LMFDB - Embedded newform 324.3.o.a.5.9

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			5.9
Character	$\chi$	$=$	324.5
Dual form			324.3.o.a.65.9

$q$-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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{23}{54}\right)$

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	−0.834538	−	0.550950i	$-0.814265\pi$
$5$	−2.73041	+	2.03271i	−0.546081	+	0.406543i	0.288457	+	0.957493i	$0.406858\pi$
$6$		0			0
$7$	−1.12154	+	0.737649i	−0.160220	+	0.105378i	−0.627087	−	0.778949i	$-0.715753\pi$
$7$	−1.12154	+	0.737649i	−0.160220	+	0.105378i	0.466867	+	0.884328i	$0.345383\pi$
$8$		0			0
$9$	−8.57013	+	2.74826i	−0.952236	+	0.305362i
$10$		0			0
$11$	−0.325590	+	2.78560i	−0.0295991	+	0.253237i	0.970335	+	0.241764i	$0.0777260\pi$
$11$	−0.325590	+	2.78560i	−0.0295991	+	0.253237i	−0.999934	+	0.0114725i	$0.996348\pi$
$12$		0			0
$13$	6.15219	+	20.5497i	0.473245	+	1.58075i	0.777966	+	0.628307i	$0.216252\pi$
$13$	6.15219	+	20.5497i	0.473245	+	1.58075i	−0.304721	+	0.952442i	$0.598563\pi$
$14$		0			0
$15$	7.29073	+	7.15043i	0.486049	+	0.476695i
$16$		0			0
$17$	5.48948	+	0.967944i	0.322911	+	0.0569379i	0.332754	−	0.943014i	$-0.392022\pi$
$17$	5.48948	+	0.967944i	0.322911	+	0.0569379i	−0.00984318	+	0.999952i	$0.503133\pi$
$18$		0			0
$19$	0.824658	+	4.67687i	0.0434031	+	0.246151i	0.998788	−	0.0492113i	$-0.0156708\pi$
$19$	0.824658	+	4.67687i	0.0434031	+	0.246151i	−0.955385	+	0.295362i	$0.904560\pi$
$20$		0			0
$21$	2.70633	+	2.98222i	0.128873	+	0.142011i
$22$		0			0
$23$	10.9269	−	16.6136i	0.475084	−	0.722330i	−0.515850	−	0.856679i	$-0.672524\pi$
$23$	10.9269	−	16.6136i	0.475084	−	0.722330i	0.990934	+	0.134349i	$0.0428943\pi$
$24$		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	−0.890654	−	0.454682i	$-0.849753\pi$
$29$	−14.1673	+	13.3662i	−0.488528	+	0.460902i	0.402126	+	0.915584i	$0.368271\pi$
$30$		0			0
$31$	−0.486900	+	8.35975i	−0.0157064	+	0.269669i	0.981307	+	0.192447i	$0.0616423\pi$
$31$	−0.486900	+	8.35975i	−0.0157064	+	0.269669i	−0.997014	+	0.0772226i	$0.975395\pi$
$32$		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	0.167979	−	0.985791i	$-0.446276\pi$
$37$	34.4216	−	12.5284i	0.930313	−	0.338606i	0.762334	+	0.647184i	$0.224054\pi$
$38$		0			0
$39$	58.0564	−	27.7620i	1.48862	−	0.711845i
$40$		0			0
$41$	−6.96530	+	29.3889i	−0.169885	+	0.716803i	0.819693	+	0.572804i	$0.194144\pi$
$41$	−6.96530	+	29.3889i	−0.169885	+	0.716803i	−0.989578	+	0.143999i	$0.954004\pi$
$42$		0			0
$43$	24.2316	+	56.1752i	0.563526	+	1.30640i	0.927093	+	0.374832i	$0.122300\pi$
$43$	24.2316	+	56.1752i	0.563526	+	1.30640i	−0.363567	+	0.931568i	$0.618441\pi$
$44$		0			0
$45$	17.8135	−	24.9245i	0.395856	−	0.553877i
$46$		0			0
$47$	16.7341	−	0.974651i	0.356045	−	0.0207373i	0.120810	−	0.992676i	$-0.461451\pi$
$47$	16.7341	−	0.974651i	0.356045	−	0.0207373i	0.235235	+	0.971938i	$0.424414\pi$
$48$		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	−0.992566	−	0.121709i	$-0.961162\pi$
$53$	−84.4954	−	48.7834i	−1.59425	−	0.920442i	−0.601686	−	0.798733i	$-0.705504\pi$
$54$		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	0.980968	+	0.194168i	$0.0622007\pi$
$59$	4.20200	+	35.9504i	0.0712204	+	0.609329i	−0.909748	+	0.415161i	$0.863725\pi$
$60$		0			0
$61$	0.599932	+	0.301297i	0.00983495	+	0.00493930i	0.453710	−	0.891149i	$-0.350100\pi$
$61$	0.599932	+	0.301297i	0.00983495	+	0.00493930i	−0.443875	+	0.896089i	$0.646397\pi$
$62$		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	−0.529455	−	0.848338i	$-0.677604\pi$
$67$	23.3316	−	24.7300i	0.348233	−	0.369105i	0.877688	+	0.479233i	$0.159085\pi$
$68$		0			0
$69$	−54.3079	−	24.6847i	−0.787071	−	0.357749i
$70$		0			0
$71$	−56.0789	+	66.8323i	−0.789844	+	0.941299i	−0.999333	−	0.0365116i	$-0.988375\pi$
$71$	−56.0789	+	66.8323i	−0.789844	+	0.941299i	0.209489	+	0.977811i	$0.432820\pi$
$72$		0			0
$73$	−70.3977	+	59.0707i	−0.964352	+	0.809187i	−0.981656	−	0.190663i	$-0.938936\pi$
$73$	−70.3977	+	59.0707i	−0.964352	+	0.809187i	0.0173037	+	0.999850i	$0.494492\pi$
$74$		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	−0.424348	−	0.905499i	$-0.639497\pi$
$79$	−31.3766	+	7.43638i	−0.397172	+	0.0941314i	0.0271762	+	0.999631i	$0.491348\pi$
$80$		0			0
$81$	65.8941	−	47.1059i	0.813508	−	0.581554i
$82$		0			0
$83$	−12.1078	−	51.0870i	−0.145878	−	0.615506i	−0.996034	−	0.0889756i	$-0.971641\pi$
$83$	−12.1078	−	51.0870i	−0.145878	−	0.615506i	0.850156	−	0.526531i	$-0.176507\pi$
$84$		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	−0.999686	−	0.0250510i	$-0.992025\pi$
$89$	−75.7179	−	90.2371i	−0.850763	−	1.01390i	0.148923	−	0.988849i	$-0.452419\pi$
$90$		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	−0.943277	−	0.332006i	$-0.892275\pi$
$97$	−34.4044	+	46.2131i	−0.354685	+	0.476424i	0.588593	+	0.808430i	$0.299682\pi$
$98$		0			0
$99$	−4.86521	−	24.7678i	−0.0491436	−	0.250179i
$100$		0			0
$101$	43.0589	−	85.7373i	0.426325	−	0.848884i	−0.573239	−	0.819388i	$-0.694314\pi$
$101$	43.0589	−	85.7373i	0.426325	−	0.848884i	0.999565	−	0.0294959i	$-0.00939018\pi$
$102$		0			0
$103$	−4.90799	+	0.573662i	−0.0476504	+	0.00556953i	−0.139885	−	0.990168i	$-0.544673\pi$
$103$	−4.90799	+	0.573662i	−0.0476504	+	0.00556953i	0.0922343	+	0.995737i	$0.470599\pi$
$104$		0			0
$105$	−13.4514	−	2.64150i	−0.128108	−	0.0251571i
$106$		0			0
$107$	−14.0709	+	8.12382i	−0.131503	+	0.0759235i	−0.564309	−	0.825564i	$-0.690857\pi$
$107$	−14.0709	+	8.12382i	−0.131503	+	0.0759235i	0.432805	+	0.901488i	$0.357524\pi$
$108$		0			0
$109$	48.9682	−	84.8154i	0.449249	−	0.778123i	−0.549088	−	0.835765i	$-0.685025\pi$
$109$	48.9682	−	84.8154i	0.449249	−	0.778123i	0.998337	+	0.0576419i	$0.0183582\pi$
$110$		0			0
$111$	−53.0921	−	96.2159i	−0.478307	−	0.866809i
$112$		0			0
$113$	−73.9777	−	31.9109i	−0.654670	−	0.282397i	0.0427221	−	0.999087i	$-0.486397\pi$
$113$	−73.9777	−	31.9109i	−0.654670	−	0.282397i	−0.697392	+	0.716690i	$0.745656\pi$
$114$		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	0.452703	−	0.891662i	$-0.350460\pi$
$127$	28.7457	+	10.4626i	0.226344	+	0.0823825i	−0.226359	+	0.974044i	$0.572682\pi$
$128$		0			0
$129$	155.267	−	97.8651i	1.20362	−	0.758644i
$130$		0			0
$131$	90.8501	+	5.29142i	0.693512	+	0.0403925i	0.401281	−	0.915955i	$-0.368565\pi$
$131$	90.8501	+	5.29142i	0.693512	+	0.0403925i	0.292231	+	0.956348i	$0.405602\pi$
$132$		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	0.178516	−	0.983937i	$-0.442870\pi$
$137$	−29.1836	−	8.73699i	−0.213019	−	0.0637737i	−0.391535	+	0.920163i	$0.628056\pi$
$138$		0			0
$139$	114.683	+	75.4283i	0.825059	+	0.542650i	0.890382	−	0.455214i	$-0.150437\pi$
$139$	114.683	+	75.4283i	0.825059	+	0.542650i	−0.0653230	+	0.997864i	$0.520808\pi$
$140$		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	−0.310431	−	0.950596i	$-0.600473\pi$
$149$	−7.06730	+	2.11581i	−0.0474315	+	0.0142001i	0.263000	+	0.964796i	$0.415288\pi$
$150$		0			0
$151$	−101.697	−	11.8866i	−0.673488	−	0.0787195i	−0.227527	−	0.973772i	$-0.573064\pi$
$151$	−101.697	−	11.8866i	−0.673488	−	0.0787195i	−0.445961	+	0.895052i	$0.647138\pi$
$152$		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	0.998664	+	0.0516804i	$0.0164577\pi$
$157$	119.595	+	160.644i	0.761753	+	1.02321i	−0.236911	+	0.971531i	$0.576135\pi$
$158$		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	−0.854563	−	0.519347i	$-0.826175\pi$
$167$	−100.555	+	74.8604i	−0.602126	+	0.448266i	0.252438	+	0.967613i	$0.418768\pi$
$168$		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	−0.995003	−	0.0998416i	$-0.968166\pi$
$173$	−0.656602	+	5.61759i	−0.00379539	+	0.0324716i	0.991208	+	0.132313i	$0.0422405\pi$
$174$		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	0.762257	−	0.647274i	$-0.224091\pi$
$179$	225.032	+	39.6793i	1.25716	+	0.221672i	0.494907	+	0.868946i	$0.335202\pi$
$180$		0			0
$181$	−29.2518	−	165.895i	−0.161612	−	0.916549i	−0.952489	−	0.304574i	$-0.901486\pi$
$181$	−29.2518	−	165.895i	−0.161612	−	0.916549i	0.790876	−	0.611976i	$-0.209625\pi$
$182$		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	0.593383	−	0.804921i	$-0.297792\pi$
$191$	273.406	−	257.945i	1.43144	−	1.35050i	0.838061	−	0.545577i	$-0.183689\pi$
$192$		0			0
$193$	−12.1104	+	207.928i	−0.0627482	+	1.07734i	0.809132	+	0.587626i	$0.199938\pi$
$193$	−12.1104	+	207.928i	−0.0627482	+	1.07734i	−0.871881	+	0.489719i	$0.837100\pi$
$194$		0			0
$195$	−102.085	+	193.813i	−0.523515	+	0.993915i
$196$		0			0
$197$	−76.7979	+	211.001i	−0.389837	+	1.07107i	0.577238	+	0.816576i	$0.304131\pi$
$197$	−76.7979	+	211.001i	−0.389837	+	1.07107i	−0.967075	+	0.254492i	$0.918092\pi$
$198$		0			0
$199$	−68.4585	+	24.9169i	−0.344013	+	0.125210i	−0.508248	−	0.861211i	$-0.669707\pi$
$199$	−68.4585	+	24.9169i	−0.344013	+	0.125210i	0.164235	+	0.986421i	$0.447484\pi$
$200$		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	−0.612336	−	0.790598i	$-0.709770\pi$
$211$	80.7991	−	187.313i	0.382934	−	0.887741i	0.995270	−	0.0971438i	$-0.0309707\pi$
$212$		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	0.0191673	−	0.999816i	$-0.493898\pi$
$223$	−172.014	−	86.3886i	−0.771363	−	0.387393i	−0.790530	+	0.612423i	$0.790195\pi$
$224$		0			0
$225$	−2.34547	−	120.694i	−0.0104243	−	0.536417i
$226$		0			0
$227$	275.719	+	205.265i	1.21462	+	0.904252i	0.997414	−	0.0718729i	$-0.0228976\pi$
$227$	275.719	+	205.265i	1.21462	+	0.904252i	0.217208	+	0.976125i	$0.430305\pi$
$228$		0			0
$229$	205.025	−	217.314i	0.895306	−	0.948969i	−0.103652	−	0.994614i	$-0.533053\pi$
$229$	205.025	−	217.314i	0.895306	−	0.948969i	0.998958	+	0.0456449i	$0.0145343\pi$
$230$		0			0
$231$	−9.18843	+	6.56776i	−0.0397768	+	0.0284319i
$232$		0			0
$233$	−256.685	+	305.905i	−1.10165	+	1.31290i	−0.155984	+	0.987760i	$0.549855\pi$
$233$	−256.685	+	305.905i	−1.10165	+	1.31290i	−0.945667	+	0.325137i	$0.894590\pi$
$234$		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	0.749135	+	0.662418i	$0.230470\pi$
$239$	199.116	+	396.473i	0.833123	+	1.65888i	0.0839882	+	0.996467i	$0.473234\pi$
$240$		0			0
$241$	245.473	−	58.1781i	1.01856	−	0.241403i	0.312773	−	0.949828i	$-0.398742\pi$
$241$	245.473	−	58.1781i	1.01856	−	0.241403i	0.705786	+	0.708425i	$0.250594\pi$
$242$		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	0.664520	−	0.747270i	$-0.268636\pi$
$251$	−46.8842	−	55.8744i	−0.186790	−	0.222607i	−0.851310	+	0.524663i	$0.824191\pi$
$252$		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	0.922425	+	0.386177i	$0.126204\pi$
$257$	349.927	+	330.139i	1.36158	+	1.28459i	0.439157	+	0.898410i	$0.355277\pi$
$258$		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	−0.417610	−	0.908626i	$-0.637132\pi$
$263$	147.438	−	293.572i	0.560599	−	1.11625i	0.978210	−	0.207619i	$-0.0665714\pi$
$264$		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	−0.467082	−	0.884214i	$-0.654695\pi$
$269$	17.5198	−	10.1151i	0.0651293	−	0.0376024i	0.532211	+	0.846612i	$0.321361\pi$
$270$		0			0
$271$	200.845	−	347.873i	0.741124	−	1.28366i	−0.210860	−	0.977516i	$-0.567626\pi$
$271$	200.845	−	347.873i	0.741124	−	1.28366i	0.951984	−	0.306148i	$-0.0990404\pi$
$272$		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	0.837131	+	0.547003i	$0.184231\pi$
$277$	19.1583	+	328.935i	0.0691636	+	1.18749i	−0.767967	+	0.640489i	$0.778732\pi$
$278$		0			0
$279$	−18.8020	−	72.9822i	−0.0673906	−	0.261585i
$280$		0			0
$281$	−2.06475	+	0.890644i	−0.00734785	+	0.00316955i	−0.399751	−	0.916624i	$-0.630903\pi$
$281$	−2.06475	+	0.890644i	−0.00734785	+	0.00316955i	0.392403	+	0.919794i	$0.371644\pi$
$282$		0			0
$283$	41.7414	+	9.89290i	0.147496	+	0.0349572i	0.303701	−	0.952768i	$-0.401778\pi$
$283$	41.7414	+	9.89290i	0.147496	+	0.0349572i	−0.156204	+	0.987725i	$0.549926\pi$
$284$		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	0.540713	−	0.841207i	$-0.318154\pi$
$293$	287.173	+	16.7259i	0.980112	+	0.0570850i	0.439399	+	0.898292i	$0.355192\pi$
$294$		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	−0.563373	−	0.826203i	$-0.690496\pi$
$307$	76.3210	−	432.838i	0.248603	−	1.40990i	0.811975	−	0.583692i	$-0.198392\pi$
$308$		0			0
$309$	3.97572	+	14.2811i	0.0128664	+	0.0462173i
$310$		0			0
$311$	144.598	−	43.2899i	0.464946	−	0.139196i	−0.0457573	−	0.998953i	$-0.514570\pi$
$311$	144.598	−	43.2899i	0.464946	−	0.139196i	0.510704	+	0.859757i	$0.329385\pi$
$312$		0			0
$313$	−300.097	−	35.0763i	−0.958775	−	0.112065i	−0.377712	−	0.925923i	$-0.623289\pi$
$313$	−300.097	−	35.0763i	−0.958775	−	0.112065i	−0.581063	+	0.813858i	$0.697363\pi$
$314$		0			0
$315$	−1.59306	+	41.0940i	−0.00505733	+	0.130457i
$316$		0			0
$317$	−159.614	−	242.682i	−0.503516	−	0.765558i	0.490886	−	0.871224i	$-0.336673\pi$
$317$	−159.614	−	242.682i	−0.503516	−	0.765558i	−0.994402	+	0.105665i	$0.966303\pi$
$318$		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	−0.583733	−	0.811946i	$-0.698408\pi$
$331$	−22.9699	+	15.1076i	−0.0693956	+	0.0456422i	0.514337	+	0.857588i	$0.328038\pi$
$332$		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	0.957775	−	0.287518i	$-0.0928301\pi$
$337$	−0.144206	−	0.481683i	−0.000427912	−	0.00142933i	−0.958203	+	0.286088i	$0.907645\pi$
$338$		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	−0.734824	−	0.678257i	$-0.762735\pi$
$347$	62.1170	−	94.4443i	0.179011	−	0.272174i	0.913836	+	0.406084i	$0.133106\pi$
$348$		0			0
$349$	13.2984	−	44.4199i	0.0381044	−	0.127278i	−0.936821	−	0.349809i	$-0.886247\pi$
$349$	13.2984	−	44.4199i	0.0381044	−	0.127278i	0.974926	+	0.222531i	$0.0714318\pi$
$350$		0			0
$351$	−421.253	+	397.478i	−1.20015	+	1.13241i
$352$		0			0
$353$	−17.3182	+	16.3388i	−0.0490599	+	0.0462857i	−0.710381	−	0.703817i	$-0.751477\pi$
$353$	−17.3182	+	16.3388i	−0.0490599	+	0.0462857i	0.661321	+	0.750103i	$0.269996\pi$
$354$		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	−0.324431	−	0.945909i	$-0.605173\pi$
$359$	191.030	−	524.850i	0.532117	−	1.46198i	0.856547	−	0.516069i	$-0.172605\pi$
$360$		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	−0.985053	−	0.172253i	$-0.944895\pi$
$367$	−159.410	−	369.555i	−0.434361	−	1.00696i	0.550692	−	0.834708i	$-0.314364\pi$
$368$		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	0.105414	+	0.994428i	$0.466383\pi$
$373$	−257.462	+	596.864i	−0.690247	+	1.60017i	−0.795660	+	0.605743i	$0.792876\pi$
$374$		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	−0.999655	−	0.0262660i	$-0.991638\pi$
$379$	−198.056	−	343.043i	−0.522575	−	0.905126i	0.477080	−	0.878860i	$-0.341695\pi$
$380$		0			0
$381$	17.6838	−	90.0517i	0.0464141	−	0.236356i
$382$		0			0
$383$	71.1395	+	608.637i	0.185743	+	1.58913i	0.688848	+	0.724906i	$0.258117\pi$
$383$	71.1395	+	608.637i	0.185743	+	1.58913i	−0.503105	+	0.864225i	$0.667809\pi$
$384$		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	0.402213	−	0.915546i	$-0.368241\pi$
$389$	−139.851	−	104.115i	−0.359514	−	0.267648i	−0.761727	+	0.647898i	$0.775648\pi$
$390$		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	−0.481361	−	0.876522i	$-0.659857\pi$
$397$	118.408	−	99.3563i	0.298257	−	0.250268i	0.779619	+	0.626255i	$0.215413\pi$
$398$		0			0
$399$	−11.7157	+	15.1164i	−0.0293626	+	0.0378858i
$400$		0			0
$401$	76.5653	+	152.454i	0.190936	+	0.380185i	0.968648	−	0.248435i	$-0.0799164\pi$
$401$	76.5653	+	152.454i	0.190936	+	0.380185i	−0.777713	+	0.628620i	$0.783620\pi$
$402$		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	−0.254105	−	0.967177i	$-0.581781\pi$
$409$	151.309	−	75.9904i	0.369949	−	0.185795i	0.624054	+	0.781381i	$0.285485\pi$
$410$		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	−0.999083	−	0.0428165i	$-0.986367\pi$
$419$	−460.866	−	434.805i	−1.09992	−	1.03772i	−0.100836	−	0.994903i	$-0.532152\pi$
$420$		0			0
$421$	−111.277	+	149.470i	−0.264315	+	0.355036i	−0.914391	−	0.404833i	$-0.867330\pi$
$421$	−111.277	+	149.470i	−0.264315	+	0.355036i	0.650076	+	0.759869i	$0.274737\pi$
$422$		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	−0.896948	−	0.442136i	$-0.854221\pi$
$431$	−414.846	+	239.512i	−0.962520	+	0.555711i	−0.0655726	+	0.997848i	$0.520887\pi$
$432$		0			0
$433$	408.999	−	708.407i	0.944571	−	1.63604i	0.187962	−	0.982176i	$-0.439812\pi$
$433$	408.999	−	708.407i	0.944571	−	1.63604i	0.756608	−	0.653868i	$-0.226855\pi$
$434$		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	0.999992	+	0.00408775i	$0.00130117\pi$
$439$	3.17667	+	54.5413i	0.00723614	+	0.124240i	−0.992756	+	0.120152i	$0.961662\pi$
$440$		0			0
$441$	41.1074	−	422.788i	0.0932140	−	0.958704i
$442$		0			0
$443$	−77.9496	+	33.6242i	−0.175959	+	0.0759011i	−0.482237	−	0.876041i	$-0.660175\pi$
$443$	−77.9496	+	33.6242i	−0.175959	+	0.0759011i	0.306278	+	0.951942i	$0.400916\pi$
$444$		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	0.686788	+	0.726858i	$0.259020\pi$
$449$	281.924	+	774.580i	0.627893	+	1.72512i	−0.0588949	+	0.998264i	$0.518758\pi$
$450$		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	0.814270	−	0.580486i	$-0.197137\pi$
$457$	85.6511	+	90.7849i	0.187420	+	0.198654i	−0.626850	+	0.779140i	$0.715656\pi$
$458$		0			0
$459$	43.1729	+	144.177i	0.0940586	+	0.314112i
$460$		0			0
$461$	478.686	+	143.309i	1.03837	+	0.310866i	0.760215	−	0.649671i	$-0.225094\pi$
$461$	478.686	+	143.309i	1.03837	+	0.310866i	0.278150	+	0.960538i	$0.410279\pi$
$462$		0			0
$463$	−550.479	−	362.056i	−1.18894	−	0.781978i	−0.208351	−	0.978054i	$-0.566810\pi$
$463$	−550.479	−	362.056i	−1.18894	−	0.781978i	−0.980589	+	0.196076i	$0.937180\pi$
$464$		0			0
$465$	−63.3256	+	57.4672i	−0.136184	+	0.123585i
$466$		0			0
$467$	590.932	−	104.197i	1.26538	−	0.223121i	0.499618	−	0.866246i	$-0.333474\pi$
$467$	590.932	−	104.197i	1.26538	−	0.223121i	0.765761	+	0.643125i	$0.222363\pi$
$468$		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	0.778897	−	0.627151i	$-0.215779\pi$
$479$	−50.5194	−	76.8111i	−0.105469	−	0.160357i	−0.884366	+	0.466794i	$0.845409\pi$
$480$		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	−0.399863	−	0.916575i	$-0.630942\pi$
$491$	178.490	−	132.881i	0.363524	−	0.270633i	0.763387	+	0.645941i	$0.223535\pi$
$492$		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	−0.975987	−	0.217828i	$-0.930103\pi$
$499$	−139.850	−	467.131i	−0.280260	−	0.936134i	0.695727	−	0.718306i	$-0.255082\pi$
$500$		0			0
$501$	268.502	+	263.335i	0.535932	+	0.525618i
$502$		0			0
$503$	−587.794	−	103.644i	−1.16858	−	0.206052i	−0.444506	−	0.895776i	$-0.646621\pi$
$503$	−587.794	−	103.644i	−1.16858	−	0.206052i	−0.724072	+	0.689724i	$0.757732\pi$
$504$		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	−0.713868	−	0.700280i	$-0.753058\pi$
$509$	107.851	−	163.980i	0.211889	−	0.322161i	0.925757	+	0.378119i	$0.123429\pi$
$510$		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	−0.598631	−	0.801025i	$-0.704289\pi$
$521$	195.289	−	536.553i	0.374836	−	1.02985i	0.973467	−	0.228828i	$-0.0734893\pi$
$522$		0			0
$523$	169.881	−	61.8316i	0.324820	−	0.118225i	−0.174463	−	0.984664i	$-0.555819\pi$
$523$	169.881	−	61.8316i	0.324820	−	0.118225i	0.499283	+	0.866439i	$0.333597\pi$
$524$		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	0.890246	−	0.455479i	$-0.150532\pi$
$541$	27.4106	+	47.4765i	0.0506665	+	0.0877570i	−0.839580	+	0.543236i	$0.817199\pi$
$542$		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	0.989262	−	0.146152i	$-0.0466888\pi$
$547$	800.139	+	401.845i	1.46278	+	0.734634i	0.473515	+	0.880786i	$0.342985\pi$
$548$		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	−0.862905	−	0.505367i	$-0.831357\pi$
$557$	−119.963	+	142.967i	−0.215374	+	0.256673i	0.647531	+	0.762039i	$0.275802\pi$
$558$		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	0.979191	+	0.202939i	$0.0650493\pi$
$563$	313.727	+	624.681i	0.557241	+	1.10956i	−0.421951	+	0.906619i	$0.638654\pi$
$564$		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	0.994246	−	0.107117i	$-0.0341619\pi$
$569$	32.8207	+	138.482i	0.0576814	+	0.243377i	−0.936565	+	0.350494i	$0.886014\pi$
$570$		0			0
$571$	−555.691	+	279.078i	−0.973189	+	0.488754i	−0.863026	−	0.505160i	$-0.831434\pi$
$571$	−555.691	+	279.078i	−0.973189	+	0.488754i	−0.110163	+	0.993914i	$0.535137\pi$
$572$		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	0.924468	+	0.381259i	$0.124509\pi$
$577$	842.690	+	707.100i	1.46047	+	1.22548i	0.535999	+	0.844219i	$0.319935\pi$
$578$		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	−0.772973	−	0.634439i	$-0.781231\pi$
$587$	115.940	−	230.856i	0.197513	−	0.393281i	0.970486	+	0.241158i	$0.0775274\pi$
$588$		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	−0.650177	+	0.759783i	$0.725305\pi$
$593$	−968.521	+	559.176i	−1.63326	+	0.942961i	−0.983080	+	0.183178i	$0.941361\pi$
$594$		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	−0.516731	−	0.856148i	$-0.672851\pi$
$599$	−894.950	−	386.044i	−1.49407	−	0.644480i	−0.977342	+	0.211667i	$0.932111\pi$
$600$		0			0
$601$	29.7319	+	510.476i	0.0494706	+	0.849378i	0.928206	+	0.372068i	$0.121351\pi$
$601$	29.7319	+	510.476i	0.0494706	+	0.849378i	−0.878735	+	0.477310i	$0.841612\pi$
$602$		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	0.320678	−	0.947188i	$-0.396089\pi$
$607$	110.564	+	26.2041i	0.182148	+	0.0431699i	−0.138529	+	0.990358i	$0.544238\pi$
$608$		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	0.681777	−	0.731560i	$-0.261208\pi$
$613$	449.826	+	163.723i	0.733810	+	0.267085i	0.0520333	+	0.998645i	$0.483430\pi$
$614$		0			0
$615$	−260.925	+	164.462i	−0.424269	+	0.267418i
$616$		0			0
$617$	−382.002	−	22.2491i	−0.619128	−	0.0360601i	−0.254285	−	0.967129i	$-0.581840\pi$
$617$	−382.002	−	22.2491i	−0.619128	−	0.0360601i	−0.364843	+	0.931069i	$0.618877\pi$
$618$		0			0
$619$	650.364	+	689.346i	1.05067	+	1.11364i	0.993332	+	0.115289i	$0.0367795\pi$
$619$	650.364	+	689.346i	1.05067	+	1.11364i	0.0573371	+	0.998355i	$0.481739\pi$
$620$		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	0.609373	+	0.792883i	$0.291421\pi$
$631$	−147.927	+	838.935i	−0.234432	+	1.32953i	−0.843806	+	0.536649i	$0.819690\pi$
$632$		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	−0.997664	−	0.0683157i	$-0.978237\pi$
$641$	−426.418	−	648.336i	−0.665238	−	1.01145i	0.332426	−	0.943129i	$-0.392133\pi$
$642$		0			0
$643$	404.817	+	543.763i	0.629575	+	0.845666i	0.996413	−	0.0846188i	$-0.0269672\pi$
$643$	404.817	+	543.763i	0.629575	+	0.845666i	−0.366838	+	0.930285i	$0.619560\pi$
$644$		0			0
$645$	−225.010	+	582.825i	−0.348853	+	0.903604i
$646$		0			0
$647$		−	470.864i		−	0.727765i	−0.931445	−	0.363883i	$-0.881451\pi$
$647$		−	470.864i		−	0.727765i	0.931445	−	0.363883i	$-0.118549\pi$
$648$		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	−0.836199	−	0.548426i	$-0.815227\pi$
$653$	−359.566	+	267.687i	−0.550637	+	0.409934i	0.285562	+	0.958360i	$0.407820\pi$
$654$		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	0.719206	+	0.694797i	$0.244506\pi$
$659$	−92.8169	+	794.099i	−0.140845	+	1.20501i	−0.860051	+	0.510209i	$0.829568\pi$
$660$		0			0
$661$	50.9942	+	170.332i	0.0771470	+	0.257689i	0.987859	−	0.155353i	$-0.0496515\pi$
$661$	50.9942	+	170.332i	0.0771470	+	0.257689i	−0.910712	+	0.413042i	$0.864466\pi$
$662$		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	−0.921022	−	0.389509i	$-0.872645\pi$
$673$	42.0757	−	140.542i	0.0625195	−	0.208830i	0.983542	+	0.180680i	$0.0578297\pi$
$674$		0			0
$675$	−356.644	+	62.9071i	−0.528362	+	0.0931957i
$676$		0			0
$677$	667.218	−	629.488i	0.985551	−	0.929820i	−0.0119883	−	0.999928i	$-0.503816\pi$
$677$	667.218	−	629.488i	0.985551	−	0.929820i	0.997539	+	0.0701086i	$0.0223346\pi$
$678$		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	−0.927611	−	0.373547i	$-0.878142\pi$
$683$	15.7714	−	43.3315i	0.0230913	−	0.0634430i	0.950703	+	0.310104i	$0.100364\pi$
$684$		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	−0.973195	−	0.229981i	$-0.926133\pi$
$691$	−326.588	−	757.115i	−0.472631	−	1.09568i	0.500564	−	0.865699i	$-0.333126\pi$
$692$		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	0.695053	−	0.718959i	$-0.255381\pi$
$701$	294.380	+	169.960i	0.419942	+	0.242454i	−0.275110	+	0.961413i	$0.588714\pi$
$702$		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	0.119945	−	0.992781i	$-0.461728\pi$
$709$	−428.776	−	215.339i	−0.604762	−	0.303723i	−0.724706	+	0.689058i	$0.758025\pi$
$710$		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	0.179976	−	0.983671i	$-0.442398\pi$
$719$	803.447	−	957.511i	1.11745	−	1.33173i	0.937474	−	0.348054i	$-0.113158\pi$
$720$		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	0.710692	−	0.703503i	$-0.248382\pi$
$727$	1207.93	−	286.284i	1.66152	−	0.393788i	0.950829	+	0.309715i	$0.100234\pi$
$728$		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	−0.787806	−	0.615923i	$-0.788783\pi$
$733$	−560.163	+	281.324i	−0.764206	+	0.383799i	0.0236007	+	0.999721i	$0.492487\pi$
$734$		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	0.937548	−	0.347856i	$-0.113090\pi$
$739$	559.999	+	469.895i	0.757780	+	0.635853i	−0.179768	+	0.983709i	$0.557535\pi$
$740$		0			0
$741$	177.716	+	248.628i	0.239832	+	0.335530i
$742$		0			0
$743$	−625.438	−	590.071i	−0.841774	−	0.794173i	0.138800	−	0.990320i	$-0.455675\pi$
$743$	−625.438	−	590.071i	−0.841774	−	0.794173i	−0.980574	+	0.196147i	$0.937157\pi$
$744$		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	0.293817	−	0.955862i	$-0.405074\pi$
$751$	600.914	−	70.2368i	0.800152	−	0.0935243i	0.506334	+	0.862337i	$0.331000\pi$
$752$		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	−0.994473	−	0.104994i	$-0.966518\pi$
$757$	−307.576	+	532.737i	−0.406309	+	0.703748i	0.588164	+	0.808742i	$0.299851\pi$
$758$		0			0
$759$	86.4439	−	143.243i	0.113892	−	0.188726i
$760$		0			0
$761$	−1221.70	−	526.991i	−1.60539	−	0.692498i	−0.610365	−	0.792120i	$-0.708977\pi$
$761$	−1221.70	−	526.991i	−1.60539	−	0.692498i	−0.995025	+	0.0996221i	$0.968237\pi$
$762$		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	−0.407574	−	0.913172i	$-0.633625\pi$
$769$	−908.671	−	215.359i	−1.18163	−	0.280051i	−0.774053	+	0.633121i	$0.781773\pi$
$770$		0			0
$771$	816.288	−	1190.23i	1.05874	−	1.54374i
$772$		0			0
$773$	389.447	+	1070.00i	0.503813	+	1.38421i	0.887524	+	0.460761i	$0.152423\pi$
$773$	389.447	+	1070.00i	0.503813	+	1.38421i	−0.383712	+	0.923453i	$0.625354\pi$
$774$		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	0.281061	−	0.959690i	$-0.409314\pi$
$787$	−384.701	−	253.022i	−0.488819	−	0.321501i	−0.769880	+	0.638188i	$0.779684\pi$
$788$		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	−0.452748	−	0.891639i	$-0.649556\pi$
$797$	−271.816	+	81.3765i	−0.341049	+	0.102103i	0.111698	+	0.993742i	$0.464371\pi$
$798$		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	$0.0399244\pi$
$809$			202.408i			0.250195i	−0.992144	+	0.125097i	$0.960076\pi$
$810$		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	0.745286	+	0.666744i	$0.232313\pi$
$821$	−109.745	+	938.930i	−0.133673	+	1.14364i	−0.878959	+	0.476897i	$0.841761\pi$
$822$		0			0
$823$	−296.748	−	991.208i	−0.360569	−	1.20438i	−0.925341	−	0.379137i	$-0.876221\pi$
$823$	−296.748	−	991.208i	−0.360569	−	1.20438i	0.564772	−	0.825247i	$-0.308964\pi$
$824$		0			0
$825$	−28.1480	+	109.286i	−0.0341188	+	0.132468i
$826$		0			0
$827$	−147.681	−	26.0402i	−0.178575	−	0.0314876i	0.0836456	−	0.996496i	$-0.473344\pi$
$827$	−147.681	−	26.0402i	−0.178575	−	0.0314876i	−0.262220	+	0.965008i	$0.584455\pi$
$828$		0			0
$829$	−161.348	−	915.052i	−0.194630	−	1.10380i	−0.912945	−	0.408083i	$-0.866197\pi$
$829$	−161.348	−	915.052i	−0.194630	−	1.10380i	0.718315	−	0.695718i	$-0.244914\pi$
$830$		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	−0.734971	−	0.678099i	$-0.762804\pi$
$839$	−84.5322	+	79.7521i	−0.100754	+	0.0950561i	0.634217	+	0.773155i	$0.281323\pi$
$840$		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	−0.987513	−	0.157537i	$-0.949645\pi$
$853$	−362.038	−	839.298i	−0.424429	−	0.983937i	0.563084	−	0.826400i	$-0.309615\pi$
$854$		0			0
$855$	131.259	+	62.7572i	0.153519	+	0.0734003i
$856$		0			0
$857$	−1466.68	+	85.4243i	−1.71141	+	0.0996783i	−0.885653	−	0.464348i	$-0.846289\pi$
$857$	−1466.68	+	85.4243i	−1.71141	+	0.0996783i	−0.825757	+	0.564026i	$0.809252\pi$
$858$		0			0
$859$	−231.419	+	536.490i	−0.269405	+	0.624552i	−0.998187	−	0.0601947i	$-0.980828\pi$
$859$	−231.419	+	536.490i	−0.269405	+	0.624552i	0.728781	+	0.684747i	$0.240087\pi$
$860$		0			0
$861$	−106.495	+	58.7639i	−0.123687	+	0.0682507i
$862$		0			0
$863$	87.1990	+	50.3444i	0.101042	+	0.0583364i	0.549669	−	0.835382i	$-0.314754\pi$
$863$	87.1990	+	50.3444i	0.101042	+	0.0583364i	−0.448628	+	0.893719i	$0.648087\pi$
$864$		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	−0.429255	−	0.903183i	$-0.641224\pi$
$877$	436.184	−	462.328i	0.497359	−	0.527170i	0.926614	+	0.376013i	$0.122705\pi$
$878$		0			0
$879$	−83.5621	−	858.923i	−0.0950650	−	0.977160i
$880$		0			0
$881$	−407.845	+	486.051i	−0.462934	+	0.551704i	−0.946121	−	0.323814i	$-0.895035\pi$
$881$	−407.845	+	486.051i	−0.462934	+	0.551704i	0.483187	+	0.875517i	$0.339479\pi$
$882$		0			0
$883$	−1118.75	+	938.746i	−1.26699	+	1.06313i	−0.272091	+	0.962271i	$0.587715\pi$
$883$	−1118.75	+	938.746i	−1.26699	+	1.06313i	−0.994901	+	0.100861i	$0.967840\pi$
$884$		0			0
$885$	−226.425	+	292.151i	−0.255848	+	0.330114i
$886$		0			0
$887$	201.690	+	401.598i	0.227385	+	0.452760i	0.978176	−	0.207780i	$-0.0666237\pi$
$887$	201.690	+	401.598i	0.227385	+	0.452760i	−0.750791	+	0.660540i	$0.770327\pi$
$888$		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	−0.258456	−	0.966023i	$-0.583214\pi$
$907$	672.187	−	902.903i	0.741110	−	0.995483i	0.999566	−	0.0294602i	$-0.00937884\pi$
$908$		0			0
$909$	−133.392	+	853.116i	−0.146745	+	0.938522i
$910$		0			0
$911$	−136.001	+	270.800i	−0.149288	+	0.297256i	−0.955830	−	0.293920i	$-0.905040\pi$
$911$	−136.001	+	270.800i	−0.149288	+	0.297256i	0.806542	+	0.591176i	$0.201336\pi$
$912$		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	−0.560154	−	0.828388i	$-0.689258\pi$
$919$	401.905	−	696.119i	0.437328	−	0.757475i	0.997482	+	0.0709138i	$0.0225915\pi$
$920$		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	−0.381669	−	0.924299i	$-0.624650\pi$
$929$	26.6859	−	11.5112i	0.0287254	−	0.0123909i	0.410394	+	0.911908i	$0.365391\pi$
$930$		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	0.321976	−	0.946748i	$-0.395653\pi$
$937$	−37.4184	−	13.6192i	−0.0399342	−	0.0145349i	−0.361910	+	0.932213i	$0.617875\pi$
$938$		0			0
$939$	35.1640	+	905.737i	0.0374484	+	0.964576i
$940$		0			0
$941$	1651.12	+	96.1667i	1.75464	+	0.102196i	0.905066	−	0.425271i	$-0.139821\pi$
$941$	1651.12	+	96.1667i	1.75464	+	0.102196i	0.849576	+	0.527467i	$0.176858\pi$
$942$		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	0.931114	−	0.364729i	$-0.118838\pi$
$947$	1428.67	+	427.715i	1.50863	+	0.451653i	0.577512	+	0.816382i	$0.304024\pi$
$948$		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	0.105398	−	0.994430i	$-0.466388\pi$
$953$	518.962	−	91.5069i	0.544556	−	0.0960198i	0.439157	+	0.898410i	$0.355277\pi$
$954$		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	0.367214	−	0.930136i	$-0.380312\pi$
$967$	−608.402	−	817.226i	−0.629165	−	0.845115i	−0.996379	+	0.0850213i	$0.972904\pi$
$968$		0			0
$969$	78.4614	−	12.2727i	0.0809715	−	0.0126653i
$970$		0			0
$971$		−	164.945i		−	0.169871i	−0.996386	−	0.0849356i	$-0.972932\pi$
$971$		−	164.945i		−	0.169871i	0.996386	−	0.0849356i	$-0.0270685\pi$
$972$		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	0.0606209	−	0.998161i	$-0.480692\pi$
$977$	1010.45	−	752.250i	1.03423	−	0.769959i	0.973614	+	0.228202i	$0.0732845\pi$
$978$		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	0.896821	+	0.442394i	$0.145871\pi$
$983$	−76.5258	+	654.720i	−0.0778492	+	0.666043i	−0.974670	+	0.223648i	$0.928203\pi$
$984$		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	0.615690	+	0.787988i	$0.288877\pi$
$991$	303.879	+	1723.38i	0.306639	+	1.73903i	−0.309052	+	0.951045i	$0.600012\pi$
$992$		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	0.148233	−	0.988952i	$-0.452641\pi$
$997$	566.121	−	1890.98i	0.567824	−	1.89667i	0.419591	−	0.907713i	$-0.362173\pi$
$998$		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.5.9	✓	324
81.65	odd	54	inner	324.3.o.a.65.9	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.9	✓	324	1.1	even	1	trivial
324.3.o.a.65.9	yes	324	81.65	odd	54	inner

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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