LMFDB - Embedded newform 324.3.d.i.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(163,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("324.163");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.d (of order $2$, degree $1$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1919698923024.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + 12x^{5} - 36x^{4} + 48x^{3} + 32x^{2} - 192x + 256 $ x^8 - 3x^7 + 2x^6 + 12x^5 - 36x^4 + 48x^3 + 32x^2 - 192*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			163.3
Root			$0.247102 + 1.98468i$ of defining polynomial
Character	$\chi$	$=$	324.163
Dual form			324.3.d.i.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.247102 - 1.98468i) q^{2} +(-3.87788 - 0.980835i) q^{4} -2.20185 q^{5} +8.35824i q^{7} +(-2.90487 + 7.45397i) q^{8} +O(q^{10})$	\(q+(0.247102 - 1.98468i) q^{2} +(-3.87788 - 0.980835i) q^{4} -2.20185 q^{5} +8.35824i q^{7} +(-2.90487 + 7.45397i) q^{8} +(-0.544081 + 4.36996i) q^{10} -5.25121i q^{11} +14.7558 q^{13} +(16.5884 + 2.06534i) q^{14} +(14.0759 + 7.60712i) q^{16} +28.2789 q^{17} +19.1376i q^{19} +(8.53851 + 2.15965i) q^{20} +(-10.4220 - 1.29759i) q^{22} -3.65696i q^{23} -20.1519 q^{25} +(3.64618 - 29.2854i) q^{26} +(8.19805 - 32.4122i) q^{28} +24.6710 q^{29} +38.0675i q^{31} +(18.5759 - 26.0564i) q^{32} +(6.98776 - 56.1244i) q^{34} -18.4036i q^{35} -4.21977 q^{37} +(37.9819 + 4.72893i) q^{38} +(6.39609 - 16.4125i) q^{40} +19.8497 q^{41} +23.3127i q^{43} +(-5.15057 + 20.3636i) q^{44} +(-7.25787 - 0.903640i) q^{46} +29.8534i q^{47} -20.8601 q^{49} +(-4.97956 + 39.9949i) q^{50} +(-57.2211 - 14.4730i) q^{52} -32.1118 q^{53} +11.5624i q^{55} +(-62.3021 - 24.2796i) q^{56} +(6.09625 - 48.9639i) q^{58} +9.19326i q^{59} +81.6430 q^{61} +(75.5517 + 9.40656i) q^{62} +(-47.1234 - 43.3057i) q^{64} -32.4900 q^{65} -7.92331i q^{67} +(-109.662 - 27.7369i) q^{68} +(-36.5252 - 4.54756i) q^{70} +62.9286i q^{71} +33.3218 q^{73} +(-1.04271 + 8.37487i) q^{74} +(18.7708 - 74.2133i) q^{76} +43.8909 q^{77} +62.0228i q^{79} +(-30.9931 - 16.7497i) q^{80} +(4.90489 - 39.3951i) q^{82} -118.999i q^{83} -62.2659 q^{85} +(46.2682 + 5.76062i) q^{86} +(39.1424 + 15.2541i) q^{88} -107.361 q^{89} +123.332i q^{91} +(-3.58687 + 14.1812i) q^{92} +(59.2494 + 7.37684i) q^{94} -42.1381i q^{95} -3.57242 q^{97} +(-5.15457 + 41.4005i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 5 q^{4} - 6 q^{5} - 27 q^{8}+O(q^{10}) $ 8 * q + 3 * q^2 + 5 * q^4 - 6 * q^5 - 27 * q^8	$ 8 q + 3 q^{2} + 5 q^{4} - 6 q^{5} - 27 q^{8} + 10 q^{10} + 46 q^{13} + 12 q^{14} + 17 q^{16} + 6 q^{17} - 36 q^{20} - 33 q^{22} + 30 q^{25} + 36 q^{26} + 6 q^{28} - 42 q^{29} - 87 q^{32} - 11 q^{34} + 28 q^{37} + 99 q^{38} - 68 q^{40} - 84 q^{41} - 111 q^{44} - 132 q^{46} - 58 q^{49} + 219 q^{50} - 110 q^{52} - 36 q^{53} - 270 q^{56} + 16 q^{58} + 34 q^{61} + 258 q^{62} - 127 q^{64} + 30 q^{65} - 375 q^{68} - 150 q^{70} + 58 q^{73} + 372 q^{74} + 15 q^{76} + 330 q^{77} - 360 q^{80} + 127 q^{82} + 140 q^{85} + 273 q^{86} - 75 q^{88} - 192 q^{89} - 258 q^{92} - 36 q^{94} + 148 q^{97} + 585 q^{98}+O(q^{100}) $ 8 * q + 3 * q^2 + 5 * q^4 - 6 * q^5 - 27 * q^8 + 10 * q^10 + 46 * q^13 + 12 * q^14 + 17 * q^16 + 6 * q^17 - 36 * q^20 - 33 * q^22 + 30 * q^25 + 36 * q^26 + 6 * q^28 - 42 * q^29 - 87 * q^32 - 11 * q^34 + 28 * q^37 + 99 * q^38 - 68 * q^40 - 84 * q^41 - 111 * q^44 - 132 * q^46 - 58 * q^49 + 219 * q^50 - 110 * q^52 - 36 * q^53 - 270 * q^56 + 16 * q^58 + 34 * q^61 + 258 * q^62 - 127 * q^64 + 30 * q^65 - 375 * q^68 - 150 * q^70 + 58 * q^73 + 372 * q^74 + 15 * q^76 + 330 * q^77 - 360 * q^80 + 127 * q^82 + 140 * q^85 + 273 * q^86 - 75 * q^88 - 192 * q^89 - 258 * q^92 - 36 * q^94 + 148 * q^97 + 585 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.247102	−	1.98468i	0.123551	−	0.992338i
$2$	0.247102	−	1.98468i	0.123551	−	0.992338i
$3$		0			0
$3$		0			0
$4$	−3.87788	−	0.980835i	−0.969470	−	0.245209i
$5$	−2.20185			−0.440370			−0.220185	−	0.975458i	$-0.570666\pi$
$5$	−2.20185			−0.440370			−0.220185	+	0.975458i	$0.570666\pi$
$6$		0			0
$7$			8.35824i			1.19403i	0.802229	+	0.597017i	$0.203647\pi$
$7$			8.35824i			1.19403i	−0.802229	+	0.597017i	$0.796353\pi$
$8$	−2.90487	+	7.45397i	−0.363109	+	0.931747i
$9$		0			0
$10$	−0.544081	+	4.36996i	−0.0544081	+	0.436996i
$11$		−	5.25121i		−	0.477383i	−0.971095	−	0.238692i	$-0.923282\pi$
$11$		−	5.25121i		−	0.477383i	0.971095	−	0.238692i	$-0.0767185\pi$
$12$		0			0
$13$	14.7558			1.13506			0.567529	−	0.823353i	$-0.307899\pi$
$13$	14.7558			1.13506			0.567529	+	0.823353i	$0.307899\pi$
$14$	16.5884	+	2.06534i	1.18489	+	0.147524i
$15$		0			0
$16$	14.0759	+	7.60712i	0.879745	+	0.475445i
$17$	28.2789			1.66346			0.831732	−	0.555178i	$-0.187350\pi$
$17$	28.2789			1.66346			0.831732	+	0.555178i	$0.187350\pi$
$18$		0			0
$19$			19.1376i			1.00724i	0.863925	+	0.503620i	$0.167999\pi$
$19$			19.1376i			1.00724i	−0.863925	+	0.503620i	$0.832001\pi$
$20$	8.53851	+	2.15965i	0.426926	+	0.107983i
$21$		0			0
$22$	−10.4220	−	1.29759i	−0.473726	−	0.0589811i
$23$		−	3.65696i		−	0.158998i	−0.996835	−	0.0794990i	$-0.974668\pi$
$23$		−	3.65696i		−	0.158998i	0.996835	−	0.0794990i	$-0.0253321\pi$
$24$		0			0
$25$	−20.1519			−0.806074
$26$	3.64618	−	29.2854i	0.140238	−	1.12636i
$27$		0			0
$28$	8.19805	−	32.4122i	0.292787	−	1.15758i
$29$	24.6710			0.850724			0.425362	−	0.905023i	$-0.360147\pi$
$29$	24.6710			0.850724			0.425362	+	0.905023i	$0.360147\pi$
$30$		0			0
$31$			38.0675i			1.22798i	0.789312	+	0.613992i	$0.210437\pi$
$31$			38.0675i			1.22798i	−0.789312	+	0.613992i	$0.789563\pi$
$32$	18.5759	−	26.0564i	0.580496	−	0.814263i
$33$		0			0
$34$	6.98776	−	56.1244i	0.205522	−	1.65072i
$35$		−	18.4036i		−	0.525817i
$36$		0			0
$37$	−4.21977			−0.114048			−0.0570239	−	0.998373i	$-0.518161\pi$
$37$	−4.21977			−0.114048			−0.0570239	+	0.998373i	$0.518161\pi$
$38$	37.9819	+	4.72893i	0.999524	+	0.124446i
$39$		0			0
$40$	6.39609	−	16.4125i	0.159902	−	0.410313i
$41$	19.8497			0.484138			0.242069	−	0.970259i	$-0.422174\pi$
$41$	19.8497			0.484138			0.242069	+	0.970259i	$0.422174\pi$
$42$		0			0
$43$			23.3127i			0.542157i	0.962557	+	0.271078i	$0.0873802\pi$
$43$			23.3127i			0.542157i	−0.962557	+	0.271078i	$0.912620\pi$
$44$	−5.15057	+	20.3636i	−0.117058	+	0.462809i
$45$		0			0
$46$	−7.25787	−	0.903640i	−0.157780	−	0.0196444i
$47$			29.8534i			0.635180i	0.948228	+	0.317590i	$0.102874\pi$
$47$			29.8534i			0.635180i	−0.948228	+	0.317590i	$0.897126\pi$
$48$		0			0
$49$	−20.8601			−0.425716
$50$	−4.97956	+	39.9949i	−0.0995912	+	0.799898i
$51$		0			0
$52$	−57.2211	−	14.4730i	−1.10041	−	0.278326i
$53$	−32.1118			−0.605883			−0.302942	−	0.953009i	$-0.597969\pi$
$53$	−32.1118			−0.605883			−0.302942	+	0.953009i	$0.597969\pi$
$54$		0			0
$55$			11.5624i			0.210225i
$56$	−62.3021	−	24.2796i	−1.11254	−	0.433564i
$57$		0			0
$58$	6.09625	−	48.9639i	0.105108	−	0.844206i
$59$			9.19326i			0.155818i	0.996960	+	0.0779089i	$0.0248243\pi$
$59$			9.19326i			0.155818i	−0.996960	+	0.0779089i	$0.975176\pi$
$60$		0			0
$61$	81.6430			1.33841			0.669205	−	0.743078i	$-0.266635\pi$
$61$	81.6430			1.33841			0.669205	+	0.743078i	$0.266635\pi$
$62$	75.5517	+	9.40656i	1.21858	+	0.151719i
$63$		0			0
$64$	−47.1234	−	43.3057i	−0.736304	−	0.676651i
$65$	−32.4900			−0.499846
$66$		0			0
$67$		−	7.92331i		−	0.118258i	−0.998250	−	0.0591292i	$-0.981168\pi$
$67$		−	7.92331i		−	0.118258i	0.998250	−	0.0591292i	$-0.0188324\pi$
$68$	−109.662	−	27.7369i	−1.61268	−	0.407896i
$69$		0			0
$70$	−36.5252	−	4.54756i	−0.521788	−	0.0649651i
$71$			62.9286i			0.886318i	0.896443	+	0.443159i	$0.146142\pi$
$71$			62.9286i			0.886318i	−0.896443	+	0.443159i	$0.853858\pi$
$72$		0			0
$73$	33.3218			0.456463			0.228232	−	0.973607i	$-0.426706\pi$
$73$	33.3218			0.456463			0.228232	+	0.973607i	$0.426706\pi$
$74$	−1.04271	+	8.37487i	−0.0140907	+	0.113174i
$75$		0			0
$76$	18.7708	−	74.2133i	0.246984	−	0.976490i
$77$	43.8909			0.570012
$78$		0			0
$79$			62.0228i			0.785099i	0.919731	+	0.392549i	$0.128407\pi$
$79$			62.0228i			0.785099i	−0.919731	+	0.392549i	$0.871593\pi$
$80$	−30.9931	−	16.7497i	−0.387414	−	0.209372i
$81$		0			0
$82$	4.90489	−	39.3951i	0.0598157	−	0.480429i
$83$		−	118.999i		−	1.43372i	−0.697216	−	0.716861i	$-0.745578\pi$
$83$		−	118.999i		−	1.43372i	0.697216	−	0.716861i	$-0.254422\pi$
$84$		0			0
$85$	−62.2659			−0.732540
$86$	46.2682	+	5.76062i	0.538003	+	0.0669839i
$87$		0			0
$88$	39.1424	+	15.2541i	0.444800	+	0.173342i
$89$	−107.361			−1.20630			−0.603152	−	0.797626i	$-0.706089\pi$
$89$	−107.361			−1.20630			−0.603152	+	0.797626i	$0.706089\pi$
$90$		0			0
$91$			123.332i			1.35530i
$92$	−3.58687	+	14.1812i	−0.0389877	+	0.154144i
$93$		0			0
$94$	59.2494	+	7.37684i	0.630313	+	0.0784770i
$95$		−	42.1381i		−	0.443559i
$96$		0			0
$97$	−3.57242			−0.0368290			−0.0184145	−	0.999830i	$-0.505862\pi$
$97$	−3.57242			−0.0368290			−0.0184145	+	0.999830i	$0.505862\pi$
$98$	−5.15457	+	41.4005i	−0.0525976	+	0.422454i
$99$		0			0
$100$	78.1465	+	19.7656i	0.781465	+	0.197656i
$101$	−15.0938			−0.149443			−0.0747216	−	0.997204i	$-0.523807\pi$
$101$	−15.0938			−0.149443			−0.0747216	+	0.997204i	$0.523807\pi$
$102$		0			0
$103$			130.265i			1.26471i	0.774680	+	0.632353i	$0.217911\pi$
$103$			130.265i			1.26471i	−0.774680	+	0.632353i	$0.782089\pi$
$104$	−42.8636	+	109.989i	−0.412150	+	1.05759i
$105$		0			0
$106$	−7.93489	+	63.7315i	−0.0748574	+	0.601241i
$107$		−	51.2733i		−	0.479190i	−0.970873	−	0.239595i	$-0.922985\pi$
$107$		−	51.2733i		−	0.479190i	0.970873	−	0.239595i	$-0.0770146\pi$
$108$		0			0
$109$	−25.4737			−0.233704			−0.116852	−	0.993149i	$-0.537280\pi$
$109$	−25.4737			−0.233704			−0.116852	+	0.993149i	$0.537280\pi$
$110$	22.9476	+	2.85709i	0.208615	+	0.0259735i
$111$		0			0
$112$	−63.5821	+	117.650i	−0.567697	+	1.05045i
$113$	−152.306			−1.34784			−0.673919	−	0.738805i	$-0.735390\pi$
$113$	−152.306			−1.34784			−0.673919	+	0.738805i	$0.735390\pi$
$114$		0			0
$115$			8.05207i			0.0700180i
$116$	−95.6712	−	24.1982i	−0.824751	−	0.208605i
$117$		0			0
$118$	18.2456	+	2.27167i	0.154624	+	0.0192514i
$119$			236.362i			1.98623i
$120$		0			0
$121$	93.4247			0.772105
$122$	20.1741	−	162.035i	0.165362	−	1.32816i
$123$		0			0
$124$	37.3380	−	147.621i	0.301113	−	1.19049i
$125$	99.4176			0.795341
$126$		0			0
$127$		−	147.428i		−	1.16085i	−0.814314	−	0.580425i	$-0.802886\pi$
$127$		−	147.428i		−	1.16085i	0.814314	−	0.580425i	$-0.197114\pi$
$128$	−97.5920	+	82.8239i	−0.762438	+	0.647062i
$129$		0			0
$130$	−8.02834	+	64.4821i	−0.0617564	+	0.496016i
$131$			130.353i			0.995063i	0.867446	+	0.497532i	$0.165760\pi$
$131$			130.353i			0.995063i	−0.867446	+	0.497532i	$0.834240\pi$
$132$		0			0
$133$	−159.956			−1.20268
$134$	−15.7252	−	1.95787i	−0.117352	−	0.0146109i
$135$		0			0
$136$	−82.1465	+	210.790i	−0.604018	+	1.54993i
$137$	−99.8358			−0.728729			−0.364364	−	0.931256i	$-0.618714\pi$
$137$	−99.8358			−0.728729			−0.364364	+	0.931256i	$0.618714\pi$
$138$		0			0
$139$		−	95.5893i		−	0.687693i	−0.939026	−	0.343847i	$-0.888270\pi$
$139$		−	95.5893i		−	0.687693i	0.939026	−	0.343847i	$-0.111730\pi$
$140$	−18.0509	+	71.3669i	−0.128935	+	0.509764i
$141$		0			0
$142$	124.893	+	15.5498i	0.879527	+	0.109505i
$143$		−	77.4857i		−	0.541858i
$144$		0			0
$145$	−54.3218			−0.374633
$146$	8.23389	−	66.1331i	0.0563965	−	0.452966i
$147$		0			0
$148$	16.3638	+	4.13889i	0.110566	+	0.0279655i
$149$	−68.6764			−0.460915			−0.230458	−	0.973082i	$-0.574022\pi$
$149$	−68.6764			−0.460915			−0.230458	+	0.973082i	$0.574022\pi$
$150$		0			0
$151$		−	105.382i		−	0.697893i	−0.937143	−	0.348946i	$-0.886539\pi$
$151$		−	105.382i		−	0.697893i	0.937143	−	0.348946i	$-0.113461\pi$
$152$	−142.651	−	55.5922i	−0.938493	−	0.365738i
$153$		0			0
$154$	10.8455	−	87.1092i	0.0704255	−	0.565644i
$155$		−	83.8190i		−	0.540768i
$156$		0			0
$157$	215.005			1.36946			0.684729	−	0.728798i	$-0.259921\pi$
$157$	215.005			1.36946			0.684729	+	0.728798i	$0.259921\pi$
$158$	123.095	+	15.3260i	0.779084	+	0.0969997i
$159$		0			0
$160$	−40.9013	+	57.3724i	−0.255633	+	0.358577i
$161$	30.5657			0.189849
$162$		0			0
$163$			33.7439i			0.207018i	0.994629	+	0.103509i	$0.0330071\pi$
$163$			33.7439i			0.207018i	−0.994629	+	0.103509i	$0.966993\pi$
$164$	−76.9746	−	19.4692i	−0.469357	−	0.118715i
$165$		0			0
$166$	−236.174	−	29.4049i	−1.42274	−	0.177138i
$167$		−	151.918i		−	0.909687i	−0.890571	−	0.454843i	$-0.849695\pi$
$167$		−	151.918i		−	0.909687i	0.890571	−	0.454843i	$-0.150305\pi$
$168$		0			0
$169$	48.7325			0.288358
$170$	−15.3860	+	123.578i	−0.0905060	+	0.726927i
$171$		0			0
$172$	22.8659	−	90.4040i	0.132941	−	0.525605i
$173$	118.801			0.686709			0.343354	−	0.939206i	$-0.388437\pi$
$173$	118.801			0.686709			0.343354	+	0.939206i	$0.388437\pi$
$174$		0			0
$175$		−	168.434i		−	0.962480i
$176$	39.9466	−	73.9157i	0.226969	−	0.419976i
$177$		0			0
$178$	−26.5291	+	213.077i	−0.149040	+	1.19706i
$179$			218.189i			1.21894i	0.792811	+	0.609468i	$0.208617\pi$
$179$			218.189i			1.21894i	−0.792811	+	0.609468i	$0.791383\pi$
$180$		0			0
$181$	184.078			1.01701			0.508503	−	0.861060i	$-0.330199\pi$
$181$	184.078			1.01701			0.508503	+	0.861060i	$0.330199\pi$
$182$	244.774	+	30.4756i	1.34491	+	0.167448i
$183$		0			0
$184$	27.2588	+	10.6230i	0.148146	+	0.0577336i
$185$	9.29129			0.0502232
$186$		0			0
$187$		−	148.498i		−	0.794110i
$188$	29.2813	−	115.768i	0.155752	−	0.615788i
$189$		0			0
$190$	−83.6305	−	10.4124i	−0.440160	−	0.0548021i
$191$		−	249.155i		−	1.30448i	−0.758013	−	0.652239i	$-0.773830\pi$
$191$		−	249.155i		−	1.30448i	0.758013	−	0.652239i	$-0.226170\pi$
$192$		0			0
$193$	−250.172			−1.29623			−0.648115	−	0.761542i	$-0.724442\pi$
$193$	−250.172			−1.29623			−0.648115	+	0.761542i	$0.724442\pi$
$194$	−0.882751	+	7.09009i	−0.00455026	+	0.0365469i
$195$		0			0
$196$	80.8930	+	20.4603i	0.412719	+	0.104389i
$197$	255.674			1.29784			0.648919	−	0.760858i	$-0.275221\pi$
$197$	255.674			1.29784			0.648919	+	0.760858i	$0.275221\pi$
$198$		0			0
$199$		−	309.110i		−	1.55332i	−0.629921	−	0.776659i	$-0.716913\pi$
$199$		−	309.110i		−	1.55332i	0.629921	−	0.776659i	$-0.283087\pi$
$200$	58.5385	−	150.211i	0.292693	−	0.751057i
$201$		0			0
$202$	−3.72970	+	29.9562i	−0.0184638	+	0.148298i
$203$			206.206i			1.01579i
$204$		0			0
$205$	−43.7060			−0.213200
$206$	258.533	+	32.1887i	1.25502	+	0.156256i
$207$		0			0
$208$	207.701	+	112.249i	0.998563	+	0.539658i
$209$	100.496			0.480840
$210$		0			0
$211$		−	393.936i		−	1.86699i	−0.358585	−	0.933497i	$-0.616741\pi$
$211$		−	393.936i		−	1.86699i	0.358585	−	0.933497i	$-0.383259\pi$
$212$	124.526	+	31.4964i	0.587386	+	0.148568i
$213$		0			0
$214$	−101.761	−	12.6697i	−0.475518	−	0.0592044i
$215$		−	51.3311i		−	0.238750i
$216$		0			0
$217$	−318.177			−1.46626
$218$	−6.29460	+	50.5570i	−0.0288743	+	0.231913i
$219$		0			0
$220$	11.3408	−	44.8376i	0.0515491	−	0.203807i
$221$	417.276			1.88813
$222$		0			0
$223$		−	103.230i		−	0.462917i	−0.972845	−	0.231458i	$-0.925650\pi$
$223$		−	103.230i		−	0.462917i	0.972845	−	0.231458i	$-0.0743497\pi$
$224$	217.786	+	155.261i	0.972258	+	0.693131i
$225$		0			0
$226$	−37.6350	+	302.278i	−0.166527	+	1.33751i
$227$			141.116i			0.621655i	0.950466	+	0.310828i	$0.100606\pi$
$227$			141.116i			0.621655i	−0.950466	+	0.310828i	$0.899394\pi$
$228$		0			0
$229$	−211.143			−0.922024			−0.461012	−	0.887394i	$-0.652513\pi$
$229$	−211.143			−0.922024			−0.461012	+	0.887394i	$0.652513\pi$
$230$	15.9808	+	1.98968i	0.0694815	+	0.00865079i
$231$		0			0
$232$	−71.6660	+	183.897i	−0.308905	+	0.792659i
$233$	−280.109			−1.20219			−0.601093	−	0.799179i	$-0.705268\pi$
$233$	−280.109			−1.20219			−0.601093	+	0.799179i	$0.705268\pi$
$234$		0			0
$235$		−	65.7328i		−	0.279714i
$236$	9.01706	−	35.6504i	0.0382079	−	0.151061i
$237$		0			0
$238$	469.101	+	58.4054i	1.97101	+	0.245401i
$239$		−	391.846i		−	1.63952i	−0.572704	−	0.819762i	$-0.694105\pi$
$239$		−	391.846i		−	1.63952i	0.572704	−	0.819762i	$-0.305895\pi$
$240$		0			0
$241$	47.3572			0.196503			0.0982514	−	0.995162i	$-0.468675\pi$
$241$	47.3572			0.196503			0.0982514	+	0.995162i	$0.468675\pi$
$242$	23.0854	−	185.418i	0.0953943	−	0.766190i
$243$		0			0
$244$	−316.602	−	80.0783i	−1.29755	−	0.328190i
$245$	45.9308			0.187473
$246$		0			0
$247$			282.390i			1.14328i
$248$	−283.754	−	110.581i	−1.14417	−	0.445892i
$249$		0			0
$250$	24.5663	−	197.312i	0.0982651	−	0.789247i
$251$		−	389.416i		−	1.55146i	−0.631065	−	0.775730i	$-0.717382\pi$
$251$		−	389.416i		−	1.55146i	0.631065	−	0.775730i	$-0.282618\pi$
$252$		0			0
$253$	−19.2035			−0.0759030
$254$	−292.597	−	36.4297i	−1.15196	−	0.143424i
$255$		0			0
$256$	140.263	+	214.155i	0.547904	+	0.836541i
$257$	65.0819			0.253237			0.126618	−	0.991952i	$-0.459588\pi$
$257$	65.0819			0.253237			0.126618	+	0.991952i	$0.459588\pi$
$258$		0			0
$259$		−	35.2698i		−	0.136177i
$260$	125.992	+	31.8673i	0.484586	+	0.122567i
$261$		0			0
$262$	258.709	+	32.2105i	0.987439	+	0.122941i
$263$			144.076i			0.547816i	0.961756	+	0.273908i	$0.0883164\pi$
$263$			144.076i			0.547816i	−0.961756	+	0.273908i	$0.911684\pi$
$264$		0			0
$265$	70.7054			0.266813
$266$	−39.5255	+	317.462i	−0.148592	+	1.19346i
$267$		0			0
$268$	−7.77146	+	30.7257i	−0.0289980	+	0.114648i
$269$	−72.4113			−0.269187			−0.134593	−	0.990901i	$-0.542973\pi$
$269$	−72.4113			−0.269187			−0.134593	+	0.990901i	$0.542973\pi$
$270$		0			0
$271$			35.4695i			0.130884i	0.997856	+	0.0654419i	$0.0208457\pi$
$271$			35.4695i			0.130884i	−0.997856	+	0.0654419i	$0.979154\pi$
$272$	398.051	+	215.121i	1.46342	+	0.790885i
$273$		0			0
$274$	−24.6696	+	198.142i	−0.0900351	+	0.723145i
$275$			105.822i			0.384806i
$276$		0			0
$277$	333.844			1.20521			0.602607	−	0.798038i	$-0.294129\pi$
$277$	333.844			1.20521			0.602607	+	0.798038i	$0.294129\pi$
$278$	−189.714	−	23.6203i	−0.682424	−	0.0849651i
$279$		0			0
$280$	137.180	+	53.4600i	0.489928	+	0.190929i
$281$	41.0769			0.146181			0.0730906	−	0.997325i	$-0.476714\pi$
$281$	41.0769			0.146181			0.0730906	+	0.997325i	$0.476714\pi$
$282$		0			0
$283$			252.398i			0.891865i	0.895067	+	0.445933i	$0.147128\pi$
$283$			252.398i			0.891865i	−0.895067	+	0.445933i	$0.852872\pi$
$284$	61.7225	−	244.029i	0.217333	−	0.859259i
$285$		0			0
$286$	−153.784	−	19.1469i	−0.537706	−	0.0669471i
$287$			165.908i			0.578077i
$288$		0			0
$289$	510.695			1.76711
$290$	−13.4230	+	107.811i	−0.0462863	+	0.371763i
$291$		0			0
$292$	−129.218	−	32.6832i	−0.442528	−	0.111929i
$293$	−40.6829			−0.138850			−0.0694248	−	0.997587i	$-0.522116\pi$
$293$	−40.6829			−0.138850			−0.0694248	+	0.997587i	$0.522116\pi$
$294$		0			0
$295$		−	20.2422i		−	0.0686175i
$296$	12.2579	−	31.4540i	0.0414117	−	0.106264i
$297$		0			0
$298$	−16.9701	+	136.300i	−0.0569465	+	0.457384i
$299$		−	53.9612i		−	0.180472i
$300$		0			0
$301$	−194.853			−0.647353
$302$	−209.149	−	26.0400i	−0.692546	−	0.0862253i
$303$		0			0
$304$	−145.582	+	269.379i	−0.478888	+	0.886116i
$305$	−179.766			−0.589396
$306$		0			0
$307$			136.830i			0.445701i	0.974853	+	0.222850i	$0.0715361\pi$
$307$			136.830i			0.445701i	−0.974853	+	0.222850i	$0.928464\pi$
$308$	−170.204	−	43.0497i	−0.552609	−	0.139772i
$309$		0			0
$310$	−166.354	−	20.7118i	−0.536625	−	0.0668124i
$311$			428.695i			1.37844i	0.724553	+	0.689219i	$0.242046\pi$
$311$			428.695i			1.37844i	−0.724553	+	0.689219i	$0.757954\pi$
$312$		0			0
$313$	−11.9741			−0.0382559			−0.0191280	−	0.999817i	$-0.506089\pi$
$313$	−11.9741			−0.0382559			−0.0191280	+	0.999817i	$0.506089\pi$
$314$	53.1281	−	426.715i	0.169198	−	1.35896i
$315$		0			0
$316$	60.8341	−	240.517i	0.192513	−	0.761130i
$317$	47.0532			0.148433			0.0742164	−	0.997242i	$-0.476354\pi$
$317$	47.0532			0.148433			0.0742164	+	0.997242i	$0.476354\pi$
$318$		0			0
$319$		−	129.553i		−	0.406121i
$320$	103.759	+	95.3526i	0.324246	+	0.297977i
$321$		0			0
$322$	7.55284	−	60.6630i	0.0234560	−	0.188394i
$323$			541.189i			1.67551i
$324$		0			0
$325$	−297.356			−0.914941
$326$	66.9708	+	8.33819i	0.205432	+	0.0255773i
$327$		0			0
$328$	−57.6607	+	147.959i	−0.175795	+	0.451094i
$329$	−249.522			−0.758426
$330$		0			0
$331$		−	84.4664i		−	0.255186i	−0.991827	−	0.127593i	$-0.959275\pi$
$331$		−	84.4664i		−	0.255186i	0.991827	−	0.127593i	$-0.0407251\pi$
$332$	−116.718	+	461.464i	−0.351561	+	1.38995i
$333$		0			0
$334$	−301.508	−	37.5392i	−0.902717	−	0.112393i
$335$			17.4459i			0.0520775i
$336$		0			0
$337$	505.116			1.49886			0.749430	−	0.662084i	$-0.230328\pi$
$337$	505.116			1.49886			0.749430	+	0.662084i	$0.230328\pi$
$338$	12.0419	−	96.7183i	0.0356269	−	0.286149i
$339$		0			0
$340$	241.460	+	61.0725i	0.710175	+	0.179625i
$341$	199.901			0.586219
$342$		0			0
$343$			235.200i			0.685714i
$344$	−173.772	−	67.7205i	−0.505153	−	0.196862i
$345$		0			0
$346$	29.3558	−	235.781i	0.0848435	−	0.681447i
$347$		−	490.460i		−	1.41343i	−0.707499	−	0.706715i	$-0.750176\pi$
$347$		−	490.460i		−	1.41343i	0.707499	−	0.706715i	$-0.249824\pi$
$348$		0			0
$349$	−373.944			−1.07147			−0.535736	−	0.844385i	$-0.679966\pi$
$349$	−373.944			−1.07147			−0.535736	+	0.844385i	$0.679966\pi$
$350$	−334.287	−	41.6203i	−0.955105	−	0.118915i
$351$		0			0
$352$	−136.828	−	97.5458i	−0.388716	−	0.277119i
$353$	−594.052			−1.68287			−0.841434	−	0.540360i	$-0.818288\pi$
$353$	−594.052			−1.68287			−0.841434	+	0.540360i	$0.818288\pi$
$354$		0			0
$355$		−	138.559i		−	0.390308i
$356$	416.333	+	105.303i	1.16948	+	0.295796i
$357$		0			0
$358$	433.035	+	53.9150i	1.20960	+	0.150601i
$359$		−	410.893i		−	1.14455i	−0.820062	−	0.572274i	$-0.806061\pi$
$359$		−	410.893i		−	1.14455i	0.820062	−	0.572274i	$-0.193939\pi$
$360$		0			0
$361$	−5.24690			−0.0145343
$362$	45.4861	−	365.336i	0.125652	−	1.00921i
$363$		0			0
$364$	120.968	−	478.267i	0.332331	−	1.31392i
$365$	−73.3697			−0.201013
$366$		0			0
$367$			538.294i			1.46674i	0.679829	+	0.733370i	$0.262054\pi$
$367$			538.294i			1.46674i	−0.679829	+	0.733370i	$0.737946\pi$
$368$	27.8189	−	51.4750i	0.0755948	−	0.139878i
$369$		0			0
$370$	2.29590	−	18.4402i	0.00620512	−	0.0498384i
$371$		−	268.398i		−	0.723445i
$372$		0			0
$373$	149.921			0.401934			0.200967	−	0.979598i	$-0.435592\pi$
$373$	149.921			0.401934			0.200967	+	0.979598i	$0.435592\pi$
$374$	−294.721	−	36.6943i	−0.788025	−	0.0981130i
$375$		0			0
$376$	−222.527	−	86.7204i	−0.591827	−	0.230639i
$377$	364.039			0.965621
$378$		0			0
$379$		−	184.361i		−	0.486442i	−0.969971	−	0.243221i	$-0.921796\pi$
$379$		−	184.361i		−	0.486442i	0.969971	−	0.243221i	$-0.0782040\pi$
$380$	−41.3305	+	163.406i	−0.108764	+	0.430017i
$381$		0			0
$382$	−494.493	−	61.5667i	−1.29448	−	0.161169i
$383$			208.439i			0.544228i	0.962265	+	0.272114i	$0.0877227\pi$
$383$			208.439i			0.544228i	−0.962265	+	0.272114i	$0.912277\pi$
$384$		0			0
$385$	−96.6412			−0.251016
$386$	−61.8181	+	496.511i	−0.160150	+	1.28630i
$387$		0			0
$388$	13.8534	+	3.50395i	0.0357047	+	0.00903080i
$389$	301.827			0.775905			0.387953	−	0.921679i	$-0.373182\pi$
$389$	301.827			0.775905			0.387953	+	0.921679i	$0.373182\pi$
$390$		0			0
$391$		−	103.415i		−	0.264487i
$392$	60.5959	−	155.491i	0.154581	−	0.396660i
$393$		0			0
$394$	63.1775	−	507.430i	0.160349	−	1.28789i
$395$		−	136.565i		−	0.345734i
$396$		0			0
$397$	−246.672			−0.621341			−0.310670	−	0.950518i	$-0.600553\pi$
$397$	−246.672			−0.621341			−0.310670	+	0.950518i	$0.600553\pi$
$398$	−613.484	−	76.3817i	−1.54142	−	0.191914i
$399$		0			0
$400$	−283.656	−	153.298i	−0.709140	−	0.383244i
$401$	−755.032			−1.88287			−0.941437	−	0.337190i	$-0.890523\pi$
$401$	−755.032			−1.88287			−0.941437	+	0.337190i	$0.890523\pi$
$402$		0			0
$403$			561.715i			1.39383i
$404$	58.5318	+	14.8045i	0.144881	+	0.0366447i
$405$		0			0
$406$	409.252	+	50.9539i	1.00801	+	0.125502i
$407$			22.1589i			0.0544445i
$408$		0			0
$409$	−261.461			−0.639268			−0.319634	−	0.947541i	$-0.603560\pi$
$409$	−261.461			−0.639268			−0.319634	+	0.947541i	$0.603560\pi$
$410$	−10.7998	+	86.7422i	−0.0263410	+	0.211566i
$411$		0			0
$412$	127.768	−	505.151i	0.310117	−	1.22610i
$413$	−76.8394			−0.186052
$414$		0			0
$415$			262.018i			0.631369i
$416$	274.101	−	384.482i	0.658897	−	0.924237i
$417$		0			0
$418$	24.8326	−	199.451i	0.0594082	−	0.477156i
$419$			392.882i			0.937667i	0.883287	+	0.468833i	$0.155326\pi$
$419$			392.882i			0.937667i	−0.883287	+	0.468833i	$0.844674\pi$
$420$		0			0
$421$	−204.901			−0.486702			−0.243351	−	0.969938i	$-0.578247\pi$
$421$	−204.901			−0.486702			−0.243351	+	0.969938i	$0.578247\pi$
$422$	−781.835	−	97.3423i	−1.85269	−	0.230669i
$423$		0			0
$424$	93.2807	−	239.361i	0.220002	−	0.564530i
$425$	−569.872			−1.34088
$426$		0			0
$427$			682.391i			1.59811i
$428$	−50.2906	+	198.832i	−0.117501	+	0.464560i
$429$		0			0
$430$	−101.876	−	12.6840i	−0.236920	−	0.0294977i
$431$			462.725i			1.07361i	0.843707	+	0.536803i	$0.180368\pi$
$431$			462.725i			1.07361i	−0.843707	+	0.536803i	$0.819632\pi$
$432$		0			0
$433$	190.574			0.440126			0.220063	−	0.975486i	$-0.429374\pi$
$433$	190.574			0.440126			0.220063	+	0.975486i	$0.429374\pi$
$434$	−78.6222	+	631.479i	−0.181157	+	1.45502i
$435$		0			0
$436$	98.7839	+	24.9855i	0.226569	+	0.0573061i
$437$	69.9853			0.160149
$438$		0			0
$439$		−	437.954i		−	0.997618i	−0.866712	−	0.498809i	$-0.833771\pi$
$439$		−	437.954i		−	0.997618i	0.866712	−	0.498809i	$-0.166229\pi$
$440$	−86.1858	−	33.5873i	−0.195877	−	0.0763347i
$441$		0			0
$442$	103.110	−	828.159i	0.233280	−	1.87366i
$443$			833.685i			1.88191i	0.338535	+	0.940954i	$0.390069\pi$
$443$			833.685i			1.88191i	−0.338535	+	0.940954i	$0.609931\pi$
$444$		0			0
$445$	236.393			0.531220
$446$	−204.879	−	25.5084i	−0.459370	−	0.0571938i
$447$		0			0
$448$	361.959	−	393.869i	0.807944	−	0.879172i
$449$	−480.789			−1.07080			−0.535399	−	0.844599i	$-0.679839\pi$
$449$	−480.789			−1.07080			−0.535399	+	0.844599i	$0.679839\pi$
$450$		0			0
$451$		−	104.235i		−	0.231119i
$452$	590.624	+	149.387i	1.30669	+	0.330502i
$453$		0			0
$454$	280.069	+	34.8700i	0.616892	+	0.0768061i
$455$		−	271.559i		−	0.596833i
$456$		0			0
$457$	−218.626			−0.478395			−0.239197	−	0.970971i	$-0.576884\pi$
$457$	−218.626			−0.478395			−0.239197	+	0.970971i	$0.576884\pi$
$458$	−52.1739	+	419.051i	−0.113917	+	0.914959i
$459$		0			0
$460$	7.89775	−	31.2250i	0.0171690	−	0.0678804i
$461$	716.947			1.55520			0.777600	−	0.628759i	$-0.216437\pi$
$461$	716.947			1.55520			0.777600	+	0.628759i	$0.216437\pi$
$462$		0			0
$463$		−	30.7439i		−	0.0664014i	−0.999449	−	0.0332007i	$-0.989430\pi$
$463$		−	30.7439i		−	0.0664014i	0.999449	−	0.0332007i	$-0.0105701\pi$
$464$	347.267	+	187.675i	0.748420	+	0.404472i
$465$		0			0
$466$	−69.2155	+	555.926i	−0.148531	+	1.19297i
$467$		−	458.639i		−	0.982096i	−0.871133	−	0.491048i	$-0.836614\pi$
$467$		−	458.639i		−	0.982096i	0.871133	−	0.491048i	$-0.163386\pi$
$468$		0			0
$469$	66.2249			0.141204
$470$	−130.458	−	16.2427i	−0.277571	−	0.0345589i
$471$		0			0
$472$	−68.5263	−	26.7052i	−0.145183	−	0.0565789i
$473$	122.420			0.258816
$474$		0			0
$475$		−	385.658i		−	0.811911i
$476$	231.832	−	916.582i	0.487041	−	1.92559i
$477$		0			0
$478$	−777.688	−	96.8260i	−1.62696	−	0.202565i
$479$		−	658.731i		−	1.37522i	−0.726080	−	0.687610i	$-0.758660\pi$
$479$		−	658.731i		−	1.37522i	0.726080	−	0.687610i	$-0.241340\pi$
$480$		0			0
$481$	−62.2659			−0.129451
$482$	11.7021	−	93.9887i	0.0242781	−	0.194997i
$483$		0			0
$484$	−362.290	−	91.6342i	−0.748533	−	0.189327i
$485$	7.86593			0.0162184
$486$		0			0
$487$			715.589i			1.46938i	0.678402	+	0.734691i	$0.262673\pi$
$487$			715.589i			1.46938i	−0.678402	+	0.734691i	$0.737327\pi$
$488$	−237.162	+	608.565i	−0.485988	+	1.24706i
$489$		0			0
$490$	11.3496	−	91.1578i	0.0231624	−	0.186036i
$491$		−	663.004i		−	1.35031i	−0.737674	−	0.675157i	$-0.764076\pi$
$491$		−	663.004i		−	1.35031i	0.737674	−	0.675157i	$-0.235924\pi$
$492$		0			0
$493$	697.668			1.41515
$494$	560.452	+	69.7790i	1.13452	+	0.141253i
$495$		0			0
$496$	−289.584	+	535.836i	−0.583839	+	1.08031i
$497$	−525.972			−1.05829
$498$		0			0
$499$			529.668i			1.06146i	0.847541	+	0.530730i	$0.178082\pi$
$499$			529.668i			1.06146i	−0.847541	+	0.530730i	$0.821918\pi$
$500$	−385.530	−	97.5122i	−0.771060	−	0.195024i
$501$		0			0
$502$	−772.865	−	96.2255i	−1.53957	−	0.191684i
$503$		−	68.3537i		−	0.135892i	−0.997689	−	0.0679460i	$-0.978355\pi$
$503$		−	68.3537i		−	0.135892i	0.997689	−	0.0679460i	$-0.0216446\pi$
$504$		0			0
$505$	33.2342			0.0658103
$506$	−4.74521	+	38.1127i	−0.00937789	+	0.0753214i
$507$		0			0
$508$	−144.602	+	571.708i	−0.284650	+	1.12541i
$509$	800.947			1.57357			0.786784	−	0.617228i	$-0.211744\pi$
$509$	800.947			1.57357			0.786784	+	0.617228i	$0.211744\pi$
$510$		0			0
$511$			278.512i			0.545033i
$512$	459.687	−	225.460i	0.897826	−	0.440351i
$513$		0			0
$514$	16.0818	−	129.166i	0.0312876	−	0.251297i
$515$		−	286.824i		−	0.556939i
$516$		0			0
$517$	156.767			0.303224
$518$	−69.9991	−	8.71523i	−0.135133	−	0.0168248i
$519$		0			0
$520$	94.3792	−	242.179i	0.181498	−	0.465730i
$521$	−208.227			−0.399668			−0.199834	−	0.979830i	$-0.564040\pi$
$521$	−208.227			−0.399668			−0.199834	+	0.979830i	$0.564040\pi$
$522$		0			0
$523$			30.5350i			0.0583843i	0.999574	+	0.0291921i	$0.00929347\pi$
$523$			30.5350i			0.0583843i	−0.999574	+	0.0291921i	$0.990707\pi$
$524$	127.855	−	505.494i	0.243998	−	0.964684i
$525$		0			0
$526$	285.943	+	35.6014i	0.543619	+	0.0676832i
$527$			1076.51i			2.04271i
$528$		0			0
$529$	515.627			0.974720
$530$	17.4714	−	140.327i	0.0329650	−	0.264769i
$531$		0			0
$532$	620.292	+	156.891i	1.16596	+	0.294907i
$533$	292.897			0.549525
$534$		0			0
$535$			112.896i			0.211021i
$536$	59.0602	+	23.0162i	0.110187	+	0.0429407i
$537$		0			0
$538$	−17.8930	+	143.713i	−0.0332583	+	0.267124i
$539$			109.541i			0.203230i
$540$		0			0
$541$	526.091			0.972442			0.486221	−	0.873836i	$-0.338375\pi$
$541$	526.091			0.972442			0.486221	+	0.873836i	$0.338375\pi$
$542$	70.3955	+	8.76458i	0.129881	+	0.0161708i
$543$		0			0
$544$	525.305	−	736.847i	0.965633	−	1.35450i
$545$	56.0892			0.102916
$546$		0			0
$547$			950.637i			1.73791i	0.494891	+	0.868955i	$0.335208\pi$
$547$			950.637i			1.73791i	−0.494891	+	0.868955i	$0.664792\pi$
$548$	387.151	+	97.9224i	0.706481	+	0.178691i
$549$		0			0
$550$	210.022	+	26.1487i	0.381858	+	0.0475432i
$551$			472.143i			0.856884i
$552$		0			0
$553$	−518.401			−0.937434
$554$	82.4936	−	662.573i	0.148905	−	1.19598i
$555$		0			0
$556$	−93.7573	+	370.684i	−0.168628	+	0.666698i
$557$	978.257			1.75630			0.878148	−	0.478390i	$-0.158779\pi$
$557$	978.257			1.75630			0.878148	+	0.478390i	$0.158779\pi$
$558$		0			0
$559$			343.997i			0.615379i
$560$	139.998	−	259.048i	0.249997	−	0.462585i
$561$		0			0
$562$	10.1502	−	81.5244i	0.0180608	−	0.145061i
$563$		−	1068.25i		−	1.89742i	−0.316142	−	0.948712i	$-0.602387\pi$
$563$		−	1068.25i		−	1.89742i	0.316142	−	0.948712i	$-0.397613\pi$
$564$		0			0
$565$	335.355			0.593548
$566$	500.928	+	62.3680i	0.885032	+	0.110191i
$567$		0			0
$568$	−469.068	−	182.799i	−0.825824	−	0.321830i
$569$	963.550			1.69341			0.846705	−	0.532063i	$-0.178583\pi$
$569$	963.550			1.69341			0.846705	+	0.532063i	$0.178583\pi$
$570$		0			0
$571$			280.744i			0.491671i	0.969312	+	0.245836i	$0.0790624\pi$
$571$			280.744i			0.491671i	−0.969312	+	0.245836i	$0.920938\pi$
$572$	−76.0006	+	300.480i	−0.132868	+	0.525315i
$573$		0			0
$574$	329.274	+	40.9962i	0.573648	+	0.0714219i
$575$			73.6944i			0.128164i
$576$		0			0
$577$	−552.228			−0.957068			−0.478534	−	0.878069i	$-0.658832\pi$
$577$	−552.228			−0.957068			−0.478534	+	0.878069i	$0.658832\pi$
$578$	126.194	−	1013.56i	0.218328	−	1.75357i
$579$		0			0
$580$	210.654	+	53.2807i	0.363196	+	0.0918633i
$581$	994.621			1.71191
$582$		0			0
$583$			168.626i			0.289238i
$584$	−96.7956	+	248.380i	−0.165746	+	0.425308i
$585$		0			0
$586$	−10.0528	+	80.7425i	−0.0171550	+	0.137786i
$587$			163.362i			0.278300i	0.990271	+	0.139150i	$0.0444370\pi$
$587$			163.362i			0.278300i	−0.990271	+	0.139150i	$0.955563\pi$
$588$		0			0
$589$	−728.520			−1.23688
$590$	−40.1742	−	5.00188i	−0.0680918	−	0.00847776i
$591$		0			0
$592$	−59.3971	−	32.1003i	−0.100333	−	0.0542234i
$593$	−818.460			−1.38020			−0.690101	−	0.723713i	$-0.742434\pi$
$593$	−818.460			−1.38020			−0.690101	+	0.723713i	$0.742434\pi$
$594$		0			0
$595$		−	520.433i		−	0.874677i
$596$	266.319	+	67.3602i	0.446844	+	0.113020i
$597$		0			0
$598$	−107.095	−	13.3339i	−0.179089	−	0.0222975i
$599$			460.551i			0.768866i	0.923153	+	0.384433i	$0.125603\pi$
$599$			460.551i			0.768866i	−0.923153	+	0.384433i	$0.874397\pi$
$600$		0			0
$601$	−324.648			−0.540180			−0.270090	−	0.962835i	$-0.587053\pi$
$601$	−324.648			−0.540180			−0.270090	+	0.962835i	$0.587053\pi$
$602$	−48.1486	+	386.721i	−0.0799811	+	0.642393i
$603$		0			0
$604$	−103.362	+	408.658i	−0.171129	+	0.676587i
$605$	−205.707			−0.340012
$606$		0			0
$607$		−	882.254i		−	1.45347i	−0.686920	−	0.726733i	$-0.741038\pi$
$607$		−	882.254i		−	1.45347i	0.686920	−	0.726733i	$-0.258962\pi$
$608$	498.657	+	355.497i	0.820159	+	0.584699i
$609$		0			0
$610$	−44.4204	+	356.777i	−0.0728204	+	0.584880i
$611$			440.510i			0.720966i
$612$		0			0
$613$	19.4869			0.0317895			0.0158947	−	0.999874i	$-0.494940\pi$
$613$	19.4869			0.0317895			0.0158947	+	0.999874i	$0.494940\pi$
$614$	271.563	+	33.8110i	0.442286	+	0.0550667i
$615$		0			0
$616$	−127.497	+	327.162i	−0.206976	+	0.531106i
$617$	96.6628			0.156666			0.0783329	−	0.996927i	$-0.475040\pi$
$617$	96.6628			0.156666			0.0783329	+	0.996927i	$0.475040\pi$
$618$		0			0
$619$		−	420.238i		−	0.678899i	−0.940624	−	0.339449i	$-0.889759\pi$
$619$		−	420.238i		−	0.678899i	0.940624	−	0.339449i	$-0.110241\pi$
$620$	−82.2126	+	325.040i	−0.132601	+	0.524258i
$621$		0			0
$622$	850.820	+	105.931i	1.36788	+	0.170307i
$623$		−	897.349i		−	1.44037i
$624$		0			0
$625$	284.894			0.455830
$626$	−2.95882	+	23.7647i	−0.00472656	+	0.0379628i
$627$		0			0
$628$	−833.763	−	210.884i	−1.32765	−	0.335803i
$629$	−119.330			−0.189714
$630$		0			0
$631$		−	483.230i		−	0.765816i	−0.923787	−	0.382908i	$-0.874923\pi$
$631$		−	483.230i		−	0.765816i	0.923787	−	0.382908i	$-0.125077\pi$
$632$	−462.316	−	180.168i	−0.731513	−	0.285076i
$633$		0			0
$634$	11.6269	−	93.3854i	0.0183390	−	0.147296i
$635$			324.614i			0.511204i
$636$		0			0
$637$	−307.807			−0.483213
$638$	−257.120	−	32.0127i	−0.403010	−	0.0501767i
$639$		0			0
$640$	214.883	−	182.366i	0.335755	−	0.284947i
$641$	90.5935			0.141331			0.0706657	−	0.997500i	$-0.477488\pi$
$641$	90.5935			0.141331			0.0706657	+	0.997500i	$0.477488\pi$
$642$		0			0
$643$		−	523.972i		−	0.814887i	−0.913230	−	0.407444i	$-0.866420\pi$
$643$		−	523.972i		−	0.814887i	0.913230	−	0.407444i	$-0.133580\pi$
$644$	−118.530	−	29.9799i	−0.184053	−	0.0465526i
$645$		0			0
$646$	1074.09	+	133.729i	1.66267	+	0.207011i
$647$			31.3018i			0.0483799i	0.999707	+	0.0241900i	$0.00770066\pi$
$647$			31.3018i			0.0483799i	−0.999707	+	0.0241900i	$0.992299\pi$
$648$		0			0
$649$	48.2758			0.0743848
$650$	−73.4772	+	590.155i	−0.113042	+	0.907931i
$651$		0			0
$652$	33.0972	−	130.855i	0.0507626	−	0.200698i
$653$	−890.229			−1.36329			−0.681646	−	0.731682i	$-0.738735\pi$
$653$	−890.229			−1.36329			−0.681646	+	0.731682i	$0.738735\pi$
$654$		0			0
$655$		−	287.018i		−	0.438196i
$656$	279.402	+	150.999i	0.425918	+	0.230181i
$657$		0			0
$658$	−61.6574	+	495.221i	−0.0937042	+	0.752615i
$659$			47.5486i			0.0721526i	0.999349	+	0.0360763i	$0.0114859\pi$
$659$			47.5486i			0.0721526i	−0.999349	+	0.0360763i	$0.988514\pi$
$660$		0			0
$661$	49.6842			0.0751652			0.0375826	−	0.999294i	$-0.488034\pi$
$661$	49.6842			0.0751652			0.0375826	+	0.999294i	$0.488034\pi$
$662$	−167.639	−	20.8718i	−0.253230	−	0.0315284i
$663$		0			0
$664$	887.015	+	345.677i	1.33587	+	0.520597i
$665$	352.200			0.529624
$666$		0			0
$667$		−	90.2207i		−	0.135263i
$668$	−149.006	+	589.119i	−0.223063	+	0.881915i
$669$		0			0
$670$	34.6246	+	4.31093i	0.0516785	+	0.00643422i
$671$		−	428.725i		−	0.638934i
$672$		0			0
$673$	32.8729			0.0488454			0.0244227	−	0.999702i	$-0.492225\pi$
$673$	32.8729			0.0488454			0.0244227	+	0.999702i	$0.492225\pi$
$674$	124.815	−	1002.49i	0.185185	−	1.48738i
$675$		0			0
$676$	−188.979	−	47.7986i	−0.279555	−	0.0707079i
$677$	−914.834			−1.35131			−0.675653	−	0.737220i	$-0.736138\pi$
$677$	−914.834			−1.35131			−0.675653	+	0.737220i	$0.736138\pi$
$678$		0			0
$679$		−	29.8591i		−	0.0439751i
$680$	180.874	−	464.128i	0.265992	−	0.682541i
$681$		0			0
$682$	49.3959	−	396.738i	0.0724279	−	0.581728i
$683$		−	870.646i		−	1.27474i	−0.770559	−	0.637369i	$-0.780023\pi$
$683$		−	870.646i		−	1.27474i	0.770559	−	0.637369i	$-0.219977\pi$
$684$		0			0
$685$	219.824			0.320910
$686$	466.796	+	58.1183i	0.680460	+	0.0847206i
$687$		0			0
$688$	−177.343	+	328.148i	−0.257766	+	0.476960i
$689$	−473.834			−0.687713
$690$		0			0
$691$		−	923.977i		−	1.33716i	−0.743641	−	0.668580i	$-0.766903\pi$
$691$		−	923.977i		−	1.33716i	0.743641	−	0.668580i	$-0.233097\pi$
$692$	−460.695	−	116.524i	−0.665744	−	0.168387i
$693$		0			0
$694$	−973.405	−	121.194i	−1.40260	−	0.174631i
$695$			210.473i			0.302840i
$696$		0			0
$697$	561.326			0.805346
$698$	−92.4023	+	742.158i	−0.132381	+	1.06326i
$699$		0			0
$700$	−165.206	+	653.167i	−0.236008	+	0.933095i
$701$	1191.44			1.69963			0.849815	−	0.527082i	$-0.176714\pi$
$701$	1191.44			1.69963			0.849815	+	0.527082i	$0.176714\pi$
$702$		0			0
$703$		−	80.7561i		−	0.114874i
$704$	−227.407	+	247.455i	−0.323022	+	0.351499i
$705$		0			0
$706$	−146.791	+	1179.00i	−0.207920	+	1.66997i
$707$		−	126.157i		−	0.178440i
$708$		0			0
$709$	−1311.91			−1.85036			−0.925182	−	0.379524i	$-0.876088\pi$
$709$	−1311.91			−1.85036			−0.925182	+	0.379524i	$0.876088\pi$
$710$	−274.995	−	34.2383i	−0.387317	−	0.0482229i
$711$		0			0
$712$	311.870	−	800.266i	0.438020	−	1.12397i
$713$	139.211			0.195247
$714$		0			0
$715$			170.612i			0.238618i
$716$	214.008	−	846.113i	0.298893	−	1.18172i
$717$		0			0
$718$	−815.489	−	101.532i	−1.13578	−	0.141410i
$719$			245.763i			0.341813i	0.985287	+	0.170906i	$0.0546695\pi$
$719$			245.763i			0.341813i	−0.985287	+	0.170906i	$0.945330\pi$
$720$		0			0
$721$	−1088.78			−1.51010
$722$	−1.29652	+	10.4134i	−0.00179573	+	0.0144230i
$723$		0			0
$724$	−713.834	−	180.550i	−0.985958	−	0.249379i
$725$	−497.166			−0.685746
$726$		0			0
$727$		−	1203.15i		−	1.65495i	−0.561505	−	0.827473i	$-0.689778\pi$
$727$		−	1203.15i		−	1.65495i	0.561505	−	0.827473i	$-0.310222\pi$
$728$	−919.314	−	358.264i	−1.26279	−	0.492121i
$729$		0			0
$730$	−18.1298	+	145.615i	−0.0248353	+	0.199473i
$731$			659.258i			0.901858i
$732$		0			0
$733$	1021.39			1.39343			0.696716	−	0.717347i	$-0.254644\pi$
$733$	1021.39			1.39343			0.696716	+	0.717347i	$0.254644\pi$
$734$	1068.34	+	133.013i	1.45550	+	0.181217i
$735$		0			0
$736$	−95.2872	−	67.9311i	−0.129466	−	0.0922977i
$737$	−41.6070			−0.0564546
$738$		0			0
$739$		−	259.300i		−	0.350879i	−0.984490	−	0.175439i	$-0.943865\pi$
$739$		−	259.300i		−	0.350879i	0.984490	−	0.175439i	$-0.0561346\pi$
$740$	−36.0305	−	9.11322i	−0.0486899	−	0.0123152i
$741$		0			0
$742$	−532.683	−	66.3217i	−0.717902	−	0.0893823i
$743$			115.781i			0.155830i	0.996960	+	0.0779149i	$0.0248262\pi$
$743$			115.781i			0.155830i	−0.996960	+	0.0779149i	$0.975174\pi$
$744$		0			0
$745$	151.215			0.202973
$746$	37.0458	−	297.545i	0.0496593	−	0.398854i
$747$		0			0
$748$	−145.652	+	575.859i	−0.194723	+	0.769866i
$749$	428.554			0.572169
$750$		0			0
$751$		−	627.673i		−	0.835783i	−0.908497	−	0.417891i	$-0.862769\pi$
$751$		−	627.673i		−	0.835783i	0.908497	−	0.417891i	$-0.137231\pi$
$752$	−227.099	+	420.215i	−0.301993	+	0.558796i
$753$		0			0
$754$	89.9548	−	722.500i	0.119303	−	0.958223i
$755$			232.035i			0.307331i
$756$		0			0
$757$	49.5546			0.0654618			0.0327309	−	0.999464i	$-0.489580\pi$
$757$	49.5546			0.0654618			0.0327309	+	0.999464i	$0.489580\pi$
$758$	−365.898	−	45.5561i	−0.482715	−	0.0601003i
$759$		0			0
$760$	314.096	+	122.406i	0.413284	+	0.161060i
$761$	26.1477			0.0343597			0.0171798	−	0.999852i	$-0.494531\pi$
$761$	26.1477			0.0343597			0.0171798	+	0.999852i	$0.494531\pi$
$762$		0			0
$763$		−	212.915i		−	0.279050i
$764$	−244.380	+	966.195i	−0.319869	+	1.26465i
$765$		0			0
$766$	413.684	+	51.5057i	0.540058	+	0.0672398i
$767$			135.653i			0.176862i
$768$		0			0
$769$	−187.175			−0.243401			−0.121700	−	0.992567i	$-0.538835\pi$
$769$	−187.175			−0.243401			−0.121700	+	0.992567i	$0.538835\pi$
$770$	−23.8802	+	191.801i	−0.0310133	+	0.249093i
$771$		0			0
$772$	970.139	+	245.378i	1.25666	+	0.317847i
$773$	−877.069			−1.13463			−0.567315	−	0.823501i	$-0.692018\pi$
$773$	−877.069			−1.13463			−0.567315	+	0.823501i	$0.692018\pi$
$774$		0			0
$775$		−	767.131i		−	0.989847i
$776$	10.3774	−	26.6287i	0.0133730	−	0.0343153i
$777$		0			0
$778$	74.5820	−	599.029i	0.0958638	−	0.769960i
$779$			379.874i			0.487644i
$780$		0			0
$781$	330.451			0.423113
$782$	−205.245	−	25.5539i	−0.262461	−	0.0326777i
$783$		0			0
$784$	−293.625	−	158.685i	−0.374522	−	0.202405i
$785$	−473.408			−0.603068
$786$		0			0
$787$		−	666.384i		−	0.846740i	−0.905957	−	0.423370i	$-0.860847\pi$
$787$		−	666.384i		−	0.846740i	0.905957	−	0.423370i	$-0.139153\pi$
$788$	−991.473	−	250.774i	−1.25821	−	0.318241i
$789$		0			0
$790$	−271.037	−	33.7455i	−0.343085	−	0.0427158i
$791$		−	1273.01i		−	1.60936i
$792$		0			0
$793$	1204.70			1.51917
$794$	−60.9532	+	489.564i	−0.0767672	+	0.616580i
$795$		0			0
$796$	−303.186	+	1198.69i	−0.380887	+	1.50590i
$797$	−181.763			−0.228059			−0.114030	−	0.993477i	$-0.536376\pi$
$797$	−181.763			−0.228059			−0.114030	+	0.993477i	$0.536376\pi$
$798$		0			0
$799$			844.222i			1.05660i
$800$	−374.338	+	525.085i	−0.467923	+	0.656357i
$801$		0			0
$802$	−186.570	+	1498.49i	−0.232631	+	1.86845i
$803$		−	174.980i		−	0.217908i
$804$		0			0
$805$	−67.3011			−0.0836038
$806$	1114.82	+	138.801i	1.38316	+	0.172210i
$807$		0			0
$808$	43.8454	−	112.508i	0.0542641	−	0.139243i
$809$	114.921			0.142053			0.0710266	−	0.997474i	$-0.477372\pi$
$809$	114.921			0.142053			0.0710266	+	0.997474i	$0.477372\pi$
$810$		0			0
$811$		−	1378.48i		−	1.69973i	−0.526997	−	0.849867i	$-0.676682\pi$
$811$		−	1378.48i		−	1.69973i	0.526997	−	0.849867i	$-0.323318\pi$
$812$	202.254	−	799.642i	0.249081	−	0.984781i
$813$		0			0
$814$	43.9782	+	5.47551i	0.0540273	+	0.00672667i
$815$		−	74.2991i		−	0.0911646i
$816$		0			0
$817$	−446.149			−0.546082
$818$	−64.6074	+	518.915i	−0.0789822	+	0.634370i
$819$		0			0
$820$	169.487	+	42.8683i	0.206691	+	0.0522784i
$821$	321.614			0.391734			0.195867	−	0.980630i	$-0.437248\pi$
$821$	321.614			0.391734			0.195867	+	0.980630i	$0.437248\pi$
$822$		0			0
$823$			65.4490i			0.0795250i	0.999209	+	0.0397625i	$0.0126601\pi$
$823$			65.4490i			0.0795250i	−0.999209	+	0.0397625i	$0.987340\pi$
$824$	−970.990	−	378.402i	−1.17839	−	0.459226i
$825$		0			0
$826$	−18.9872	+	152.501i	−0.0229869	+	0.184626i
$827$			778.406i			0.941240i	0.882336	+	0.470620i	$0.155970\pi$
$827$			778.406i			0.941240i	−0.882336	+	0.470620i	$0.844030\pi$
$828$		0			0
$829$	−81.3426			−0.0981214			−0.0490607	−	0.998796i	$-0.515623\pi$
$829$	−81.3426			−0.0981214			−0.0490607	+	0.998796i	$0.515623\pi$
$830$	520.021	+	64.7451i	0.626531	+	0.0780062i
$831$		0			0
$832$	−695.342	−	639.008i	−0.835748	−	0.768039i
$833$	−589.900			−0.708163
$834$		0			0
$835$			334.500i			0.400599i
$836$	−389.710	−	98.5695i	−0.466160	−	0.117906i
$837$		0			0
$838$	779.744	+	97.0820i	0.930483	+	0.115850i
$839$		−	639.396i		−	0.762093i	−0.924556	−	0.381046i	$-0.875564\pi$
$839$		−	639.396i		−	0.762093i	0.924556	−	0.381046i	$-0.124436\pi$
$840$		0			0
$841$	−232.342			−0.276269
$842$	−50.6315	+	406.663i	−0.0601325	+	0.482973i
$843$		0			0
$844$	−386.386	+	1527.64i	−0.457803	+	1.81000i
$845$	−107.302			−0.126984
$846$		0			0
$847$			780.866i			0.921920i
$848$	−452.003	−	244.278i	−0.533023	−	0.288064i
$849$		0			0
$850$	−140.816	+	1131.01i	−0.165666	+	1.33060i
$851$			15.4315i			0.0181334i
$852$		0			0
$853$	77.6138			0.0909892			0.0454946	−	0.998965i	$-0.485514\pi$
$853$	77.6138			0.0909892			0.0454946	+	0.998965i	$0.485514\pi$
$854$	1354.33	+	168.620i	1.58586	+	0.197448i
$855$		0			0
$856$	382.190	+	148.942i	0.446484	+	0.173998i
$857$	−872.021			−1.01753			−0.508763	−	0.860906i	$-0.669897\pi$
$857$	−872.021			−1.01753			−0.508763	+	0.860906i	$0.669897\pi$
$858$		0			0
$859$			158.089i			0.184038i	0.995757	+	0.0920191i	$0.0293321\pi$
$859$			158.089i			0.184038i	−0.995757	+	0.0920191i	$0.970668\pi$
$860$	−50.3474	+	199.056i	−0.0585434	+	0.231461i
$861$		0			0
$862$	918.358	+	114.340i	1.06538	+	0.132645i
$863$			685.963i			0.794859i	0.917633	+	0.397429i	$0.130098\pi$
$863$			685.963i			0.794859i	−0.917633	+	0.397429i	$0.869902\pi$
$864$		0			0
$865$	−261.581			−0.302406
$866$	47.0913	−	378.229i	0.0543779	−	0.436754i
$867$		0			0
$868$	1233.85	+	312.079i	1.42149	+	0.359538i
$869$	325.695			0.374793
$870$		0			0
$871$		−	116.915i		−	0.134230i
$872$	73.9978	−	189.880i	0.0848598	−	0.217752i
$873$		0			0
$874$	17.2935	−	138.898i	0.0197866	−	0.158922i
$875$			830.956i			0.949664i
$876$		0			0
$877$	−917.810			−1.04653			−0.523267	−	0.852169i	$-0.675287\pi$
$877$	−917.810			−1.04653			−0.523267	+	0.852169i	$0.675287\pi$
$878$	−869.197	−	108.219i	−0.989974	−	0.123257i
$879$		0			0
$880$	−87.9565	+	162.751i	−0.0999506	+	0.184945i
$881$	−657.430			−0.746231			−0.373116	−	0.927785i	$-0.621711\pi$
$881$	−657.430			−0.746231			−0.373116	+	0.927785i	$0.621711\pi$
$882$		0			0
$883$			618.879i			0.700882i	0.936585	+	0.350441i	$0.113968\pi$
$883$			618.879i			0.700882i	−0.936585	+	0.350441i	$0.886032\pi$
$884$	−1618.15	−	409.279i	−1.83048	−	0.462985i
$885$		0			0
$886$	1654.60	+	206.005i	1.86749	+	0.232511i
$887$		−	127.992i		−	0.144297i	−0.997394	−	0.0721487i	$-0.977014\pi$
$887$		−	127.992i		−	0.144297i	0.997394	−	0.0721487i	$-0.0229856\pi$
$888$		0			0
$889$	1232.24			1.38609
$890$	58.4131	−	469.164i	0.0656327	−	0.527150i
$891$		0			0
$892$	−101.252	+	400.315i	−0.113511	+	0.448784i
$893$	−571.323			−0.639779
$894$		0			0
$895$		−	480.420i		−	0.536783i
$896$	−692.262	−	815.697i	−0.772613	−	0.910376i
$897$		0			0
$898$	−118.804	+	954.210i	−0.132298	+	1.06259i
$899$			939.164i			1.04468i
$900$		0			0
$901$	−908.086			−1.00786
$902$	−206.872	−	25.7566i	−0.229349	−	0.0285550i
$903$		0			0
$904$	442.429	−	1135.28i	0.489412	−	1.25584i
$905$	−405.313			−0.447859
$906$		0			0
$907$			15.9286i			0.0175619i	0.999961	+	0.00878094i	$0.00279510\pi$
$907$			15.9286i			0.0175619i	−0.999961	+	0.00878094i	$0.997205\pi$
$908$	138.411	−	547.230i	0.152435	−	0.602676i
$909$		0			0
$910$	−538.957	−	67.1027i	−0.592260	−	0.0737393i
$911$		−	50.7208i		−	0.0556760i	−0.999612	−	0.0278380i	$-0.991138\pi$
$911$		−	50.7208i		−	0.0556760i	0.999612	−	0.0278380i	$-0.00886226\pi$
$912$		0			0
$913$	−624.889			−0.684435
$914$	−54.0230	+	433.903i	−0.0591061	+	0.474729i
$915$		0			0
$916$	818.789	+	207.097i	0.893875	+	0.226088i
$917$	−1089.52			−1.18814
$918$		0			0
$919$			1065.04i			1.15892i	0.815002	+	0.579458i	$0.196736\pi$
$919$			1065.04i			1.15892i	−0.815002	+	0.579458i	$0.803264\pi$
$920$	−60.0199	−	23.3902i	−0.0652390	−	0.0254242i
$921$		0			0
$922$	177.159	−	1422.91i	0.192146	−	1.54328i
$923$			928.559i			1.00602i
$924$		0			0
$925$	85.0361			0.0919309
$926$	−61.0166	−	7.59686i	−0.0658927	−	0.00820396i
$927$		0			0
$928$	458.285	−	642.838i	0.493841	−	0.692713i
$929$	−343.399			−0.369643			−0.184822	−	0.982772i	$-0.559171\pi$
$929$	−343.399			−0.369643			−0.184822	+	0.982772i	$0.559171\pi$
$930$		0			0
$931$		−	399.212i		−	0.428799i
$932$	1086.23	+	274.741i	1.16548	+	0.294786i
$933$		0			0
$934$	−910.249	−	113.330i	−0.974571	−	0.121339i
$935$			326.971i			0.349702i
$936$		0			0
$937$	−267.742			−0.285744			−0.142872	−	0.989741i	$-0.545634\pi$
$937$	−267.742			−0.285744			−0.142872	+	0.989741i	$0.545634\pi$
$938$	16.3643	−	131.435i	0.0174459	−	0.140123i
$939$		0			0
$940$	−64.4730	+	254.904i	−0.0685883	+	0.271175i
$941$	1220.25			1.29676			0.648380	−	0.761317i	$-0.275447\pi$
$941$	1220.25			1.29676			0.648380	+	0.761317i	$0.275447\pi$
$942$		0			0
$943$		−	72.5893i		−	0.0769770i
$944$	−69.9342	+	129.404i	−0.0740828	+	0.137080i
$945$		0			0
$946$	30.2503	−	242.964i	0.0319770	−	0.256833i
$947$		−	1611.78i		−	1.70198i	−0.525180	−	0.850991i	$-0.676002\pi$
$947$		−	1611.78i		−	1.70198i	0.525180	−	0.850991i	$-0.323998\pi$
$948$		0			0
$949$	491.689			0.518113
$950$	−765.406	−	95.2967i	−0.805690	−	0.100312i
$951$		0			0
$952$	−1761.83	−	686.600i	−1.85066	−	0.721218i
$953$	242.459			0.254416			0.127208	−	0.991876i	$-0.459398\pi$
$953$	242.459			0.254416			0.127208	+	0.991876i	$0.459398\pi$
$954$		0			0
$955$			548.603i			0.574453i
$956$	−384.336	+	1519.53i	−0.402026	+	1.58947i
$957$		0			0
$958$	−1307.37	−	162.774i	−1.36468	−	0.169910i
$959$		−	834.451i		−	0.870127i
$960$		0			0
$961$	−488.137			−0.507947
$962$	−15.3860	+	123.578i	−0.0159938	+	0.128459i
$963$		0			0
$964$	−183.646	−	46.4496i	−0.190504	−	0.0481842i
$965$	550.842			0.570821
$966$		0			0
$967$			1782.64i			1.84347i	0.387815	+	0.921737i	$0.373230\pi$
$967$			1782.64i			1.84347i	−0.387815	+	0.921737i	$0.626770\pi$
$968$	−271.387	+	696.386i	−0.280358	+	0.719407i
$969$		0			0
$970$	1.94369	−	15.6113i	0.00200380	−	0.0160941i
$971$		−	645.136i		−	0.664404i	−0.943208	−	0.332202i	$-0.892208\pi$
$971$		−	645.136i		−	0.664404i	0.943208	−	0.332202i	$-0.107792\pi$
$972$		0			0
$973$	798.958			0.821129
$974$	1420.21	+	176.823i	1.45812	+	0.181544i
$975$		0			0
$976$	1149.20	+	621.068i	1.17746	+	0.636340i
$977$	1379.56			1.41203			0.706017	−	0.708195i	$-0.250490\pi$
$977$	1379.56			1.41203			0.706017	+	0.708195i	$0.250490\pi$
$978$		0			0
$979$			563.776i			0.575869i
$980$	−178.114	−	45.0505i	−0.181749	−	0.0459699i
$981$		0			0
$982$	−1315.85	−	163.830i	−1.33997	−	0.166833i
$983$			738.782i			0.751558i	0.926709	+	0.375779i	$0.122625\pi$
$983$			738.782i			0.751558i	−0.926709	+	0.375779i	$0.877375\pi$
$984$		0			0
$985$	−562.956			−0.571529
$986$	172.395	−	1384.65i	0.174843	−	1.40431i
$987$		0			0
$988$	276.977	−	1095.07i	0.280342	−	1.10837i
$989$	85.2536			0.0862018
$990$		0			0
$991$		−	1533.69i		−	1.54762i	−0.633416	−	0.773811i	$-0.718348\pi$
$991$		−	1533.69i		−	1.54762i	0.633416	−	0.773811i	$-0.281652\pi$
$992$	991.904	+	707.137i	0.999903	+	0.712840i
$993$		0			0
$994$	−129.969	+	1043.88i	−0.130753	+	1.05018i
$995$			680.615i			0.684035i
$996$		0			0
$997$	1742.55			1.74779			0.873896	−	0.486113i	$-0.161586\pi$
$997$	1742.55			1.74779			0.873896	+	0.486113i	$0.161586\pi$
$998$	1051.22	+	130.882i	1.05333	+	0.131144i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.d.i.163.3		8
3.2	odd	2		324.3.d.g.163.6		8
4.3	odd	2	inner	324.3.d.i.163.4		8
9.2	odd	6		108.3.f.c.91.7		16
9.4	even	3		36.3.f.c.7.8	yes	16
9.5	odd	6		108.3.f.c.19.1		16
9.7	even	3		36.3.f.c.31.2	yes	16
12.11	even	2		324.3.d.g.163.5		8
36.7	odd	6		36.3.f.c.31.8	yes	16
36.11	even	6		108.3.f.c.91.1		16
36.23	even	6		108.3.f.c.19.7		16
36.31	odd	6		36.3.f.c.7.2	✓	16
72.5	odd	6		1728.3.o.g.127.3		16
72.11	even	6		1728.3.o.g.1279.3		16
72.13	even	6		576.3.o.g.511.5		16
72.29	odd	6		1728.3.o.g.1279.4		16
72.43	odd	6		576.3.o.g.319.5		16
72.59	even	6		1728.3.o.g.127.4		16
72.61	even	6		576.3.o.g.319.4		16
72.67	odd	6		576.3.o.g.511.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.2	✓	16	36.31	odd	6
36.3.f.c.7.8	yes	16	9.4	even	3
36.3.f.c.31.2	yes	16	9.7	even	3
36.3.f.c.31.8	yes	16	36.7	odd	6
108.3.f.c.19.1		16	9.5	odd	6
108.3.f.c.19.7		16	36.23	even	6
108.3.f.c.91.1		16	36.11	even	6
108.3.f.c.91.7		16	9.2	odd	6
324.3.d.g.163.5		8	12.11	even	2
324.3.d.g.163.6		8	3.2	odd	2
324.3.d.i.163.3		8	1.1	even	1	trivial
324.3.d.i.163.4		8	4.3	odd	2	inner
576.3.o.g.319.4		16	72.61	even	6
576.3.o.g.319.5		16	72.43	odd	6
576.3.o.g.511.4		16	72.67	odd	6
576.3.o.g.511.5		16	72.13	even	6
1728.3.o.g.127.3		16	72.5	odd	6
1728.3.o.g.127.4		16	72.59	even	6
1728.3.o.g.1279.3		16	72.11	even	6
1728.3.o.g.1279.4		16	72.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.247102 - 1.98468i) q^{2} +(-3.87788 - 0.980835i) q^{4} -2.20185 q^{5} +8.35824i q^{7} +(-2.90487 + 7.45397i) q^{8} +O(q^{10})\)	\(q+(0.247102 - 1.98468i) q^{2} +(-3.87788 - 0.980835i) q^{4} -2.20185 q^{5} +8.35824i q^{7} +(-2.90487 + 7.45397i) q^{8} +(-0.544081 + 4.36996i) q^{10} -5.25121i q^{11} +14.7558 q^{13} +(16.5884 + 2.06534i) q^{14} +(14.0759 + 7.60712i) q^{16} +28.2789 q^{17} +19.1376i q^{19} +(8.53851 + 2.15965i) q^{20} +(-10.4220 - 1.29759i) q^{22} -3.65696i q^{23} -20.1519 q^{25} +(3.64618 - 29.2854i) q^{26} +(8.19805 - 32.4122i) q^{28} +24.6710 q^{29} +38.0675i q^{31} +(18.5759 - 26.0564i) q^{32} +(6.98776 - 56.1244i) q^{34} -18.4036i q^{35} -4.21977 q^{37} +(37.9819 + 4.72893i) q^{38} +(6.39609 - 16.4125i) q^{40} +19.8497 q^{41} +23.3127i q^{43} +(-5.15057 + 20.3636i) q^{44} +(-7.25787 - 0.903640i) q^{46} +29.8534i q^{47} -20.8601 q^{49} +(-4.97956 + 39.9949i) q^{50} +(-57.2211 - 14.4730i) q^{52} -32.1118 q^{53} +11.5624i q^{55} +(-62.3021 - 24.2796i) q^{56} +(6.09625 - 48.9639i) q^{58} +9.19326i q^{59} +81.6430 q^{61} +(75.5517 + 9.40656i) q^{62} +(-47.1234 - 43.3057i) q^{64} -32.4900 q^{65} -7.92331i q^{67} +(-109.662 - 27.7369i) q^{68} +(-36.5252 - 4.54756i) q^{70} +62.9286i q^{71} +33.3218 q^{73} +(-1.04271 + 8.37487i) q^{74} +(18.7708 - 74.2133i) q^{76} +43.8909 q^{77} +62.0228i q^{79} +(-30.9931 - 16.7497i) q^{80} +(4.90489 - 39.3951i) q^{82} -118.999i q^{83} -62.2659 q^{85} +(46.2682 + 5.76062i) q^{86} +(39.1424 + 15.2541i) q^{88} -107.361 q^{89} +123.332i q^{91} +(-3.58687 + 14.1812i) q^{92} +(59.2494 + 7.37684i) q^{94} -42.1381i q^{95} -3.57242 q^{97} +(-5.15457 + 41.4005i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 5 q^{4} - 6 q^{5} - 27 q^{8}+O(q^{10}) \) 8 * q + 3 * q^2 + 5 * q^4 - 6 * q^5 - 27 * q^8	\( 8 q + 3 q^{2} + 5 q^{4} - 6 q^{5} - 27 q^{8} + 10 q^{10} + 46 q^{13} + 12 q^{14} + 17 q^{16} + 6 q^{17} - 36 q^{20} - 33 q^{22} + 30 q^{25} + 36 q^{26} + 6 q^{28} - 42 q^{29} - 87 q^{32} - 11 q^{34} + 28 q^{37} + 99 q^{38} - 68 q^{40} - 84 q^{41} - 111 q^{44} - 132 q^{46} - 58 q^{49} + 219 q^{50} - 110 q^{52} - 36 q^{53} - 270 q^{56} + 16 q^{58} + 34 q^{61} + 258 q^{62} - 127 q^{64} + 30 q^{65} - 375 q^{68} - 150 q^{70} + 58 q^{73} + 372 q^{74} + 15 q^{76} + 330 q^{77} - 360 q^{80} + 127 q^{82} + 140 q^{85} + 273 q^{86} - 75 q^{88} - 192 q^{89} - 258 q^{92} - 36 q^{94} + 148 q^{97} + 585 q^{98}+O(q^{100}) \) 8 * q + 3 * q^2 + 5 * q^4 - 6 * q^5 - 27 * q^8 + 10 * q^10 + 46 * q^13 + 12 * q^14 + 17 * q^16 + 6 * q^17 - 36 * q^20 - 33 * q^22 + 30 * q^25 + 36 * q^26 + 6 * q^28 - 42 * q^29 - 87 * q^32 - 11 * q^34 + 28 * q^37 + 99 * q^38 - 68 * q^40 - 84 * q^41 - 111 * q^44 - 132 * q^46 - 58 * q^49 + 219 * q^50 - 110 * q^52 - 36 * q^53 - 270 * q^56 + 16 * q^58 + 34 * q^61 + 258 * q^62 - 127 * q^64 + 30 * q^65 - 375 * q^68 - 150 * q^70 + 58 * q^73 + 372 * q^74 + 15 * q^76 + 330 * q^77 - 360 * q^80 + 127 * q^82 + 140 * q^85 + 273 * q^86 - 75 * q^88 - 192 * q^89 - 258 * q^92 - 36 * q^94 + 148 * q^97 + 585 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more