LMFDB - Embedded newform 324.3.o.a.65.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(5,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("324.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.o (of order $54$, degree $18$, 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:	$324$
Relative dimension:	$18$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			65.9
Character	$\chi$	$=$	324.65
Dual form			324.3.o.a.5.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.463613 + 2.96396i) q^{3} +(-2.73041 - 2.03271i) q^{5} +(-1.12154 - 0.737649i) q^{7} +(-8.57013 - 2.74826i) q^{9} +O(q^{10})$	\(q+(-0.463613 + 2.96396i) q^{3} +(-2.73041 - 2.03271i) q^{5} +(-1.12154 - 0.737649i) q^{7} +(-8.57013 - 2.74826i) q^{9} +(-0.325590 - 2.78560i) q^{11} +(6.15219 - 20.5497i) q^{13} +(7.29073 - 7.15043i) q^{15} +(5.48948 - 0.967944i) q^{17} +(0.824658 - 4.67687i) q^{19} +(2.70633 - 2.98222i) q^{21} +(10.9269 + 16.6136i) q^{23} +(-3.84688 - 12.8495i) q^{25} +(12.1190 - 24.1274i) q^{27} +(-14.1673 - 13.3662i) q^{29} +(-0.486900 - 8.35975i) q^{31} +(8.40736 + 0.326405i) q^{33} +(1.56284 + 4.29386i) q^{35} +(34.4216 + 12.5284i) q^{37} +(58.0564 + 27.7620i) q^{39} +(-6.96530 - 29.3889i) q^{41} +(24.2316 - 56.1752i) q^{43} +(17.8135 + 24.9245i) q^{45} +(16.7341 + 0.974651i) q^{47} +(-18.6942 - 43.3380i) q^{49} +(0.323952 + 16.7194i) q^{51} +(-84.4954 + 48.7834i) q^{53} +(-4.77333 + 8.26766i) q^{55} +(13.4797 + 4.61251i) q^{57} +(4.20200 - 35.9504i) q^{59} +(0.599932 - 0.301297i) q^{61} +(7.58450 + 9.40404i) q^{63} +(-58.5697 + 43.6035i) q^{65} +(23.3316 + 24.7300i) q^{67} +(-54.3079 + 24.6847i) q^{69} +(-56.0789 - 66.8323i) q^{71} +(-70.3977 - 59.0707i) q^{73} +(39.8688 - 5.44482i) q^{75} +(-1.68963 + 3.36434i) q^{77} +(-31.3766 - 7.43638i) q^{79} +(65.8941 + 47.1059i) q^{81} +(-12.1078 + 51.0870i) q^{83} +(-16.9561 - 8.51566i) q^{85} +(46.1849 - 35.7946i) q^{87} +(-75.7179 + 90.2371i) q^{89} +(-22.0584 + 18.5092i) q^{91} +(25.0037 + 2.43254i) q^{93} +(-11.7584 + 11.0935i) q^{95} +(-34.4044 - 46.2131i) q^{97} +(-4.86521 + 24.7678i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q+O(q^{10}) $ 324 * q	$ 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) $ 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{31}{54}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.463613	+	2.96396i	−0.154538	+	0.987987i
$3$	−0.463613	+	2.96396i	−0.154538	+	0.987987i
$4$		0			0
$5$	−2.73041	−	2.03271i	−0.546081	−	0.406543i	0.288457	−	0.957493i	$-0.406858\pi$
$5$	−2.73041	−	2.03271i	−0.546081	−	0.406543i	−0.834538	+	0.550950i	$0.814265\pi$
$6$		0			0
$7$	−1.12154	−	0.737649i	−0.160220	−	0.105378i	0.466867	−	0.884328i	$-0.345383\pi$
$7$	−1.12154	−	0.737649i	−0.160220	−	0.105378i	−0.627087	+	0.778949i	$0.715753\pi$
$8$		0			0
$9$	−8.57013	−	2.74826i	−0.952236	−	0.305362i
$10$		0			0
$11$	−0.325590	−	2.78560i	−0.0295991	−	0.253237i	−0.999934	−	0.0114725i	$-0.996348\pi$
$11$	−0.325590	−	2.78560i	−0.0295991	−	0.253237i	0.970335	−	0.241764i	$-0.0777260\pi$
$12$		0			0
$13$	6.15219	−	20.5497i	0.473245	−	1.58075i	−0.304721	−	0.952442i	$-0.598563\pi$
$13$	6.15219	−	20.5497i	0.473245	−	1.58075i	0.777966	−	0.628307i	$-0.216252\pi$
$14$		0			0
$15$	7.29073	−	7.15043i	0.486049	−	0.476695i
$16$		0			0
$17$	5.48948	−	0.967944i	0.322911	−	0.0569379i	−0.00984318	−	0.999952i	$-0.503133\pi$
$17$	5.48948	−	0.967944i	0.322911	−	0.0569379i	0.332754	+	0.943014i	$0.392022\pi$
$18$		0			0
$19$	0.824658	−	4.67687i	0.0434031	−	0.246151i	−0.955385	−	0.295362i	$-0.904560\pi$
$19$	0.824658	−	4.67687i	0.0434031	−	0.246151i	0.998788	+	0.0492113i	$0.0156708\pi$
$20$		0			0
$21$	2.70633	−	2.98222i	0.128873	−	0.142011i
$22$		0			0
$23$	10.9269	+	16.6136i	0.475084	+	0.722330i	0.990934	−	0.134349i	$-0.0428943\pi$
$23$	10.9269	+	16.6136i	0.475084	+	0.722330i	−0.515850	+	0.856679i	$0.672524\pi$
$24$		0			0
$25$	−3.84688	−	12.8495i	−0.153875	−	0.513979i
$26$		0			0
$27$	12.1190	−	24.1274i	0.448850	−	0.893607i
$28$		0			0
$29$	−14.1673	−	13.3662i	−0.488528	−	0.460902i	0.402126	−	0.915584i	$-0.368271\pi$
$29$	−14.1673	−	13.3662i	−0.488528	−	0.460902i	−0.890654	+	0.454682i	$0.849753\pi$
$30$		0			0
$31$	−0.486900	−	8.35975i	−0.0157064	−	0.269669i	−0.997014	−	0.0772226i	$-0.975395\pi$
$31$	−0.486900	−	8.35975i	−0.0157064	−	0.269669i	0.981307	−	0.192447i	$-0.0616423\pi$
$32$		0			0
$33$	8.40736	+	0.326405i	0.254769	+	0.00989106i
$34$		0			0
$35$	1.56284	+	4.29386i	0.0446524	+	0.122682i
$36$		0			0
$37$	34.4216	+	12.5284i	0.930313	+	0.338606i	0.762334	−	0.647184i	$-0.224054\pi$
$37$	34.4216	+	12.5284i	0.930313	+	0.338606i	0.167979	+	0.985791i	$0.446276\pi$
$38$		0			0
$39$	58.0564	+	27.7620i	1.48862	+	0.711845i
$40$		0			0
$41$	−6.96530	−	29.3889i	−0.169885	−	0.716803i	−0.989578	−	0.143999i	$-0.954004\pi$
$41$	−6.96530	−	29.3889i	−0.169885	−	0.716803i	0.819693	−	0.572804i	$-0.194144\pi$
$42$		0			0
$43$	24.2316	−	56.1752i	0.563526	−	1.30640i	−0.363567	−	0.931568i	$-0.618441\pi$
$43$	24.2316	−	56.1752i	0.563526	−	1.30640i	0.927093	−	0.374832i	$-0.122300\pi$
$44$		0			0
$45$	17.8135	+	24.9245i	0.395856	+	0.553877i
$46$		0			0
$47$	16.7341	+	0.974651i	0.356045	+	0.0207373i	0.235235	−	0.971938i	$-0.424414\pi$
$47$	16.7341	+	0.974651i	0.356045	+	0.0207373i	0.120810	+	0.992676i	$0.461451\pi$
$48$		0			0
$49$	−18.6942	−	43.3380i	−0.381514	−	0.884449i
$50$		0			0
$51$	0.323952	+	16.7194i	0.00635200	+	0.327831i
$52$		0			0
$53$	−84.4954	+	48.7834i	−1.59425	+	0.920442i	−0.601686	+	0.798733i	$0.705504\pi$
$53$	−84.4954	+	48.7834i	−1.59425	+	0.920442i	−0.992566	+	0.121709i	$0.961162\pi$
$54$		0			0
$55$	−4.77333	+	8.26766i	−0.0867879	+	0.150321i
$56$		0			0
$57$	13.4797	+	4.61251i	0.236486	+	0.0809212i
$58$		0			0
$59$	4.20200	−	35.9504i	0.0712204	−	0.609329i	−0.909748	−	0.415161i	$-0.863725\pi$
$59$	4.20200	−	35.9504i	0.0712204	−	0.609329i	0.980968	−	0.194168i	$-0.0622007\pi$
$60$		0			0
$61$	0.599932	−	0.301297i	0.00983495	−	0.00493930i	−0.443875	−	0.896089i	$-0.646397\pi$
$61$	0.599932	−	0.301297i	0.00983495	−	0.00493930i	0.453710	+	0.891149i	$0.350100\pi$
$62$		0			0
$63$	7.58450	+	9.40404i	0.120389	+	0.149270i
$64$		0			0
$65$	−58.5697	+	43.6035i	−0.901072	+	0.670823i
$66$		0			0
$67$	23.3316	+	24.7300i	0.348233	+	0.369105i	0.877688	−	0.479233i	$-0.159085\pi$
$67$	23.3316	+	24.7300i	0.348233	+	0.369105i	−0.529455	+	0.848338i	$0.677604\pi$
$68$		0			0
$69$	−54.3079	+	24.6847i	−0.787071	+	0.357749i
$70$		0			0
$71$	−56.0789	−	66.8323i	−0.789844	−	0.941299i	0.209489	−	0.977811i	$-0.432820\pi$
$71$	−56.0789	−	66.8323i	−0.789844	−	0.941299i	−0.999333	+	0.0365116i	$0.988375\pi$
$72$		0			0
$73$	−70.3977	−	59.0707i	−0.964352	−	0.809187i	0.0173037	−	0.999850i	$-0.494492\pi$
$73$	−70.3977	−	59.0707i	−0.964352	−	0.809187i	−0.981656	+	0.190663i	$0.938936\pi$
$74$		0			0
$75$	39.8688	−	5.44482i	0.531584	−	0.0725975i
$76$		0			0
$77$	−1.68963	+	3.36434i	−0.0219433	+	0.0436927i
$78$		0			0
$79$	−31.3766	−	7.43638i	−0.397172	−	0.0941314i	0.0271762	−	0.999631i	$-0.491348\pi$
$79$	−31.3766	−	7.43638i	−0.397172	−	0.0941314i	−0.424348	+	0.905499i	$0.639497\pi$
$80$		0			0
$81$	65.8941	+	47.1059i	0.813508	+	0.581554i
$82$		0			0
$83$	−12.1078	+	51.0870i	−0.145878	+	0.615506i	0.850156	+	0.526531i	$0.176507\pi$
$83$	−12.1078	+	51.0870i	−0.145878	+	0.615506i	−0.996034	+	0.0889756i	$0.971641\pi$
$84$		0			0
$85$	−16.9561	−	8.51566i	−0.199483	−	0.100184i
$86$		0			0
$87$	46.1849	−	35.7946i	0.530861	−	0.411432i
$88$		0			0
$89$	−75.7179	+	90.2371i	−0.850763	+	1.01390i	0.148923	+	0.988849i	$0.452419\pi$
$89$	−75.7179	+	90.2371i	−0.850763	+	1.01390i	−0.999686	+	0.0250510i	$0.992025\pi$
$90$		0			0
$91$	−22.0584	+	18.5092i	−0.242400	+	0.203398i
$92$		0			0
$93$	25.0037	+	2.43254i	0.268857	+	0.0261563i
$94$		0			0
$95$	−11.7584	+	11.0935i	−0.123772	+	0.116773i
$96$		0			0
$97$	−34.4044	−	46.2131i	−0.354685	−	0.476424i	0.588593	−	0.808430i	$-0.299682\pi$
$97$	−34.4044	−	46.2131i	−0.354685	−	0.476424i	−0.943277	+	0.332006i	$0.892275\pi$
$98$		0			0
$99$	−4.86521	+	24.7678i	−0.0491436	+	0.250179i
$100$		0			0
$101$	43.0589	+	85.7373i	0.426325	+	0.848884i	0.999565	+	0.0294959i	$0.00939018\pi$
$101$	43.0589	+	85.7373i	0.426325	+	0.848884i	−0.573239	+	0.819388i	$0.694314\pi$
$102$		0			0
$103$	−4.90799	−	0.573662i	−0.0476504	−	0.00556953i	0.0922343	−	0.995737i	$-0.470599\pi$
$103$	−4.90799	−	0.573662i	−0.0476504	−	0.00556953i	−0.139885	+	0.990168i	$0.544673\pi$
$104$		0			0
$105$	−13.4514	+	2.64150i	−0.128108	+	0.0251571i
$106$		0			0
$107$	−14.0709	−	8.12382i	−0.131503	−	0.0759235i	0.432805	−	0.901488i	$-0.357524\pi$
$107$	−14.0709	−	8.12382i	−0.131503	−	0.0759235i	−0.564309	+	0.825564i	$0.690857\pi$
$108$		0			0
$109$	48.9682	+	84.8154i	0.449249	+	0.778123i	0.998337	−	0.0576419i	$-0.0183582\pi$
$109$	48.9682	+	84.8154i	0.449249	+	0.778123i	−0.549088	+	0.835765i	$0.685025\pi$
$110$		0			0
$111$	−53.0921	+	96.2159i	−0.478307	+	0.866809i
$112$		0			0
$113$	−73.9777	+	31.9109i	−0.654670	+	0.282397i	−0.697392	−	0.716690i	$-0.745656\pi$
$113$	−73.9777	+	31.9109i	−0.654670	+	0.282397i	0.0427221	+	0.999087i	$0.486397\pi$
$114$		0			0
$115$	3.93569	−	67.5731i	0.0342234	−	0.587593i
$116$		0			0
$117$	−109.201	+	159.206i	−0.933342	+	1.36073i
$118$		0			0
$119$	−6.87069	−	2.96373i	−0.0577369	−	0.0249053i
$120$		0			0
$121$	110.085	−	26.0906i	0.909792	−	0.215625i
$122$		0			0
$123$	90.3368	−	7.01979i	0.734445	−	0.0570715i
$124$		0			0
$125$	−44.7214	+	122.871i	−0.357771	+	0.982969i
$126$		0			0
$127$	28.7457	−	10.4626i	0.226344	−	0.0823825i	−0.226359	−	0.974044i	$-0.572682\pi$
$127$	28.7457	−	10.4626i	0.226344	−	0.0823825i	0.452703	+	0.891662i	$0.350460\pi$
$128$		0			0
$129$	155.267	+	97.8651i	1.20362	+	0.758644i
$130$		0			0
$131$	90.8501	−	5.29142i	0.693512	−	0.0403925i	0.292231	−	0.956348i	$-0.405602\pi$
$131$	90.8501	−	5.29142i	0.693512	−	0.0403925i	0.401281	+	0.915955i	$0.368565\pi$
$132$		0			0
$133$	−4.37478	+	4.63699i	−0.0328931	+	0.0348646i
$134$		0			0
$135$	−82.1337	+	41.2432i	−0.608398	+	0.305505i
$136$		0			0
$137$	−29.1836	+	8.73699i	−0.213019	+	0.0637737i	−0.391535	−	0.920163i	$-0.628056\pi$
$137$	−29.1836	+	8.73699i	−0.213019	+	0.0637737i	0.178516	+	0.983937i	$0.442870\pi$
$138$		0			0
$139$	114.683	−	75.4283i	0.825059	−	0.542650i	−0.0653230	−	0.997864i	$-0.520808\pi$
$139$	114.683	−	75.4283i	0.825059	−	0.542650i	0.890382	+	0.455214i	$0.150437\pi$
$140$		0			0
$141$	−10.6470	+	49.1474i	−0.0755105	+	0.348563i
$142$		0			0
$143$	−59.2465	−	10.4467i	−0.414311	−	0.0730542i
$144$		0			0
$145$	11.5129	+	65.2931i	0.0793995	+	0.450297i
$146$		0			0
$147$	137.119	−	35.3168i	0.932782	−	0.240250i
$148$		0			0
$149$	−7.06730	−	2.11581i	−0.0474315	−	0.0142001i	0.263000	−	0.964796i	$-0.415288\pi$
$149$	−7.06730	−	2.11581i	−0.0474315	−	0.0142001i	−0.310431	+	0.950596i	$0.600473\pi$
$150$		0			0
$151$	−101.697	+	11.8866i	−0.673488	+	0.0787195i	−0.445961	−	0.895052i	$-0.647138\pi$
$151$	−101.697	+	11.8866i	−0.673488	+	0.0787195i	−0.227527	+	0.973772i	$0.573064\pi$
$152$		0			0
$153$	−49.7057	−	6.79114i	−0.324874	−	0.0443865i
$154$		0			0
$155$	−15.6635	+	23.8152i	−0.101055	+	0.153647i
$156$		0			0
$157$	119.595	−	160.644i	0.761753	−	1.02321i	−0.236911	−	0.971531i	$-0.576135\pi$
$157$	119.595	−	160.644i	0.761753	−	1.02321i	0.998664	−	0.0516804i	$-0.0164577\pi$
$158$		0			0
$159$	−105.419	−	273.058i	−0.663012	−	1.71734i
$160$		0			0
$161$		−	26.6931i		−	0.165795i
$162$		0			0
$163$	6.31642			0.0387510			0.0193755	−	0.999812i	$-0.493832\pi$
$163$	6.31642			0.0387510			0.0193755	+	0.999812i	$0.493832\pi$
$164$		0			0
$165$	−22.2920	−	17.9810i	−0.135103	−	0.108976i
$166$		0			0
$167$	−100.555	−	74.8604i	−0.602126	−	0.448266i	0.252438	−	0.967613i	$-0.418768\pi$
$167$	−100.555	−	74.8604i	−0.602126	−	0.448266i	−0.854563	+	0.519347i	$0.826175\pi$
$168$		0			0
$169$	−243.245	−	159.984i	−1.43932	−	0.946654i
$170$		0			0
$171$	−19.9207	+	37.8150i	−0.116495	+	0.221140i
$172$		0			0
$173$	−0.656602	−	5.61759i	−0.00379539	−	0.0324716i	0.991208	−	0.132313i	$-0.0422405\pi$
$173$	−0.656602	−	5.61759i	−0.00379539	−	0.0324716i	−0.995003	+	0.0998416i	$0.968166\pi$
$174$		0			0
$175$	−5.16397	+	17.2489i	−0.0295084	+	0.0985649i
$176$		0			0
$177$	104.608	+	29.1216i	0.591003	+	0.164529i
$178$		0			0
$179$	225.032	−	39.6793i	1.25716	−	0.221672i	0.494907	−	0.868946i	$-0.335202\pi$
$179$	225.032	−	39.6793i	1.25716	−	0.221672i	0.762257	+	0.647274i	$0.224091\pi$
$180$		0			0
$181$	−29.2518	+	165.895i	−0.161612	+	0.916549i	0.790876	+	0.611976i	$0.209625\pi$
$181$	−29.2518	+	165.895i	−0.161612	+	0.916549i	−0.952489	+	0.304574i	$0.901486\pi$
$182$		0			0
$183$	0.614897	+	1.91786i	0.00336009	+	0.0104801i
$184$		0			0
$185$	−68.5182	−	104.177i	−0.370369	−	0.563118i
$186$		0			0
$187$	−4.48363	−	14.9764i	−0.0239766	−	0.0800875i
$188$		0			0
$189$	−31.3895	+	18.1203i	−0.166082	+	0.0958747i
$190$		0			0
$191$	273.406	+	257.945i	1.43144	+	1.35050i	0.838061	+	0.545577i	$0.183689\pi$
$191$	273.406	+	257.945i	1.43144	+	1.35050i	0.593383	+	0.804921i	$0.297792\pi$
$192$		0			0
$193$	−12.1104	−	207.928i	−0.0627482	−	1.07734i	−0.871881	−	0.489719i	$-0.837100\pi$
$193$	−12.1104	−	207.928i	−0.0627482	−	1.07734i	0.809132	−	0.587626i	$-0.199938\pi$
$194$		0			0
$195$	−102.085	−	193.813i	−0.523515	−	0.993915i
$196$		0			0
$197$	−76.7979	−	211.001i	−0.389837	−	1.07107i	−0.967075	−	0.254492i	$-0.918092\pi$
$197$	−76.7979	−	211.001i	−0.389837	−	1.07107i	0.577238	−	0.816576i	$-0.304131\pi$
$198$		0			0
$199$	−68.4585	−	24.9169i	−0.344013	−	0.125210i	0.164235	−	0.986421i	$-0.447484\pi$
$199$	−68.4585	−	24.9169i	−0.344013	−	0.125210i	−0.508248	+	0.861211i	$0.669707\pi$
$200$		0			0
$201$	−84.1157	+	57.6888i	−0.418486	+	0.287009i
$202$		0			0
$203$	6.02968	+	25.4412i	0.0297028	+	0.125326i
$204$		0			0
$205$	−40.7211	+	94.4021i	−0.198640	+	0.460498i
$206$		0			0
$207$	−47.9867	−	172.411i	−0.231820	−	0.832901i
$208$		0			0
$209$	−13.2964	−	0.774427i	−0.0636191	−	0.00370539i
$210$		0			0
$211$	80.7991	+	187.313i	0.382934	+	0.887741i	0.995270	+	0.0971438i	$0.0309707\pi$
$211$	80.7991	+	187.313i	0.382934	+	0.887741i	−0.612336	+	0.790598i	$0.709770\pi$
$212$		0			0
$213$	224.087	−	135.231i	1.05205	−	0.634889i
$214$		0			0
$215$	−180.350	+	104.125i	−0.838838	+	0.484303i
$216$		0			0
$217$	−5.62049	+	9.73497i	−0.0259009	+	0.0448616i
$218$		0			0
$219$	207.720	−	181.270i	0.948495	−	0.827717i
$220$		0			0
$221$	13.8813	−	118.762i	0.0628115	−	0.537386i
$222$		0			0
$223$	−172.014	+	86.3886i	−0.771363	+	0.387393i	−0.790530	−	0.612423i	$-0.790195\pi$
$223$	−172.014	+	86.3886i	−0.771363	+	0.387393i	0.0191673	+	0.999816i	$0.493898\pi$
$224$		0			0
$225$	−2.34547	+	120.694i	−0.0104243	+	0.536417i
$226$		0			0
$227$	275.719	−	205.265i	1.21462	−	0.904252i	0.217208	−	0.976125i	$-0.430305\pi$
$227$	275.719	−	205.265i	1.21462	−	0.904252i	0.997414	+	0.0718729i	$0.0228976\pi$
$228$		0			0
$229$	205.025	+	217.314i	0.895306	+	0.948969i	0.998958	−	0.0456449i	$-0.0145343\pi$
$229$	205.025	+	217.314i	0.895306	+	0.948969i	−0.103652	+	0.994614i	$0.533053\pi$
$230$		0			0
$231$	−9.18843	−	6.56776i	−0.0397768	−	0.0284319i
$232$		0			0
$233$	−256.685	−	305.905i	−1.10165	−	1.31290i	−0.945667	−	0.325137i	$-0.894590\pi$
$233$	−256.685	−	305.905i	−1.10165	−	1.31290i	−0.155984	−	0.987760i	$-0.549855\pi$
$234$		0			0
$235$	−43.7098	−	36.6768i	−0.185999	−	0.156072i
$236$		0			0
$237$	36.5877	−	89.5513i	0.154379	−	0.377854i
$238$		0			0
$239$	199.116	−	396.473i	0.833123	−	1.65888i	0.0839882	−	0.996467i	$-0.473234\pi$
$239$	199.116	−	396.473i	0.833123	−	1.65888i	0.749135	−	0.662418i	$-0.230470\pi$
$240$		0			0
$241$	245.473	+	58.1781i	1.01856	+	0.241403i	0.705786	−	0.708425i	$-0.250594\pi$
$241$	245.473	+	58.1781i	1.01856	+	0.241403i	0.312773	+	0.949828i	$0.398742\pi$
$242$		0			0
$243$	−170.169	+	173.469i	−0.700286	+	0.713863i
$244$		0			0
$245$	−37.0509	+	156.330i	−0.151228	+	0.638083i
$246$		0			0
$247$	−91.0349	−	45.7195i	−0.368562	−	0.185099i
$248$		0			0
$249$	−145.807	−	59.5718i	−0.585569	−	0.239244i
$250$		0			0
$251$	−46.8842	+	55.8744i	−0.186790	+	0.222607i	−0.851310	−	0.524663i	$-0.824191\pi$
$251$	−46.8842	+	55.8744i	−0.186790	+	0.222607i	0.664520	+	0.747270i	$0.268636\pi$
$252$		0			0
$253$	42.7211	−	35.8473i	0.168858	−	0.141689i
$254$		0			0
$255$	33.1011	−	46.3092i	0.129808	−	0.181605i
$256$		0			0
$257$	349.927	−	330.139i	1.36158	−	1.28459i	0.439157	−	0.898410i	$-0.355277\pi$
$257$	349.927	−	330.139i	1.36158	−	1.28459i	0.922425	−	0.386177i	$-0.126204\pi$
$258$		0			0
$259$	−29.3636	−	39.4422i	−0.113373	−	0.152287i
$260$		0			0
$261$	84.6818	+	153.485i	0.324451	+	0.588065i
$262$		0			0
$263$	147.438	+	293.572i	0.560599	+	1.11625i	0.978210	+	0.207619i	$0.0665714\pi$
$263$	147.438	+	293.572i	0.560599	+	1.11625i	−0.417610	+	0.908626i	$0.637132\pi$
$264$		0			0
$265$	329.869	+	38.5562i	1.24479	+	0.145495i
$266$		0			0
$267$	−232.355	−	266.260i	−0.870245	−	0.997228i
$268$		0			0
$269$	17.5198	+	10.1151i	0.0651293	+	0.0376024i	0.532211	−	0.846612i	$-0.321361\pi$
$269$	17.5198	+	10.1151i	0.0651293	+	0.0376024i	−0.467082	+	0.884214i	$0.654695\pi$
$270$		0			0
$271$	200.845	+	347.873i	0.741124	+	1.28366i	0.951984	+	0.306148i	$0.0990404\pi$
$271$	200.845	+	347.873i	0.741124	+	1.28366i	−0.210860	+	0.977516i	$0.567626\pi$
$272$		0			0
$273$	−44.6340	−	73.9614i	−0.163495	−	0.270921i
$274$		0			0
$275$	−34.5410	+	14.8995i	−0.125604	+	0.0541801i
$276$		0			0
$277$	19.1583	−	328.935i	0.0691636	−	1.18749i	−0.767967	−	0.640489i	$-0.778732\pi$
$277$	19.1583	−	328.935i	0.0691636	−	1.18749i	0.837131	−	0.547003i	$-0.184231\pi$
$278$		0			0
$279$	−18.8020	+	72.9822i	−0.0673906	+	0.261585i
$280$		0			0
$281$	−2.06475	−	0.890644i	−0.00734785	−	0.00316955i	0.392403	−	0.919794i	$-0.371644\pi$
$281$	−2.06475	−	0.890644i	−0.00734785	−	0.00316955i	−0.399751	+	0.916624i	$0.630903\pi$
$282$		0			0
$283$	41.7414	−	9.89290i	0.147496	−	0.0349572i	−0.156204	−	0.987725i	$-0.549926\pi$
$283$	41.7414	−	9.89290i	0.147496	−	0.0349572i	0.303701	+	0.952768i	$0.401778\pi$
$284$		0			0
$285$	−27.4292	−	39.9945i	−0.0962430	−	0.140331i
$286$		0			0
$287$	−13.8668	+	38.0988i	−0.0483165	+	0.132749i
$288$		0			0
$289$	−242.374	+	88.2168i	−0.838663	+	0.305248i
$290$		0			0
$291$	152.924	−	80.5483i	0.525513	−	0.276798i
$292$		0			0
$293$	287.173	−	16.7259i	0.980112	−	0.0570850i	0.439399	−	0.898292i	$-0.355192\pi$
$293$	287.173	−	16.7259i	0.980112	−	0.0570850i	0.540713	+	0.841207i	$0.318154\pi$
$294$		0			0
$295$	−84.5500	+	89.6178i	−0.286610	+	0.303789i
$296$		0			0
$297$	−71.1551	−	25.9030i	−0.239579	−	0.0872154i
$298$		0			0
$299$	408.629	−	122.336i	1.36665	−	0.409149i
$300$		0			0
$301$	−68.6144	+	45.1284i	−0.227955	+	0.149928i
$302$		0			0
$303$	−274.085	+	87.8759i	−0.904569	+	0.290019i
$304$		0			0
$305$	−2.25051	−	0.396826i	−0.00737872	−	0.00130107i
$306$		0			0
$307$	76.3210	+	432.838i	0.248603	+	1.40990i	0.811975	+	0.583692i	$0.198392\pi$
$307$	76.3210	+	432.838i	0.248603	+	1.40990i	−0.563373	+	0.826203i	$0.690496\pi$
$308$		0			0
$309$	3.97572	−	14.2811i	0.0128664	−	0.0462173i
$310$		0			0
$311$	144.598	+	43.2899i	0.464946	+	0.139196i	0.510704	−	0.859757i	$-0.329385\pi$
$311$	144.598	+	43.2899i	0.464946	+	0.139196i	−0.0457573	+	0.998953i	$0.514570\pi$
$312$		0			0
$313$	−300.097	+	35.0763i	−0.958775	+	0.112065i	−0.581063	−	0.813858i	$-0.697363\pi$
$313$	−300.097	+	35.0763i	−0.958775	+	0.112065i	−0.377712	+	0.925923i	$0.623289\pi$
$314$		0			0
$315$	−1.59306	−	41.0940i	−0.00505733	−	0.130457i
$316$		0			0
$317$	−159.614	+	242.682i	−0.503516	+	0.765558i	−0.994402	−	0.105665i	$-0.966303\pi$
$317$	−159.614	+	242.682i	−0.503516	+	0.765558i	0.490886	+	0.871224i	$0.336673\pi$
$318$		0			0
$319$	−32.6201	+	43.8163i	−0.102257	+	0.137355i
$320$		0			0
$321$	30.6021	−	37.9392i	0.0953337	−	0.118191i
$322$		0			0
$323$		−	26.4718i		−	0.0819561i
$324$		0			0
$325$	−287.720			−0.885292
$326$		0			0
$327$	−274.092	+	105.818i	−0.838201	+	0.323603i
$328$		0			0
$329$	−18.0491	−	13.4370i	−0.0548603	−	0.0408420i
$330$		0			0
$331$	−22.9699	−	15.1076i	−0.0693956	−	0.0456422i	0.514337	−	0.857588i	$-0.328038\pi$
$331$	−22.9699	−	15.1076i	−0.0693956	−	0.0456422i	−0.583733	+	0.811946i	$0.698408\pi$
$332$		0			0
$333$	−260.566	−	201.970i	−0.782480	−	0.606516i
$334$		0			0
$335$	−13.4357	−	114.950i	−0.0401065	−	0.343133i
$336$		0			0
$337$	−0.144206	+	0.481683i	−0.000427912	+	0.00142933i	−0.958203	−	0.286088i	$-0.907645\pi$
$337$	−0.144206	+	0.481683i	−0.000427912	+	0.00142933i	0.957775	+	0.287518i	$0.0928301\pi$
$338$		0			0
$339$	−60.2855	−	234.061i	−0.177833	−	0.690446i
$340$		0			0
$341$	−23.1284	+	4.07816i	−0.0678252	+	0.0119594i
$342$		0			0
$343$	−22.4239	+	127.172i	−0.0653759	+	0.370765i
$344$		0			0
$345$	198.460	+	42.9930i	0.575245	+	0.124617i
$346$		0			0
$347$	62.1170	+	94.4443i	0.179011	+	0.272174i	0.913836	−	0.406084i	$-0.133106\pi$
$347$	62.1170	+	94.4443i	0.179011	+	0.272174i	−0.734824	+	0.678257i	$0.762735\pi$
$348$		0			0
$349$	13.2984	+	44.4199i	0.0381044	+	0.127278i	0.974926	−	0.222531i	$-0.0714318\pi$
$349$	13.2984	+	44.4199i	0.0381044	+	0.127278i	−0.936821	+	0.349809i	$0.886247\pi$
$350$		0			0
$351$	−421.253	−	397.478i	−1.20015	−	1.13241i
$352$		0			0
$353$	−17.3182	−	16.3388i	−0.0490599	−	0.0462857i	0.661321	−	0.750103i	$-0.269996\pi$
$353$	−17.3182	−	16.3388i	−0.0490599	−	0.0462857i	−0.710381	+	0.703817i	$0.751477\pi$
$354$		0			0
$355$	17.2675	+	296.472i	0.0486409	+	0.835131i
$356$		0			0
$357$	11.9697	−	18.9904i	0.0335286	−	0.0531945i
$358$		0			0
$359$	191.030	+	524.850i	0.532117	+	1.46198i	0.856547	+	0.516069i	$0.172605\pi$
$359$	191.030	+	524.850i	0.532117	+	1.46198i	−0.324431	+	0.945909i	$0.605173\pi$
$360$		0			0
$361$	318.036	+	115.756i	0.880986	+	0.320653i
$362$		0			0
$363$	26.2947	+	338.383i	0.0724372	+	0.932185i
$364$		0			0
$365$	72.1406	+	304.385i	0.197646	+	0.833932i
$366$		0			0
$367$	−159.410	+	369.555i	−0.434361	+	1.00696i	0.550692	+	0.834708i	$0.314364\pi$
$367$	−159.410	+	369.555i	−0.434361	+	1.00696i	−0.985053	+	0.172253i	$0.944895\pi$
$368$		0			0
$369$	−21.0749	+	271.009i	−0.0571136	+	0.734442i
$370$		0			0
$371$	130.750	+	7.61533i	0.352426	+	0.0205265i
$372$		0			0
$373$	−257.462	−	596.864i	−0.690247	−	1.60017i	−0.795660	−	0.605743i	$-0.792876\pi$
$373$	−257.462	−	596.864i	−0.690247	−	1.60017i	0.105414	−	0.994428i	$-0.466383\pi$
$374$		0			0
$375$	−343.452	−	189.517i	−0.915871	−	0.505379i
$376$		0			0
$377$	−361.831	+	208.903i	−0.959763	+	0.554120i
$378$		0			0
$379$	−198.056	+	343.043i	−0.522575	+	0.905126i	0.477080	+	0.878860i	$0.341695\pi$
$379$	−198.056	+	343.043i	−0.522575	+	0.905126i	−0.999655	+	0.0262660i	$0.991638\pi$
$380$		0			0
$381$	17.6838	+	90.0517i	0.0464141	+	0.236356i
$382$		0			0
$383$	71.1395	−	608.637i	0.185743	−	1.58913i	−0.503105	−	0.864225i	$-0.667809\pi$
$383$	71.1395	−	608.637i	0.185743	−	1.58913i	0.688848	−	0.724906i	$-0.258117\pi$
$384$		0			0
$385$	11.4521	−	5.75147i	0.0297458	−	0.0149389i
$386$		0			0
$387$	−362.052	+	414.834i	−0.935535	+	1.07192i
$388$		0			0
$389$	−139.851	+	104.115i	−0.359514	+	0.267648i	−0.761727	−	0.647898i	$-0.775648\pi$
$389$	−139.851	+	104.115i	−0.359514	+	0.267648i	0.402213	+	0.915546i	$0.368241\pi$
$390$		0			0
$391$	76.0642	+	80.6233i	0.194538	+	0.206198i
$392$		0			0
$393$	−26.4357	+	271.729i	−0.0672665	+	0.691423i
$394$		0			0
$395$	70.5548	+	84.0839i	0.178620	+	0.212871i
$396$		0			0
$397$	118.408	+	99.3563i	0.298257	+	0.250268i	0.779619	−	0.626255i	$-0.215413\pi$
$397$	118.408	+	99.3563i	0.298257	+	0.250268i	−0.481361	+	0.876522i	$0.659857\pi$
$398$		0			0
$399$	−11.7157	−	15.1164i	−0.0293626	−	0.0378858i
$400$		0			0
$401$	76.5653	−	152.454i	0.190936	−	0.380185i	−0.777713	−	0.628620i	$-0.783620\pi$
$401$	76.5653	−	152.454i	0.190936	−	0.380185i	0.968648	+	0.248435i	$0.0799164\pi$
$402$		0			0
$403$	−174.786	−	41.4251i	−0.433712	−	0.102792i
$404$		0			0
$405$	−84.1650	−	262.562i	−0.207815	−	0.648301i
$406$		0			0
$407$	23.6919	−	99.9639i	0.0582110	−	0.245612i
$408$		0			0
$409$	151.309	+	75.9904i	0.369949	+	0.185795i	0.624054	−	0.781381i	$-0.285485\pi$
$409$	151.309	+	75.9904i	0.369949	+	0.185795i	−0.254105	+	0.967177i	$0.581781\pi$
$410$		0			0
$411$	−12.3662	−	90.5496i	−0.0300881	−	0.220315i
$412$		0			0
$413$	−31.2315	+	37.2203i	−0.0756211	+	0.0901217i
$414$		0			0
$415$	136.905	−	114.877i	0.329891	−	0.276811i
$416$		0			0
$417$	170.398	+	374.886i	0.408628	+	0.899007i
$418$		0			0
$419$	−460.866	+	434.805i	−1.09992	+	1.03772i	−0.100836	+	0.994903i	$0.532152\pi$
$419$	−460.866	+	434.805i	−1.09992	+	1.03772i	−0.999083	+	0.0428165i	$0.986367\pi$
$420$		0			0
$421$	−111.277	−	149.470i	−0.264315	−	0.355036i	0.650076	−	0.759869i	$-0.274737\pi$
$421$	−111.277	−	149.470i	−0.264315	−	0.355036i	−0.914391	+	0.404833i	$0.867330\pi$
$422$		0			0
$423$	−140.735	−	54.3426i	−0.332707	−	0.128470i
$424$		0			0
$425$	−33.5550	−	66.8134i	−0.0789528	−	0.157208i
$426$		0			0
$427$	−0.895101	−	0.104622i	−0.00209625	−	0.000245017i
$428$		0			0
$429$	58.4312	−	170.761i	0.136203	−	0.398044i
$430$		0			0
$431$	−414.846	−	239.512i	−0.962520	−	0.555711i	−0.0655726	−	0.997848i	$-0.520887\pi$
$431$	−414.846	−	239.512i	−0.962520	−	0.555711i	−0.896948	+	0.442136i	$0.854221\pi$
$432$		0			0
$433$	408.999	+	708.407i	0.944571	+	1.63604i	0.756608	+	0.653868i	$0.226855\pi$
$433$	408.999	+	708.407i	0.944571	+	1.63604i	0.187962	+	0.982176i	$0.439812\pi$
$434$		0			0
$435$	−198.864	+	3.85315i	−0.457158	+	0.00885783i
$436$		0			0
$437$	86.7105	−	37.4033i	0.198422	−	0.0855910i
$438$		0			0
$439$	3.17667	−	54.5413i	0.00723614	−	0.124240i	−0.992756	−	0.120152i	$-0.961662\pi$
$439$	3.17667	−	54.5413i	0.00723614	−	0.124240i	0.999992	−	0.00408775i	$-0.00130117\pi$
$440$		0			0
$441$	41.1074	+	422.788i	0.0932140	+	0.958704i
$442$		0			0
$443$	−77.9496	−	33.6242i	−0.175959	−	0.0759011i	0.306278	−	0.951942i	$-0.400916\pi$
$443$	−77.9496	−	33.6242i	−0.175959	−	0.0759011i	−0.482237	+	0.876041i	$0.660175\pi$
$444$		0			0
$445$	390.167	−	92.4712i	0.876779	−	0.207800i
$446$		0			0
$447$	9.54767	−	19.9663i	0.0213594	−	0.0446673i
$448$		0			0
$449$	281.924	−	774.580i	0.627893	−	1.72512i	−0.0588949	−	0.998264i	$-0.518758\pi$
$449$	281.924	−	774.580i	0.627893	−	1.72512i	0.686788	−	0.726858i	$-0.259020\pi$
$450$		0			0
$451$	−79.5979	+	28.9713i	−0.176492	+	0.0642379i
$452$		0			0
$453$	11.9164	−	306.936i	0.0263055	−	0.677563i
$454$		0			0
$455$	97.8524	−	5.69925i	0.215060	−	0.0125258i
$456$		0			0
$457$	85.6511	−	90.7849i	0.187420	−	0.198654i	−0.626850	−	0.779140i	$-0.715656\pi$
$457$	85.6511	−	90.7849i	0.187420	−	0.198654i	0.814270	+	0.580486i	$0.197137\pi$
$458$		0			0
$459$	43.1729	−	144.177i	0.0940586	−	0.314112i
$460$		0			0
$461$	478.686	−	143.309i	1.03837	−	0.310866i	0.278150	−	0.960538i	$-0.410279\pi$
$461$	478.686	−	143.309i	1.03837	−	0.310866i	0.760215	+	0.649671i	$0.225094\pi$
$462$		0			0
$463$	−550.479	+	362.056i	−1.18894	+	0.781978i	−0.980589	−	0.196076i	$-0.937180\pi$
$463$	−550.479	+	362.056i	−1.18894	+	0.781978i	−0.208351	+	0.978054i	$0.566810\pi$
$464$		0			0
$465$	−63.3256	−	57.4672i	−0.136184	−	0.123585i
$466$		0			0
$467$	590.932	+	104.197i	1.26538	+	0.223121i	0.765761	−	0.643125i	$-0.222363\pi$
$467$	590.932	+	104.197i	1.26538	+	0.223121i	0.499618	+	0.866246i	$0.333474\pi$
$468$		0			0
$469$	−7.92525	−	44.9463i	−0.0168982	−	0.0958344i
$470$		0			0
$471$	420.697	+	428.952i	0.893200	+	0.910727i
$472$		0			0
$473$	−164.371	−	49.2095i	−0.347508	−	0.104037i
$474$		0			0
$475$	−63.2676	+	7.39493i	−0.133195	+	0.0155683i
$476$		0			0
$477$	858.205	−	185.865i	1.79917	−	0.389653i
$478$		0			0
$479$	−50.5194	+	76.8111i	−0.105469	+	0.160357i	−0.884366	−	0.466794i	$-0.845409\pi$
$479$	−50.5194	+	76.8111i	−0.105469	+	0.160357i	0.778897	+	0.627151i	$0.215779\pi$
$480$		0			0
$481$	469.224	−	630.277i	0.975517	−	1.31035i
$482$		0			0
$483$	79.1172	+	12.3753i	0.163804	+	0.0256216i
$484$		0			0
$485$			196.115i			0.404361i
$486$		0			0
$487$	−779.390			−1.60039			−0.800196	−	0.599739i	$-0.795271\pi$
$487$	−779.390			−1.60039			−0.800196	+	0.599739i	$0.795271\pi$
$488$		0			0
$489$	−2.92837	+	18.7216i	−0.00598850	+	0.0382855i
$490$		0			0
$491$	178.490	+	132.881i	0.363524	+	0.270633i	0.763387	−	0.645941i	$-0.223535\pi$
$491$	178.490	+	132.881i	0.363524	+	0.270633i	−0.399863	+	0.916575i	$0.630942\pi$
$492$		0			0
$493$	−90.7088	−	59.6601i	−0.183994	−	0.121015i
$494$		0			0
$495$	63.6298	−	57.7365i	0.128545	−	0.116639i
$496$		0			0
$497$	13.5961	+	116.322i	0.0273563	+	0.234048i
$498$		0			0
$499$	−139.850	+	467.131i	−0.280260	+	0.936134i	0.695727	+	0.718306i	$0.255082\pi$
$499$	−139.850	+	467.131i	−0.280260	+	0.936134i	−0.975987	+	0.217828i	$0.930103\pi$
$500$		0			0
$501$	268.502	−	263.335i	0.535932	−	0.525618i
$502$		0			0
$503$	−587.794	+	103.644i	−1.16858	+	0.206052i	−0.724072	−	0.689724i	$-0.757732\pi$
$503$	−587.794	+	103.644i	−1.16858	+	0.206052i	−0.444506	+	0.895776i	$0.646621\pi$
$504$		0			0
$505$	56.7110	−	321.624i	0.112299	−	0.636879i
$506$		0			0
$507$	586.959	−	646.796i	1.15771	−	1.27573i
$508$		0			0
$509$	107.851	+	163.980i	0.211889	+	0.322161i	0.925757	−	0.378119i	$-0.123429\pi$
$509$	107.851	+	163.980i	0.211889	+	0.322161i	−0.713868	+	0.700280i	$0.753058\pi$
$510$		0			0
$511$	35.3805	+	118.179i	0.0692377	+	0.231270i
$512$		0			0
$513$	−102.847	−	76.5756i	−0.200481	−	0.149270i
$514$		0			0
$515$	12.2347	+	11.5429i	0.0237568	+	0.0224133i
$516$		0			0
$517$	−2.73347	−	46.9319i	−0.00528718	−	0.0907774i
$518$		0			0
$519$	16.9547	+	0.658245i	0.0326681	+	0.00126830i
$520$		0			0
$521$	195.289	+	536.553i	0.374836	+	1.02985i	0.973467	+	0.228828i	$0.0734893\pi$
$521$	195.289	+	536.553i	0.374836	+	1.02985i	−0.598631	+	0.801025i	$0.704289\pi$
$522$		0			0
$523$	169.881	+	61.8316i	0.324820	+	0.118225i	0.499283	−	0.866439i	$-0.333597\pi$
$523$	169.881	+	61.8316i	0.324820	+	0.118225i	−0.174463	+	0.984664i	$0.555819\pi$
$524$		0			0
$525$	−48.7309	−	23.3026i	−0.0928207	−	0.0443859i
$526$		0			0
$527$	−10.7646	−	45.4194i	−0.0204262	−	0.0861849i
$528$		0			0
$529$	52.9128	−	122.666i	0.100024	−	0.231882i
$530$		0			0
$531$	−134.813	+	296.551i	−0.253885	+	0.558477i
$532$		0			0
$533$	−646.786	−	37.6710i	−1.21348	−	0.0706773i
$534$		0			0
$535$	21.9058	+	50.7834i	0.0409454	+	0.0949221i
$536$		0			0
$537$	13.2799	+	685.383i	0.0247298	+	1.27632i
$538$		0			0
$539$	−114.636	+	66.1850i	−0.212682	+	0.122792i
$540$		0			0
$541$	27.4106	−	47.4765i	0.0506665	−	0.0877570i	−0.839580	−	0.543236i	$-0.817199\pi$
$541$	27.4106	−	47.4765i	0.0506665	−	0.0877570i	0.890246	+	0.455479i	$0.150532\pi$
$542$		0			0
$543$	−478.146	−	163.613i	−0.880564	−	0.301312i
$544$		0			0
$545$	38.7022	−	331.119i	0.0710133	−	0.607557i
$546$		0			0
$547$	800.139	−	401.845i	1.46278	−	0.734634i	0.473515	−	0.880786i	$-0.342985\pi$
$547$	800.139	−	401.845i	1.46278	−	0.734634i	0.989262	+	0.146152i	$0.0466888\pi$
$548$		0			0
$549$	−5.96954	+	0.933385i	−0.0108735	+	0.00170015i
$550$		0			0
$551$	−74.1949	+	55.2361i	−0.134655	+	0.100247i
$552$		0			0
$553$	29.7047	+	31.4851i	0.0537155	+	0.0569351i
$554$		0			0
$555$	340.542	−	154.788i	0.613589	−	0.278896i
$556$		0			0
$557$	−119.963	−	142.967i	−0.215374	−	0.256673i	0.647531	−	0.762039i	$-0.275802\pi$
$557$	−119.963	−	142.967i	−0.215374	−	0.256673i	−0.862905	+	0.505367i	$0.831357\pi$
$558$		0			0
$559$	−1005.31	−	843.553i	−1.79840	−	1.50904i
$560$		0			0
$561$	46.4680	−	6.34606i	0.0828307	−	0.0113121i
$562$		0			0
$563$	313.727	−	624.681i	0.557241	−	1.10956i	−0.421951	−	0.906619i	$-0.638654\pi$
$563$	313.727	−	624.681i	0.557241	−	1.10956i	0.979191	−	0.202939i	$-0.0650493\pi$
$564$		0			0
$565$	266.855	+	63.2457i	0.472309	+	0.111939i
$566$		0			0
$567$	−39.1553	−	101.438i	−0.0690571	−	0.178903i
$568$		0			0
$569$	32.8207	−	138.482i	0.0576814	−	0.243377i	−0.936565	−	0.350494i	$-0.886014\pi$
$569$	32.8207	−	138.482i	0.0576814	−	0.243377i	0.994246	+	0.107117i	$0.0341619\pi$
$570$		0			0
$571$	−555.691	−	279.078i	−0.973189	−	0.488754i	−0.110163	−	0.993914i	$-0.535137\pi$
$571$	−555.691	−	279.078i	−0.973189	−	0.488754i	−0.863026	+	0.505160i	$0.831434\pi$
$572$		0			0
$573$	−891.293	+	690.777i	−1.55549	+	1.20554i
$574$		0			0
$575$	171.441	−	204.316i	0.298159	−	0.355332i
$576$		0			0
$577$	842.690	−	707.100i	1.46047	−	1.22548i	0.535999	−	0.844219i	$-0.319935\pi$
$577$	842.690	−	707.100i	1.46047	−	1.22548i	0.924468	−	0.381259i	$-0.124509\pi$
$578$		0			0
$579$	621.904	+	60.5032i	1.07410	+	0.104496i
$580$		0			0
$581$	51.2638	−	48.3649i	0.0882337	−	0.0832442i
$582$		0			0
$583$	163.402	+	219.487i	0.280278	+	0.376479i
$584$		0			0
$585$	621.783	−	212.723i	1.06288	−	0.363629i
$586$		0			0
$587$	115.940	+	230.856i	0.197513	+	0.393281i	0.970486	−	0.241158i	$-0.0775274\pi$
$587$	115.940	+	230.856i	0.197513	+	0.393281i	−0.772973	+	0.634439i	$0.781231\pi$
$588$		0			0
$589$	−39.4990	−	4.61677i	−0.0670611	−	0.00783831i
$590$		0			0
$591$	661.002	−	129.803i	1.11845	−	0.219633i
$592$		0			0
$593$	−968.521	−	559.176i	−1.63326	−	0.942961i	−0.983080	−	0.183178i	$-0.941361\pi$
$593$	−968.521	−	559.176i	−1.63326	−	0.942961i	−0.650177	−	0.759783i	$-0.725305\pi$
$594$		0			0
$595$	12.7354	+	22.0583i	0.0214040	+	0.0370728i
$596$		0			0
$597$	105.591	−	191.357i	0.176869	−	0.320530i
$598$		0			0
$599$	−894.950	+	386.044i	−1.49407	+	0.644480i	−0.977342	−	0.211667i	$-0.932111\pi$
$599$	−894.950	+	386.044i	−1.49407	+	0.644480i	−0.516731	+	0.856148i	$0.672851\pi$
$600$		0			0
$601$	29.7319	−	510.476i	0.0494706	−	0.849378i	−0.878735	−	0.477310i	$-0.841612\pi$
$601$	29.7319	−	510.476i	0.0494706	−	0.849378i	0.928206	−	0.372068i	$-0.121351\pi$
$602$		0			0
$603$	−131.990	−	276.061i	−0.218889	−	0.457812i
$604$		0			0
$605$	−353.611	−	152.533i	−0.584481	−	0.252121i
$606$		0			0
$607$	110.564	−	26.2041i	0.182148	−	0.0431699i	−0.138529	−	0.990358i	$-0.544238\pi$
$607$	110.564	−	26.2041i	0.182148	−	0.0431699i	0.320678	+	0.947188i	$0.396089\pi$
$608$		0			0
$609$	−78.2022	+	6.07685i	−0.128411	+	0.00997840i
$610$		0			0
$611$	122.980	−	337.885i	0.201277	−	0.553004i
$612$		0			0
$613$	449.826	−	163.723i	0.733810	−	0.267085i	0.0520333	−	0.998645i	$-0.483430\pi$
$613$	449.826	−	163.723i	0.733810	−	0.267085i	0.681777	+	0.731560i	$0.261208\pi$
$614$		0			0
$615$	−260.925	−	164.462i	−0.424269	−	0.267418i
$616$		0			0
$617$	−382.002	+	22.2491i	−0.619128	+	0.0360601i	−0.364843	−	0.931069i	$-0.618877\pi$
$617$	−382.002	+	22.2491i	−0.619128	+	0.0360601i	−0.254285	+	0.967129i	$0.581840\pi$
$618$		0			0
$619$	650.364	−	689.346i	1.05067	−	1.11364i	0.0573371	−	0.998355i	$-0.481739\pi$
$619$	650.364	−	689.346i	1.05067	−	1.11364i	0.993332	−	0.115289i	$-0.0367795\pi$
$620$		0			0
$621$	533.265	−	62.2988i	0.858720	−	0.100320i
$622$		0			0
$623$	151.484	−	45.3514i	0.243153	−	0.0727951i
$624$		0			0
$625$	91.7104	−	60.3189i	0.146737	−	0.0965102i
$626$		0			0
$627$	8.45975	−	39.0509i	0.0134924	−	0.0622822i
$628$		0			0
$629$	201.084	+	35.4564i	0.319688	+	0.0563696i
$630$		0			0
$631$	−147.927	−	838.935i	−0.234432	−	1.32953i	−0.843806	−	0.536649i	$-0.819690\pi$
$631$	−147.927	−	838.935i	−0.234432	−	1.32953i	0.609373	−	0.792883i	$-0.291421\pi$
$632$		0			0
$633$	−592.649	+	152.644i	−0.936255	+	0.241145i
$634$		0			0
$635$	−99.7548	−	29.8646i	−0.157094	−	0.0470309i
$636$		0			0
$637$	−1005.59	+	117.537i	−1.57864	+	0.184517i
$638$		0			0
$639$	296.931	+	726.880i	0.464681	+	1.13753i
$640$		0			0
$641$	−426.418	+	648.336i	−0.665238	+	1.01145i	0.332426	+	0.943129i	$0.392133\pi$
$641$	−426.418	+	648.336i	−0.665238	+	1.01145i	−0.997664	+	0.0683157i	$0.978237\pi$
$642$		0			0
$643$	404.817	−	543.763i	0.629575	−	0.845666i	−0.366838	−	0.930285i	$-0.619560\pi$
$643$	404.817	−	543.763i	0.629575	−	0.845666i	0.996413	+	0.0846188i	$0.0269672\pi$
$644$		0			0
$645$	−225.010	−	582.825i	−0.348853	−	0.903604i
$646$		0			0
$647$			470.864i			0.727765i	0.931445	+	0.363883i	$0.118549\pi$
$647$			470.864i			0.727765i	−0.931445	+	0.363883i	$0.881451\pi$
$648$		0			0
$649$	−101.512			−0.156412
$650$		0			0
$651$	−26.2483	−	21.1722i	−0.0403200	−	0.0325225i
$652$		0			0
$653$	−359.566	−	267.687i	−0.550637	−	0.409934i	0.285562	−	0.958360i	$-0.407820\pi$
$653$	−359.566	−	267.687i	−0.550637	−	0.409934i	−0.836199	+	0.548426i	$0.815227\pi$
$654$		0			0
$655$	−258.814	−	170.224i	−0.395135	−	0.259885i
$656$		0			0
$657$	440.975	+	699.714i	0.671195	+	1.06501i
$658$		0			0
$659$	−92.8169	−	794.099i	−0.140845	−	1.20501i	−0.860051	−	0.510209i	$-0.829568\pi$
$659$	−92.8169	−	794.099i	−0.140845	−	1.20501i	0.719206	−	0.694797i	$-0.244506\pi$
$660$		0			0
$661$	50.9942	−	170.332i	0.0771470	−	0.257689i	−0.910712	−	0.413042i	$-0.864466\pi$
$661$	50.9942	−	170.332i	0.0771470	−	0.257689i	0.987859	+	0.155353i	$0.0496515\pi$
$662$		0			0
$663$	345.571	+	96.2035i	0.521224	+	0.145103i
$664$		0			0
$665$	21.3706	−	3.76821i	0.0321362	−	0.00566649i
$666$		0			0
$667$	67.2547	−	381.421i	0.100832	−	0.571845i
$668$		0			0
$669$	−176.305	−	549.893i	−0.263534	−	0.821963i
$670$		0			0
$671$	−1.03463	−	1.57307i	−0.00154192	−	0.00234437i
$672$		0			0
$673$	42.0757	+	140.542i	0.0625195	+	0.208830i	0.983542	−	0.180680i	$-0.0578297\pi$
$673$	42.0757	+	140.542i	0.0625195	+	0.208830i	−0.921022	+	0.389509i	$0.872645\pi$
$674$		0			0
$675$	−356.644	−	62.9071i	−0.528362	−	0.0931957i
$676$		0			0
$677$	667.218	+	629.488i	0.985551	+	0.929820i	0.997539	−	0.0701086i	$-0.0223346\pi$
$677$	667.218	+	629.488i	0.985551	+	0.929820i	−0.0119883	+	0.999928i	$0.503816\pi$
$678$		0			0
$679$	4.49687	+	77.2083i	0.00662279	+	0.113709i
$680$		0			0
$681$	480.571	+	912.384i	0.705685	+	1.33977i
$682$		0			0
$683$	15.7714	+	43.3315i	0.0230913	+	0.0634430i	0.950703	−	0.310104i	$-0.100364\pi$
$683$	15.7714	+	43.3315i	0.0230913	+	0.0634430i	−0.927611	+	0.373547i	$0.878142\pi$
$684$		0			0
$685$	97.4429	+	35.4663i	0.142252	+	0.0517756i
$686$		0			0
$687$	−739.162	+	506.937i	−1.07593	+	0.737899i
$688$		0			0
$689$	482.655	+	2036.48i	0.700515	+	2.95571i
$690$		0			0
$691$	−326.588	+	757.115i	−0.472631	+	1.09568i	0.500564	+	0.865699i	$0.333126\pi$
$691$	−326.588	+	757.115i	−0.472631	+	1.09568i	−0.973195	+	0.229981i	$0.926133\pi$
$692$		0			0
$693$	23.7265	−	24.1893i	0.0342373	−	0.0349051i
$694$		0			0
$695$	−466.456	−	27.1680i	−0.671160	−	0.0390906i
$696$		0			0
$697$	−66.6827	−	154.588i	−0.0956710	−	0.221790i
$698$		0			0
$699$	1025.69	−	618.982i	1.46737	−	0.885525i
$700$		0			0
$701$	294.380	−	169.960i	0.419942	−	0.242454i	−0.275110	−	0.961413i	$-0.588714\pi$
$701$	294.380	−	169.960i	0.419942	−	0.242454i	0.695053	+	0.718959i	$0.255381\pi$
$702$		0			0
$703$	86.9798	−	150.653i	0.123727	−	0.214301i
$704$		0			0
$705$	128.973	−	112.550i	0.182941	−	0.159646i
$706$		0			0
$707$	14.9517	−	127.920i	0.0211481	−	0.180934i
$708$		0			0
$709$	−428.776	+	215.339i	−0.604762	+	0.303723i	−0.724706	−	0.689058i	$-0.758025\pi$
$709$	−428.776	+	215.339i	−0.604762	+	0.303723i	0.119945	+	0.992781i	$0.461728\pi$
$710$		0			0
$711$	248.464	+	149.962i	0.349457	+	0.210917i
$712$		0			0
$713$	133.565	−	99.4355i	0.187328	−	0.139461i
$714$		0			0
$715$	140.532	+	148.955i	0.196548	+	0.208329i
$716$		0			0
$717$	1082.82	+	773.983i	1.51021	+	1.07947i
$718$		0			0
$719$	803.447	+	957.511i	1.11745	+	1.33173i	0.937474	+	0.348054i	$0.113158\pi$
$719$	803.447	+	957.511i	1.11745	+	1.33173i	0.179976	+	0.983671i	$0.442398\pi$
$720$		0			0
$721$	5.08136	+	4.26376i	0.00704765	+	0.00591368i
$722$		0			0
$723$	−286.242	+	700.600i	−0.395909	+	0.969018i
$724$		0			0
$725$	−117.248	+	233.460i	−0.161722	+	0.322014i
$726$		0			0
$727$	1207.93	+	286.284i	1.66152	+	0.393788i	0.950829	−	0.309715i	$-0.100234\pi$
$727$	1207.93	+	286.284i	1.66152	+	0.393788i	0.710692	+	0.703503i	$0.248382\pi$
$728$		0			0
$729$	−435.262	−	584.798i	−0.597067	−	0.802192i
$730$		0			0
$731$	78.6446	−	331.828i	0.107585	−	0.453937i
$732$		0			0
$733$	−560.163	−	281.324i	−0.764206	−	0.383799i	0.0236007	−	0.999721i	$-0.492487\pi$
$733$	−560.163	−	281.324i	−0.764206	−	0.383799i	−0.787806	+	0.615923i	$0.788783\pi$
$734$		0			0
$735$	−446.179	−	182.294i	−0.607047	−	0.248019i
$736$		0			0
$737$	61.2915	−	73.0444i	0.0831635	−	0.0991104i
$738$		0			0
$739$	559.999	−	469.895i	0.757780	−	0.635853i	−0.179768	−	0.983709i	$-0.557535\pi$
$739$	559.999	−	469.895i	0.757780	−	0.635853i	0.937548	+	0.347856i	$0.113090\pi$
$740$		0			0
$741$	177.716	−	248.628i	0.239832	−	0.335530i
$742$		0			0
$743$	−625.438	+	590.071i	−0.841774	+	0.794173i	−0.980574	−	0.196147i	$-0.937157\pi$
$743$	−625.438	+	590.071i	−0.841774	+	0.794173i	0.138800	+	0.990320i	$0.455675\pi$
$744$		0			0
$745$	14.9958	+	20.1428i	0.0201285	+	0.0270373i
$746$		0			0
$747$	244.166	−	404.547i	0.326862	−	0.541562i
$748$		0			0
$749$	9.78853	+	19.4906i	0.0130688	+	0.0260221i
$750$		0			0
$751$	600.914	+	70.2368i	0.800152	+	0.0935243i	0.506334	−	0.862337i	$-0.331000\pi$
$751$	600.914	+	70.2368i	0.800152	+	0.0935243i	0.293817	+	0.955862i	$0.405074\pi$
$752$		0			0
$753$	−143.873	−	164.867i	−0.191067	−	0.218947i
$754$		0			0
$755$	301.836	+	174.265i	0.399782	+	0.230814i
$756$		0			0
$757$	−307.576	−	532.737i	−0.406309	−	0.703748i	0.588164	−	0.808742i	$-0.299851\pi$
$757$	−307.576	−	532.737i	−0.406309	−	0.703748i	−0.994473	+	0.104994i	$0.966518\pi$
$758$		0			0
$759$	86.4439	+	143.243i	0.113892	+	0.188726i
$760$		0			0
$761$	−1221.70	+	526.991i	−1.60539	+	0.692498i	−0.995025	−	0.0996221i	$-0.968237\pi$
$761$	−1221.70	+	526.991i	−1.60539	+	0.692498i	−0.610365	+	0.792120i	$0.708977\pi$
$762$		0			0
$763$	7.64417	−	131.245i	0.0100186	−	0.172012i
$764$		0			0
$765$	121.912	+	119.580i	0.159363	+	0.156314i
$766$		0			0
$767$	−712.920	−	307.524i	−0.929491	−	0.400943i
$768$		0			0
$769$	−908.671	+	215.359i	−1.18163	+	0.280051i	−0.774053	−	0.633121i	$-0.781773\pi$
$769$	−908.671	+	215.359i	−1.18163	+	0.280051i	−0.407574	+	0.913172i	$0.633625\pi$
$770$		0			0
$771$	816.288	+	1190.23i	1.05874	+	1.54374i
$772$		0			0
$773$	389.447	−	1070.00i	0.503813	−	1.38421i	−0.383712	−	0.923453i	$-0.625354\pi$
$773$	389.447	−	1070.00i	0.503813	−	1.38421i	0.887524	−	0.460761i	$-0.152423\pi$
$774$		0			0
$775$	−105.545	+	38.4153i	−0.136187	+	0.0495682i
$776$		0			0
$777$	130.519	−	68.7467i	0.167978	−	0.0884772i
$778$		0			0
$779$	−143.192	+	8.33998i	−0.183815	+	0.0107060i
$780$		0			0
$781$	−167.909	+	177.973i	−0.214993	+	0.227879i
$782$		0			0
$783$	−494.183	+	179.836i	−0.631141	+	0.229676i
$784$		0			0
$785$	−653.087	+	195.522i	−0.831958	+	0.249072i
$786$		0			0
$787$	−384.701	+	253.022i	−0.488819	+	0.321501i	−0.769880	−	0.638188i	$-0.779684\pi$
$787$	−384.701	+	253.022i	−0.488819	+	0.321501i	0.281061	+	0.959690i	$0.409314\pi$
$788$		0			0
$789$	−938.491	+	300.895i	−1.18947	+	0.381363i
$790$		0			0
$791$	106.508	+	18.7802i	0.134650	+	0.0237424i
$792$		0			0
$793$	−2.50068	−	14.1821i	−0.00315345	−	0.0178841i
$794$		0			0
$795$	−267.211	+	959.845i	−0.336114	+	1.20735i
$796$		0			0
$797$	−271.816	−	81.3765i	−0.341049	−	0.102103i	0.111698	−	0.993742i	$-0.464371\pi$
$797$	−271.816	−	81.3765i	−0.341049	−	0.102103i	−0.452748	+	0.891639i	$0.649556\pi$
$798$		0			0
$799$	92.8051	−	10.8474i	0.116152	−	0.0135762i
$800$		0			0
$801$	896.907	−	565.250i	1.11973	−	0.705681i
$802$		0			0
$803$	−141.627	+	215.333i	−0.176372	+	0.268160i
$804$		0			0
$805$	−54.2593	+	72.8829i	−0.0674029	+	0.0905378i
$806$		0			0
$807$	−38.1030	+	47.2385i	−0.0472156	+	0.0585359i
$808$		0			0
$809$		−	202.408i		−	0.250195i	−0.992144	−	0.125097i	$-0.960076\pi$
$809$		−	202.408i		−	0.250195i	0.992144	−	0.125097i	$-0.0399244\pi$
$810$		0			0
$811$	803.261			0.990458			0.495229	−	0.868763i	$-0.335084\pi$
$811$	803.261			0.990458			0.495229	+	0.868763i	$0.335084\pi$
$812$		0			0
$813$	−1124.20	+	434.017i	−1.38278	+	0.533846i
$814$		0			0
$815$	−17.2464	−	12.8395i	−0.0211612	−	0.0157539i
$816$		0			0
$817$	−242.741	−	159.653i	−0.297113	−	0.195414i
$818$		0			0
$819$	239.912	−	98.0040i	0.292932	−	0.119663i
$820$		0			0
$821$	−109.745	−	938.930i	−0.133673	−	1.14364i	−0.878959	−	0.476897i	$-0.841761\pi$
$821$	−109.745	−	938.930i	−0.133673	−	1.14364i	0.745286	−	0.666744i	$-0.232313\pi$
$822$		0			0
$823$	−296.748	+	991.208i	−0.360569	+	1.20438i	0.564772	+	0.825247i	$0.308964\pi$
$823$	−296.748	+	991.208i	−0.360569	+	1.20438i	−0.925341	+	0.379137i	$0.876221\pi$
$824$		0			0
$825$	−28.1480	−	109.286i	−0.0341188	−	0.132468i
$826$		0			0
$827$	−147.681	+	26.0402i	−0.178575	+	0.0314876i	−0.262220	−	0.965008i	$-0.584455\pi$
$827$	−147.681	+	26.0402i	−0.178575	+	0.0314876i	0.0836456	+	0.996496i	$0.473344\pi$
$828$		0			0
$829$	−161.348	+	915.052i	−0.194630	+	1.10380i	0.718315	+	0.695718i	$0.244914\pi$
$829$	−161.348	+	915.052i	−0.194630	+	1.10380i	−0.912945	+	0.408083i	$0.866197\pi$
$830$		0			0
$831$	966.070	+	209.283i	1.16254	+	0.251845i
$832$		0			0
$833$	−144.570	−	219.808i	−0.173554	−	0.263875i
$834$		0			0
$835$	122.386	+	408.799i	0.146570	+	0.489579i
$836$		0			0
$837$	−207.600	−	89.5639i	−0.248028	−	0.107006i
$838$		0			0
$839$	−84.5322	−	79.7521i	−0.100754	−	0.0950561i	0.634217	−	0.773155i	$-0.281323\pi$
$839$	−84.5322	−	79.7521i	−0.100754	−	0.0950561i	−0.734971	+	0.678099i	$0.762804\pi$
$840$		0			0
$841$	−26.8416	−	460.853i	−0.0319163	−	0.547982i
$842$		0			0
$843$	3.59708	−	5.70691i	0.00426700	−	0.00676976i
$844$		0			0
$845$	338.954	+	931.269i	0.401129	+	1.10209i
$846$		0			0
$847$	−142.710	−	51.9424i	−0.168489	−	0.0613251i
$848$		0			0
$849$	9.97029	+	128.306i	0.0117436	+	0.151127i
$850$		0			0
$851$	167.980	+	708.763i	0.197391	+	0.832859i
$852$		0			0
$853$	−362.038	+	839.298i	−0.424429	+	0.983937i	0.563084	+	0.826400i	$0.309615\pi$
$853$	−362.038	+	839.298i	−0.424429	+	0.983937i	−0.987513	+	0.157537i	$0.949645\pi$
$854$		0			0
$855$	131.259	−	62.7572i	0.153519	−	0.0734003i
$856$		0			0
$857$	−1466.68	−	85.4243i	−1.71141	−	0.0996783i	−0.825757	−	0.564026i	$-0.809252\pi$
$857$	−1466.68	−	85.4243i	−1.71141	−	0.0996783i	−0.885653	+	0.464348i	$0.846289\pi$
$858$		0			0
$859$	−231.419	−	536.490i	−0.269405	−	0.624552i	0.728781	−	0.684747i	$-0.240087\pi$
$859$	−231.419	−	536.490i	−0.269405	−	0.624552i	−0.998187	+	0.0601947i	$0.980828\pi$
$860$		0			0
$861$	−106.495	−	58.7639i	−0.123687	−	0.0682507i
$862$		0			0
$863$	87.1990	−	50.3444i	0.101042	−	0.0583364i	−0.448628	−	0.893719i	$-0.648087\pi$
$863$	87.1990	−	50.3444i	0.101042	−	0.0583364i	0.549669	+	0.835382i	$0.314754\pi$
$864$		0			0
$865$	−9.62616	+	16.6730i	−0.0111285	+	0.0192751i
$866$		0			0
$867$	−149.104	−	759.284i	−0.171976	−	0.875761i
$868$		0			0
$869$	−10.4989	+	89.8238i	−0.0120816	+	0.103365i
$870$		0			0
$871$	651.736	−	327.314i	0.748262	−	0.375791i
$872$		0			0
$873$	167.844	+	490.605i	0.192261	+	0.561975i
$874$		0			0
$875$	140.793	−	104.816i	0.160906	−	0.119790i
$876$		0			0
$877$	436.184	+	462.328i	0.497359	+	0.527170i	0.926614	−	0.376013i	$-0.122705\pi$
$877$	436.184	+	462.328i	0.497359	+	0.527170i	−0.429255	+	0.903183i	$0.641224\pi$
$878$		0			0
$879$	−83.5621	+	858.923i	−0.0950650	+	0.977160i
$880$		0			0
$881$	−407.845	−	486.051i	−0.462934	−	0.551704i	0.483187	−	0.875517i	$-0.339479\pi$
$881$	−407.845	−	486.051i	−0.462934	−	0.551704i	−0.946121	+	0.323814i	$0.895035\pi$
$882$		0			0
$883$	−1118.75	−	938.746i	−1.26699	−	1.06313i	−0.994901	−	0.100861i	$-0.967840\pi$
$883$	−1118.75	−	938.746i	−1.26699	−	1.06313i	−0.272091	−	0.962271i	$-0.587715\pi$
$884$		0			0
$885$	−226.425	−	292.151i	−0.255848	−	0.330114i
$886$		0			0
$887$	201.690	−	401.598i	0.227385	−	0.452760i	−0.750791	−	0.660540i	$-0.770327\pi$
$887$	201.690	−	401.598i	0.227385	−	0.452760i	0.978176	+	0.207780i	$0.0666237\pi$
$888$		0			0
$889$	−39.9572	−	9.47003i	−0.0449462	−	0.0106525i
$890$		0			0
$891$	109.764	−	198.892i	0.123192	−	0.223223i
$892$		0			0
$893$	18.3582	−	77.4595i	0.0205579	−	0.0867407i
$894$		0			0
$895$	−695.086	−	349.086i	−0.776633	−	0.390040i
$896$		0			0
$897$	173.152	+	1267.88i	0.193034	+	1.41346i
$898$		0			0
$899$	−104.840	+	124.943i	−0.116618	+	0.138980i
$900$		0			0
$901$	−416.616	+	349.583i	−0.462393	+	0.387994i
$902$		0			0
$903$	−101.948	−	224.292i	−0.112899	−	0.248386i
$904$		0			0
$905$	417.087	−	393.501i	0.460870	−	0.434808i
$906$		0			0
$907$	672.187	+	902.903i	0.741110	+	0.995483i	0.999566	+	0.0294602i	$0.00937884\pi$
$907$	672.187	+	902.903i	0.741110	+	0.995483i	−0.258456	+	0.966023i	$0.583214\pi$
$908$		0			0
$909$	−133.392	−	853.116i	−0.146745	−	0.938522i
$910$		0			0
$911$	−136.001	−	270.800i	−0.149288	−	0.297256i	0.806542	−	0.591176i	$-0.201336\pi$
$911$	−136.001	−	270.800i	−0.149288	−	0.297256i	−0.955830	+	0.293920i	$0.905040\pi$
$912$		0			0
$913$	146.250	+	17.0942i	0.160187	+	0.0187231i
$914$		0			0
$915$	2.21954	−	6.48645i	0.00242573	−	0.00708902i
$916$		0			0
$917$	−105.795	−	61.0810i	−0.115371	−	0.0666096i
$918$		0			0
$919$	401.905	+	696.119i	0.437328	+	0.757475i	0.997482	−	0.0709138i	$-0.0225915\pi$
$919$	401.905	+	696.119i	0.437328	+	0.757475i	−0.560154	+	0.828388i	$0.689258\pi$
$920$		0			0
$921$	−1318.30	+	25.5431i	−1.43138	+	0.0277341i
$922$		0			0
$923$	−1718.39	+	741.242i	−1.86175	+	0.803079i
$924$		0			0
$925$	28.5680	−	490.494i	0.0308844	−	0.530264i
$926$		0			0
$927$	40.4855	+	18.4048i	0.0436737	+	0.0198542i
$928$		0			0
$929$	26.6859	+	11.5112i	0.0287254	+	0.0123909i	0.410394	−	0.911908i	$-0.365391\pi$
$929$	26.6859	+	11.5112i	0.0287254	+	0.0123909i	−0.381669	+	0.924299i	$0.624650\pi$
$930$		0			0
$931$	−218.102	+	51.6912i	−0.234267	+	0.0555222i
$932$		0			0
$933$	−195.347	+	408.514i	−0.209375	+	0.437850i
$934$		0			0
$935$	−18.2005	+	50.0055i	−0.0194658	+	0.0534818i
$936$		0			0
$937$	−37.4184	+	13.6192i	−0.0399342	+	0.0145349i	−0.361910	−	0.932213i	$-0.617875\pi$
$937$	−37.4184	+	13.6192i	−0.0399342	+	0.0145349i	0.321976	+	0.946748i	$0.395653\pi$
$938$		0			0
$939$	35.1640	−	905.737i	0.0374484	−	0.964576i
$940$		0			0
$941$	1651.12	−	96.1667i	1.75464	−	0.102196i	0.849576	−	0.527467i	$-0.176858\pi$
$941$	1651.12	−	96.1667i	1.75464	−	0.102196i	0.905066	+	0.425271i	$0.139821\pi$
$942$		0			0
$943$	412.146	−	436.849i	0.437058	−	0.463254i
$944$		0			0
$945$	122.539	+	14.3299i	0.129671	+	0.0151639i
$946$		0			0
$947$	1428.67	−	427.715i	1.50863	−	0.451653i	0.577512	−	0.816382i	$-0.304024\pi$
$947$	1428.67	−	427.715i	1.50863	−	0.451653i	0.931114	+	0.364729i	$0.118838\pi$
$948$		0			0
$949$	−1646.99	+	1083.24i	−1.73550	+	1.14145i
$950$		0			0
$951$	−645.301	−	585.602i	−0.678550	−	0.615775i
$952$		0			0
$953$	518.962	+	91.5069i	0.544556	+	0.0960198i	0.439157	−	0.898410i	$-0.355277\pi$
$953$	518.962	+	91.5069i	0.544556	+	0.0960198i	0.105398	+	0.994430i	$0.466388\pi$
$954$		0			0
$955$	−222.181	−	1260.05i	−0.232650	−	1.31942i
$956$		0			0
$957$	−114.747	−	116.998i	−0.119903	−	0.122255i
$958$		0			0
$959$	39.1754	+	11.7284i	0.0408503	+	0.0122298i
$960$		0			0
$961$	884.854	−	103.425i	0.920764	−	0.107622i
$962$		0			0
$963$	98.2627	+	108.293i	0.102038	+	0.112453i
$964$		0			0
$965$	−389.591	+	592.344i	−0.403721	+	0.613828i
$966$		0			0
$967$	−608.402	+	817.226i	−0.629165	+	0.845115i	−0.996379	−	0.0850213i	$-0.972904\pi$
$967$	−608.402	+	817.226i	−0.629165	+	0.845115i	0.367214	+	0.930136i	$0.380312\pi$
$968$		0			0
$969$	78.4614	+	12.2727i	0.0809715	+	0.0126653i
$970$		0			0
$971$			164.945i			0.169871i	0.996386	+	0.0849356i	$0.0270685\pi$
$971$			164.945i			0.169871i	−0.996386	+	0.0849356i	$0.972932\pi$
$972$		0			0
$973$	−184.262			−0.189375
$974$		0			0
$975$	133.391	−	852.790i	0.136811	−	0.874657i
$976$		0			0
$977$	1010.45	+	752.250i	1.03423	+	0.769959i	0.973614	−	0.228202i	$-0.0732845\pi$
$977$	1010.45	+	752.250i	1.03423	+	0.769959i	0.0606209	+	0.998161i	$0.480692\pi$
$978$		0			0
$979$	276.018	+	181.540i	0.281938	+	0.185434i
$980$		0			0
$981$	−186.569	−	861.456i	−0.190182	−	0.878140i
$982$		0			0
$983$	−76.5258	−	654.720i	−0.0778492	−	0.666043i	−0.974670	−	0.223648i	$-0.928203\pi$
$983$	−76.5258	−	654.720i	−0.0778492	−	0.666043i	0.896821	−	0.442394i	$-0.145871\pi$
$984$		0			0
$985$	−219.214	+	732.225i	−0.222552	+	0.743376i
$986$		0			0
$987$	48.1946	−	47.2671i	0.0488294	−	0.0478897i
$988$		0			0
$989$	1198.05	−	211.248i	1.21137	−	0.213598i
$990$		0			0
$991$	303.879	−	1723.38i	0.306639	−	1.73903i	−0.309052	−	0.951045i	$-0.600012\pi$
$991$	303.879	−	1723.38i	0.306639	−	1.73903i	0.615690	−	0.787988i	$-0.288877\pi$
$992$		0			0
$993$	55.4274	−	61.0779i	0.0558181	−	0.0615085i
$994$		0			0
$995$	136.271	+	207.190i	0.136956	+	0.208231i
$996$		0			0
$997$	566.121	+	1890.98i	0.567824	+	1.89667i	0.419591	+	0.907713i	$0.362173\pi$
$997$	566.121	+	1890.98i	0.567824	+	1.89667i	0.148233	+	0.988952i	$0.452641\pi$
$998$		0			0
$999$	719.432	−	678.671i	0.720152	−	0.679350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.65.9	yes	324
81.5	odd	54	inner	324.3.o.a.5.9	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.9	✓	324	81.5	odd	54	inner
324.3.o.a.65.9	yes	324	1.1	even	1	trivial

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.o (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.463613 + 2.96396i) q^{3} +(-2.73041 - 2.03271i) q^{5} +(-1.12154 - 0.737649i) q^{7} +(-8.57013 - 2.74826i) q^{9} +O(q^{10})\)	\(q+(-0.463613 + 2.96396i) q^{3} +(-2.73041 - 2.03271i) q^{5} +(-1.12154 - 0.737649i) q^{7} +(-8.57013 - 2.74826i) q^{9} +(-0.325590 - 2.78560i) q^{11} +(6.15219 - 20.5497i) q^{13} +(7.29073 - 7.15043i) q^{15} +(5.48948 - 0.967944i) q^{17} +(0.824658 - 4.67687i) q^{19} +(2.70633 - 2.98222i) q^{21} +(10.9269 + 16.6136i) q^{23} +(-3.84688 - 12.8495i) q^{25} +(12.1190 - 24.1274i) q^{27} +(-14.1673 - 13.3662i) q^{29} +(-0.486900 - 8.35975i) q^{31} +(8.40736 + 0.326405i) q^{33} +(1.56284 + 4.29386i) q^{35} +(34.4216 + 12.5284i) q^{37} +(58.0564 + 27.7620i) q^{39} +(-6.96530 - 29.3889i) q^{41} +(24.2316 - 56.1752i) q^{43} +(17.8135 + 24.9245i) q^{45} +(16.7341 + 0.974651i) q^{47} +(-18.6942 - 43.3380i) q^{49} +(0.323952 + 16.7194i) q^{51} +(-84.4954 + 48.7834i) q^{53} +(-4.77333 + 8.26766i) q^{55} +(13.4797 + 4.61251i) q^{57} +(4.20200 - 35.9504i) q^{59} +(0.599932 - 0.301297i) q^{61} +(7.58450 + 9.40404i) q^{63} +(-58.5697 + 43.6035i) q^{65} +(23.3316 + 24.7300i) q^{67} +(-54.3079 + 24.6847i) q^{69} +(-56.0789 - 66.8323i) q^{71} +(-70.3977 - 59.0707i) q^{73} +(39.8688 - 5.44482i) q^{75} +(-1.68963 + 3.36434i) q^{77} +(-31.3766 - 7.43638i) q^{79} +(65.8941 + 47.1059i) q^{81} +(-12.1078 + 51.0870i) q^{83} +(-16.9561 - 8.51566i) q^{85} +(46.1849 - 35.7946i) q^{87} +(-75.7179 + 90.2371i) q^{89} +(-22.0584 + 18.5092i) q^{91} +(25.0037 + 2.43254i) q^{93} +(-11.7584 + 11.0935i) q^{95} +(-34.4044 - 46.2131i) q^{97} +(-4.86521 + 24.7678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 324 * q	\( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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