LMFDB - Embedded newform 324.3.d.i.163.4

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

$q$-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	$-0.796353\pi$
$7$		−	8.35824i		−	1.19403i	0.802229	−	0.597017i	$-0.203647\pi$
$8$	−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	$0.0767185\pi$
$11$			5.25121i			0.477383i	−0.971095	+	0.238692i	$0.923282\pi$
$12$		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	$-0.832001\pi$
$19$		−	19.1376i		−	1.00724i	0.863925	−	0.503620i	$-0.167999\pi$
$20$	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	$0.0253321\pi$
$23$			3.65696i			0.158998i	−0.996835	+	0.0794990i	$0.974668\pi$
$24$		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	$-0.789563\pi$
$31$		−	38.0675i		−	1.22798i	0.789312	−	0.613992i	$-0.210437\pi$
$32$	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	$-0.912620\pi$
$43$		−	23.3127i		−	0.542157i	0.962557	−	0.271078i	$-0.0873802\pi$
$44$	−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	$-0.897126\pi$
$47$		−	29.8534i		−	0.635180i	0.948228	−	0.317590i	$-0.102874\pi$
$48$		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	$-0.975176\pi$
$59$		−	9.19326i		−	0.155818i	0.996960	−	0.0779089i	$-0.0248243\pi$
$60$		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	$0.0188324\pi$
$67$			7.92331i			0.118258i	−0.998250	+	0.0591292i	$0.981168\pi$
$68$	−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	$-0.853858\pi$
$71$		−	62.9286i		−	0.886318i	0.896443	−	0.443159i	$-0.146142\pi$
$72$		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	$-0.871593\pi$
$79$		−	62.0228i		−	0.785099i	0.919731	−	0.392549i	$-0.128407\pi$
$80$	−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	$0.254422\pi$
$83$			118.999i			1.43372i	−0.697216	+	0.716861i	$0.745578\pi$
$84$		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	$-0.782089\pi$
$103$		−	130.265i		−	1.26471i	0.774680	−	0.632353i	$-0.217911\pi$
$104$	−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	$0.0770146\pi$
$107$			51.2733i			0.479190i	−0.970873	+	0.239595i	$0.922985\pi$
$108$		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	$0.197114\pi$
$127$			147.428i			1.16085i	−0.814314	+	0.580425i	$0.802886\pi$
$128$	−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	$-0.834240\pi$
$131$		−	130.353i		−	0.995063i	0.867446	−	0.497532i	$-0.165760\pi$
$132$		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	$0.111730\pi$
$139$			95.5893i			0.687693i	−0.939026	+	0.343847i	$0.888270\pi$
$140$	−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	$0.113461\pi$
$151$			105.382i			0.697893i	−0.937143	+	0.348946i	$0.886539\pi$
$152$	−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	$-0.966993\pi$
$163$		−	33.7439i		−	0.207018i	0.994629	−	0.103509i	$-0.0330071\pi$
$164$	−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	$0.150305\pi$
$167$			151.918i			0.909687i	−0.890571	+	0.454843i	$0.849695\pi$
$168$		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	$-0.791383\pi$
$179$		−	218.189i		−	1.21894i	0.792811	−	0.609468i	$-0.208617\pi$
$180$		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	$0.226170\pi$
$191$			249.155i			1.30448i	−0.758013	+	0.652239i	$0.773830\pi$
$192$		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	$0.283087\pi$
$199$			309.110i			1.55332i	−0.629921	+	0.776659i	$0.716913\pi$
$200$	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	$0.383259\pi$
$211$			393.936i			1.86699i	−0.358585	+	0.933497i	$0.616741\pi$
$212$	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	$0.0743497\pi$
$223$			103.230i			0.462917i	−0.972845	+	0.231458i	$0.925650\pi$
$224$	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	$-0.899394\pi$
$227$		−	141.116i		−	0.621655i	0.950466	−	0.310828i	$-0.100606\pi$
$228$		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	$0.305895\pi$
$239$			391.846i			1.63952i	−0.572704	+	0.819762i	$0.694105\pi$
$240$		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	$0.282618\pi$
$251$			389.416i			1.55146i	−0.631065	+	0.775730i	$0.717382\pi$
$252$		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	$-0.911684\pi$
$263$		−	144.076i		−	0.547816i	0.961756	−	0.273908i	$-0.0883164\pi$
$264$		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	$-0.979154\pi$
$271$		−	35.4695i		−	0.130884i	0.997856	−	0.0654419i	$-0.0208457\pi$
$272$	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	$-0.852872\pi$
$283$		−	252.398i		−	0.891865i	0.895067	−	0.445933i	$-0.147128\pi$
$284$	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	$-0.928464\pi$
$307$		−	136.830i		−	0.445701i	0.974853	−	0.222850i	$-0.0715361\pi$
$308$	−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	$-0.757954\pi$
$311$		−	428.695i		−	1.37844i	0.724553	−	0.689219i	$-0.242046\pi$
$312$		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	$0.0407251\pi$
$331$			84.4664i			0.255186i	−0.991827	+	0.127593i	$0.959275\pi$
$332$	−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	$0.249824\pi$
$347$			490.460i			1.41343i	−0.707499	+	0.706715i	$0.750176\pi$
$348$		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	$0.193939\pi$
$359$			410.893i			1.14455i	−0.820062	+	0.572274i	$0.806061\pi$
$360$		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	$-0.737946\pi$
$367$		−	538.294i		−	1.46674i	0.679829	−	0.733370i	$-0.262054\pi$
$368$	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	$0.0782040\pi$
$379$			184.361i			0.486442i	−0.969971	+	0.243221i	$0.921796\pi$
$380$	−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	$-0.912277\pi$
$383$		−	208.439i		−	0.544228i	0.962265	−	0.272114i	$-0.0877227\pi$
$384$		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	$-0.844674\pi$
$419$		−	392.882i		−	0.937667i	0.883287	−	0.468833i	$-0.155326\pi$
$420$		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	$-0.819632\pi$
$431$		−	462.725i		−	1.07361i	0.843707	−	0.536803i	$-0.180368\pi$
$432$		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	$0.166229\pi$
$439$			437.954i			0.997618i	−0.866712	+	0.498809i	$0.833771\pi$
$440$	−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	$-0.609931\pi$
$443$		−	833.685i		−	1.88191i	0.338535	−	0.940954i	$-0.390069\pi$
$444$		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	$0.0105701\pi$
$463$			30.7439i			0.0664014i	−0.999449	+	0.0332007i	$0.989430\pi$
$464$	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	$0.163386\pi$
$467$			458.639i			0.982096i	−0.871133	+	0.491048i	$0.836614\pi$
$468$		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	$0.241340\pi$
$479$			658.731i			1.37522i	−0.726080	+	0.687610i	$0.758660\pi$
$480$		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	$-0.737327\pi$
$487$		−	715.589i		−	1.46938i	0.678402	−	0.734691i	$-0.262673\pi$
$488$	−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	$0.235924\pi$
$491$			663.004i			1.35031i	−0.737674	+	0.675157i	$0.764076\pi$
$492$		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	$-0.821918\pi$
$499$		−	529.668i		−	1.06146i	0.847541	−	0.530730i	$-0.178082\pi$
$500$	−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	$0.0216446\pi$
$503$			68.3537i			0.135892i	−0.997689	+	0.0679460i	$0.978355\pi$
$504$		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	$-0.990707\pi$
$523$		−	30.5350i		−	0.0583843i	0.999574	−	0.0291921i	$-0.00929347\pi$
$524$	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	$-0.664792\pi$
$547$		−	950.637i		−	1.73791i	0.494891	−	0.868955i	$-0.335208\pi$
$548$	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	$0.397613\pi$
$563$			1068.25i			1.89742i	−0.316142	+	0.948712i	$0.602387\pi$
$564$		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	$-0.920938\pi$
$571$		−	280.744i		−	0.491671i	0.969312	−	0.245836i	$-0.0790624\pi$
$572$	−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	$-0.955563\pi$
$587$		−	163.362i		−	0.278300i	0.990271	−	0.139150i	$-0.0444370\pi$
$588$		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	$-0.874397\pi$
$599$		−	460.551i		−	0.768866i	0.923153	−	0.384433i	$-0.125603\pi$
$600$		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	$0.258962\pi$
$607$			882.254i			1.45347i	−0.686920	+	0.726733i	$0.741038\pi$
$608$	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	$0.110241\pi$
$619$			420.238i			0.678899i	−0.940624	+	0.339449i	$0.889759\pi$
$620$	−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	$0.125077\pi$
$631$			483.230i			0.765816i	−0.923787	+	0.382908i	$0.874923\pi$
$632$	−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	$0.133580\pi$
$643$			523.972i			0.814887i	−0.913230	+	0.407444i	$0.866420\pi$
$644$	−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	$-0.992299\pi$
$647$		−	31.3018i		−	0.0483799i	0.999707	−	0.0241900i	$-0.00770066\pi$
$648$		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	$-0.988514\pi$
$659$		−	47.5486i		−	0.0721526i	0.999349	−	0.0360763i	$-0.0114859\pi$
$660$		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	$0.219977\pi$
$683$			870.646i			1.27474i	−0.770559	+	0.637369i	$0.780023\pi$
$684$		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	$0.233097\pi$
$691$			923.977i			1.33716i	−0.743641	+	0.668580i	$0.766903\pi$
$692$	−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	$-0.945330\pi$
$719$		−	245.763i		−	0.341813i	0.985287	−	0.170906i	$-0.0546695\pi$
$720$		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	$0.310222\pi$
$727$			1203.15i			1.65495i	−0.561505	+	0.827473i	$0.689778\pi$
$728$	−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	$0.0561346\pi$
$739$			259.300i			0.350879i	−0.984490	+	0.175439i	$0.943865\pi$
$740$	−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	$-0.975174\pi$
$743$		−	115.781i		−	0.155830i	0.996960	−	0.0779149i	$-0.0248262\pi$
$744$		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	$0.137231\pi$
$751$			627.673i			0.835783i	−0.908497	+	0.417891i	$0.862769\pi$
$752$	−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	$0.139153\pi$
$787$			666.384i			0.846740i	−0.905957	+	0.423370i	$0.860847\pi$
$788$	−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	$0.323318\pi$
$811$			1378.48i			1.69973i	−0.526997	+	0.849867i	$0.676682\pi$
$812$	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	$-0.987340\pi$
$823$		−	65.4490i		−	0.0795250i	0.999209	−	0.0397625i	$-0.0126601\pi$
$824$	−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	$-0.844030\pi$
$827$		−	778.406i		−	0.941240i	0.882336	−	0.470620i	$-0.155970\pi$
$828$		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	$0.124436\pi$
$839$			639.396i			0.762093i	−0.924556	+	0.381046i	$0.875564\pi$
$840$		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	$-0.970668\pi$
$859$		−	158.089i		−	0.184038i	0.995757	−	0.0920191i	$-0.0293321\pi$
$860$	−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	$-0.869902\pi$
$863$		−	685.963i		−	0.794859i	0.917633	−	0.397429i	$-0.130098\pi$
$864$		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	$-0.886032\pi$
$883$		−	618.879i		−	0.700882i	0.936585	−	0.350441i	$-0.113968\pi$
$884$	−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	$0.0229856\pi$
$887$			127.992i			0.144297i	−0.997394	+	0.0721487i	$0.977014\pi$
$888$		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	$-0.997205\pi$
$907$		−	15.9286i		−	0.0175619i	0.999961	−	0.00878094i	$-0.00279510\pi$
$908$	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	$0.00886226\pi$
$911$			50.7208i			0.0556760i	−0.999612	+	0.0278380i	$0.991138\pi$
$912$		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	$-0.803264\pi$
$919$		−	1065.04i		−	1.15892i	0.815002	−	0.579458i	$-0.196736\pi$
$920$	−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	$0.323998\pi$
$947$			1611.78i			1.70198i	−0.525180	+	0.850991i	$0.676002\pi$
$948$		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	$-0.626770\pi$
$967$		−	1782.64i		−	1.84347i	0.387815	−	0.921737i	$-0.373230\pi$
$968$	−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	$0.107792\pi$
$971$			645.136i			0.664404i	−0.943208	+	0.332202i	$0.892208\pi$
$972$		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	$-0.877375\pi$
$983$		−	738.782i		−	0.751558i	0.926709	−	0.375779i	$-0.122625\pi$
$984$		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	$0.281652\pi$
$991$			1533.69i			1.54762i	−0.633416	+	0.773811i	$0.718348\pi$
$992$	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.163.4		8
3.2	odd	2		324.3.d.g.163.5		8
4.3	odd	2	inner	324.3.d.i.163.3		8
9.2	odd	6		108.3.f.c.91.1		16
9.4	even	3		36.3.f.c.7.2	✓	16
9.5	odd	6		108.3.f.c.19.7		16
9.7	even	3		36.3.f.c.31.8	yes	16
12.11	even	2		324.3.d.g.163.6		8
36.7	odd	6		36.3.f.c.31.2	yes	16
36.11	even	6		108.3.f.c.91.7		16
36.23	even	6		108.3.f.c.19.1		16
36.31	odd	6		36.3.f.c.7.8	yes	16
72.5	odd	6		1728.3.o.g.127.4		16
72.11	even	6		1728.3.o.g.1279.4		16
72.13	even	6		576.3.o.g.511.4		16
72.29	odd	6		1728.3.o.g.1279.3		16
72.43	odd	6		576.3.o.g.319.4		16
72.59	even	6		1728.3.o.g.127.3		16
72.61	even	6		576.3.o.g.319.5		16
72.67	odd	6		576.3.o.g.511.5		16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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