694i	$-0.609234\pi$
$509$	158.209	−	91.3419i	0.310823	−	0.179454i	0.647295	+	0.762240i	$0.275900\pi$
$510$		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	$-0.985405\pi$
$521$		−	47.7611i		−	0.0916720i	0.998949	−	0.0458360i	$-0.0145952\pi$
$522$		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	−0.756184	−	0.654359i	$-0.772938\pi$
$547$	103.164	−	178.686i	0.188600	−	0.326665i	0.944784	+	0.327695i	$0.106272\pi$
$548$		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	$-0.803882\pi$
$557$		−	643.753i		−	1.15575i	0.816125	−	0.577876i	$-0.196118\pi$
$558$		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	0.173494	−	0.984835i	$-0.444494\pi$
$563$	626.694	−	361.822i	1.11313	−	0.642668i	0.939639	+	0.342167i	$0.111161\pi$
$564$		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	0.760563	−	0.649264i	$-0.224923\pi$
$569$	329.204	+	190.066i	0.578566	+	0.334035i	−0.181997	+	0.983299i	$0.558256\pi$
$570$		0			0
$571$	20.7292	+	35.9040i	0.0363033	+	0.0628791i	0.883606	−	0.468231i	$-0.155108\pi$
$571$	20.7292	+	35.9040i	0.0363033	+	0.0628791i	−0.847303	+	0.531110i	$0.821775\pi$
$572$		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	0.929275	−	0.369388i	$-0.120433\pi$
$587$	630.446	+	363.988i	1.07401	+	0.620082i	0.144738	+	0.989470i	$0.453766\pi$
$588$		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	$-0.885064\pi$
$593$		−	418.998i		−	0.706573i	0.935515	−	0.353286i	$-0.114936\pi$
$594$		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	0.294610	−	0.955618i	$-0.404810\pi$
$599$	760.433	−	439.036i	1.26950	−	0.732948i	0.974894	+	0.222669i	$0.0714771\pi$
$600$		0			0
$601$	266.229	−	461.122i	0.442977	−	0.767259i	−0.554932	−	0.831896i	$-0.687256\pi$
$601$	266.229	−	461.122i	0.442977	−	0.767259i	0.997909	+	0.0646372i	$0.0205890\pi$
$602$		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	0.902329	−	0.431049i	$-0.141856\pi$
$607$	47.2643	+	81.8641i	0.0778653	+	0.134867i	−0.824463	+	0.565915i	$0.808523\pi$
$608$		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	−0.360971	−	0.932577i	$-0.617555\pi$
$617$	164.232	−	94.8195i	0.266179	−	0.153678i	0.627150	+	0.778899i	$0.284221\pi$
$618$		0			0
$619$	−47.7312	+	82.6728i	−0.0771101	+	0.133559i	−0.902002	−	0.431732i	$-0.857903\pi$
$619$	−47.7312	+	82.6728i	−0.0771101	+	0.133559i	0.824892	+	0.565291i	$0.191236\pi$
$620$		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	0.268084	−	0.963395i	$-0.413609\pi$
$641$	−277.039	−	159.949i	−0.432198	−	0.249530i	−0.700283	+	0.713866i	$0.746943\pi$
$642$		0			0
$643$	76.1741	+	131.937i	0.118467	+	0.205190i	0.919160	−	0.393884i	$-0.128869\pi$
$643$	76.1741	+	131.937i	0.118467	+	0.205190i	−0.800693	+	0.599074i	$0.795535\pi$
$644$		0			0
$645$	−501.542	+	21.6220i	−0.777584	+	0.0335225i
$646$		0			0
$647$		−	632.862i		−	0.978148i	−0.872242	−	0.489074i	$-0.837335\pi$
$647$		−	632.862i		−	0.978148i	0.872242	−	0.489074i	$-0.162665\pi$
$648$		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	0.152529	−	0.988299i	$-0.451258\pi$
$653$	708.299	−	408.937i	1.08468	−	0.626243i	0.932156	+	0.362056i	$0.117925\pi$
$654$		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	0.193660	−	0.981069i	$-0.437964\pi$
$659$	−368.474	−	212.738i	−0.559141	−	0.322820i	−0.752800	+	0.658249i	$0.771297\pi$
$660$		0			0
$661$	−142.986	−	247.659i	−0.216318	−	0.374673i	0.737362	−	0.675498i	$-0.236071\pi$
$661$	−142.986	−	247.659i	−0.216318	−	0.374673i	−0.953679	+	0.300825i	$0.902738\pi$
$662$		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	−0.0492769	+	0.998785i	$0.515692\pi$
$673$	−598.709	+	1036.99i	−0.889612	+	1.54085i	−0.840335	+	0.542068i	$0.817642\pi$
$674$		0			0
$675$	−124.638	−	51.8676i	−0.184650	−	0.0768408i
$676$		0			0
$677$	−784.232	−	452.777i	−1.15839	−	0.668799i	−0.207475	−	0.978240i	$-0.566525\pi$
$677$	−784.232	−	452.777i	−1.15839	−	0.668799i	−0.950918	+	0.309442i	$0.899858\pi$
$678$		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	$-0.992730\pi$
$683$		−	31.1970i		−	0.0456764i	0.999739	−	0.0228382i	$-0.00727026\pi$
$684$		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	−0.930093	−	0.367324i	$-0.880274\pi$
$691$	−101.532	+	175.858i	−0.146935	+	0.254498i	0.783158	+	0.621822i	$0.213607\pi$
$692$		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	$0.149288\pi$
$701$			633.699i			0.903993i	−0.892020	+	0.451997i	$0.850712\pi$
$702$		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	−0.808534	−	0.588450i	$-0.799738\pi$
$709$	74.6901	−	129.367i	0.105346	−	0.182464i	0.913879	+	0.405986i	$0.133072\pi$
$710$		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	$0.0573285\pi$
$719$			257.590i			0.358262i	−0.983825	+	0.179131i	$0.942671\pi$
$720$		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	−0.577980	−	0.816051i	$-0.696159\pi$
$727$	303.691	−	526.008i	0.417731	−	0.723532i	0.995711	+	0.0925193i	$0.0294920\pi$
$728$		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	−0.992013	−	0.126134i	$-0.959743\pi$
$733$	−443.643	−	768.411i	−0.605242	−	1.04831i	0.386771	−	0.922176i	$-0.373590\pi$
$734$		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	−0.793951	−	0.607982i	$-0.791979\pi$
$743$	−493.648	+	285.008i	−0.664399	+	0.383591i	0.129552	+	0.991573i	$0.458646\pi$
$744$		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	0.972516	−	0.232836i	$-0.0748004\pi$
$751$	213.747	+	370.221i	0.284617	+	0.492970i	−0.687900	+	0.725806i	$0.741467\pi$
$752$		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	−0.999962	−	0.00868376i	$-0.997236\pi$
$761$	−1135.73	+	655.716i	−1.49242	+	0.861651i	−0.492461	+	0.870335i	$0.663903\pi$
$762$		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	0.934950	+	0.354780i	$0.115444\pi$
$769$	595.762	+	1031.89i	0.774724	+	1.34186i	−0.160226	+	0.987080i	$0.551222\pi$
$770$		0			0
$771$	194.656	+	305.920i	0.252473	+	0.396783i
$772$		0			0
$773$		−	204.848i		−	0.265003i	−0.991183	−	0.132502i	$-0.957699\pi$
$773$		−	204.848i		−	0.265003i	0.991183	−	0.132502i	$-0.0423010\pi$
$774$		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	0.905239	−	0.424903i	$-0.139692\pi$
$787$	66.6137	+	115.378i	0.0846426	+	0.146605i	−0.820596	+	0.571508i	$0.806358\pi$
$788$		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	−0.131251	−	0.991349i	$-0.541899\pi$
$797$	527.341	−	304.460i	0.661657	−	0.382008i	0.792908	+	0.609341i	$0.208566\pi$
$798$		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	$0.0323869\pi$
$809$			164.342i			0.203142i	−0.994828	+	0.101571i	$0.967613\pi$
$810$		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	0.651078	−	0.759011i	$-0.274317\pi$
$821$	262.140	+	151.347i	0.319293	+	0.184344i	−0.331784	+	0.943355i	$0.607651\pi$
$822$		0			0
$823$	−348.559	−	603.723i	−0.423523	−	0.733563i	0.572758	−	0.819724i	$-0.305873\pi$
$823$	−348.559	−	603.723i	−0.423523	−	0.733563i	−0.996281	+	0.0861609i	$0.972540\pi$
$824$		0			0
$825$	169.389	+	266.210i	0.205320	+	0.322678i
$826$		0			0
$827$		−	454.516i		−	0.549596i	−0.961502	−	0.274798i	$-0.911389\pi$
$827$		−	454.516i		−	0.549596i	0.961502	−	0.274798i	$-0.0886110\pi$
$828$		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	0.991554	+	0.129696i	$0.0414001\pi$
$839$	1342.11	+	774.866i	1.59965	+	0.923559i	0.608097	+	0.793863i	$0.291933\pi$
$840$		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	0.245312	−	0.969444i	$-0.421110\pi$
$853$	820.773	−	1421.62i	0.962219	−	1.66661i	0.716907	−	0.697169i	$-0.245557\pi$
$854$		0			0
$855$	266.969	−	186.497i	0.312245	−	0.218126i
$856$		0			0
$857$	275.953	+	159.321i	0.321998	+	0.185906i	0.652283	−	0.757976i	$-0.273811\pi$
$857$	275.953	+	159.321i	0.321998	+	0.185906i	−0.330285	+	0.943881i	$0.607145\pi$
$858$		0			0
$859$	−314.166	−	544.152i	−0.365735	−	0.633471i	0.623159	−	0.782095i	$-0.285849\pi$
$859$	−314.166	−	544.152i	−0.365735	−	0.633471i	−0.988894	+	0.148624i	$0.952516\pi$
$860$		0			0
$861$	1068.71	−	46.0731i	1.24124	−	0.0535111i
$862$		0			0
$863$			183.620i			0.212770i	0.994325	+	0.106385i	$0.0339276\pi$
$863$			183.620i			0.212770i	−0.994325	+	0.106385i	$0.966072\pi$
$864$		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	0.902682	+	0.430308i	$0.141595\pi$
$877$	722.647	+	1251.66i	0.823999	+	1.42721i	−0.0786834	+	0.996900i	$0.525072\pi$
$878$		0			0
$879$	−471.859	−	741.568i	−0.536814	−	0.843650i
$880$		0			0
$881$			608.977i			0.691234i	0.938376	+	0.345617i	$0.112330\pi$
$881$			608.977i			0.691234i	−0.938376	+	0.345617i	$0.887670\pi$
$882$		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	−0.573173	+	0.819434i	$0.694288\pi$
$887$	−1392.07	+	803.710i	−1.56941	+	0.906100i	−0.996237	+	0.0866653i	$0.972379\pi$
$888$		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	−0.630279	−	0.776369i	$-0.717060\pi$
$907$	323.994	−	561.175i	0.357215	−	0.618715i	0.987495	+	0.157653i	$0.0503929\pi$
$908$		0			0
$909$	182.251	+	85.2289i	0.200496	+	0.0937611i
$910$		0			0
$911$	173.671	+	100.269i	0.190638	+	0.110065i	0.592281	−	0.805731i	$-0.298227\pi$
$911$	173.671	+	100.269i	0.190638	+	0.110065i	−0.401643	+	0.915796i	$0.631561\pi$
$912$		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	0.130643	−	0.991429i	$-0.458296\pi$
$929$	−615.591	−	355.411i	−0.662638	−	0.382574i	−0.793281	+	0.608855i	$0.791629\pi$
$930$		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	−0.440850	−	0.897581i	$-0.645323\pi$
$941$	109.205	−	63.0496i	0.116052	−	0.0670027i	0.556902	+	0.830578i	$0.311990\pi$
$942$		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	0.736467	−	0.676473i	$-0.236493\pi$
$947$	491.359	+	283.686i	0.518858	+	0.299563i	−0.217609	+	0.976036i	$0.569826\pi$
$948$		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	$-0.848532\pi$
$953$		−	873.128i		−	0.916189i	0.888903	−	0.458095i	$-0.151468\pi$
$954$		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	0.562553	−	0.826761i	$-0.309819\pi$
$967$	−420.374	−	728.109i	−0.434720	−	0.752957i	−0.997273	+	0.0738046i	$0.976486\pi$
$968$		0			0
$969$	−625.747	+	26.9766i	−0.645766	+	0.0278396i
$970$		0			0
$971$			258.099i			0.265807i	0.991129	+	0.132903i	$0.0424300\pi$
$971$			258.099i			0.265807i	−0.991129	+	0.132903i	$0.957570\pi$
$972$		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	−0.914434	−	0.404736i	$-0.867364\pi$
$977$	−997.653	+	575.995i	−1.02114	+	0.589555i	−0.106706	+	0.994291i	$0.534030\pi$
$978$		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	0.754467	−	0.656338i	$-0.227896\pi$
$983$	553.718	+	319.689i	0.563294	+	0.325218i	−0.191172	+	0.981556i	$0.561229\pi$
$984$		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	−0.525441	−	0.850830i	$-0.676100\pi$
$997$	472.697	−	818.736i	0.474120	−	0.821199i	0.999561	+	0.0296306i	$0.00943309\pi$
$998$		0			0
$999$	−8.85430	−	68.1217i	−0.00886317	−	0.0681899i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.h.a.11.3	✓	16	4.3	odd	2
90.3.h.a.41.3	yes	16	36.23	even	6
270.3.h.a.71.6		16	36.31	odd	6
270.3.h.a.251.6		16	12.11	even	2
450.3.i.g.101.6		16	20.19	odd	2
450.3.i.g.401.6		16	180.59	even	6
450.3.k.c.149.3		32	180.167	odd	12
450.3.k.c.149.14		32	180.23	odd	12
450.3.k.c.299.3		32	20.3	even	4
450.3.k.c.299.14		32	20.7	even	4
720.3.bs.d.401.5		16	9.5	odd	6	inner
720.3.bs.d.641.5		16	1.1	even	1	trivial
810.3.d.c.161.1		16	36.11	even	6
810.3.d.c.161.13		16	36.7	odd	6
1350.3.i.g.251.2		16	60.59	even	2
1350.3.i.g.1151.2		16	180.139	odd	6
1350.3.k.b.449.3		32	180.103	even	12
1350.3.k.b.449.14		32	180.67	even	12
1350.3.k.b.899.3		32	60.47	odd	4
1350.3.k.b.899.14		32	60.23	odd	4
2160.3.bs.d.881.1		16	9.4	even	3
2160.3.bs.d.1601.1		16	3.2	odd	2

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

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

Introduction

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