LMFDB - Embedded newform 1512.2.j.d.323.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.17
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.d.323.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.682616 - 1.23856i) q^{2} +(-1.06807 + 1.69092i) q^{4} +0.381416 q^{5} +1.00000i q^{7} +(2.82340 + 0.168622i) q^{8} +O(q^{10})$	\(q+(-0.682616 - 1.23856i) q^{2} +(-1.06807 + 1.69092i) q^{4} +0.381416 q^{5} +1.00000i q^{7} +(2.82340 + 0.168622i) q^{8} +(-0.260361 - 0.472408i) q^{10} +2.13458i q^{11} -6.49722i q^{13} +(1.23856 - 0.682616i) q^{14} +(-1.71845 - 3.61206i) q^{16} +6.97095i q^{17} +6.19245 q^{19} +(-0.407380 + 0.644946i) q^{20} +(2.64381 - 1.45710i) q^{22} -1.82497 q^{23} -4.85452 q^{25} +(-8.04722 + 4.43511i) q^{26} +(-1.69092 - 1.06807i) q^{28} +0.694888 q^{29} -1.67769i q^{31} +(-3.30072 + 4.59405i) q^{32} +(8.63395 - 4.75848i) q^{34} +0.381416i q^{35} +8.06690i q^{37} +(-4.22707 - 7.66974i) q^{38} +(1.07689 + 0.0643151i) q^{40} -1.31125i q^{41} +7.67301 q^{43} +(-3.60941 - 2.27988i) q^{44} +(1.24575 + 2.26034i) q^{46} +6.82360 q^{47} -1.00000 q^{49} +(3.31377 + 6.01263i) q^{50} +(10.9863 + 6.93950i) q^{52} -0.954792 q^{53} +0.814162i q^{55} +(-0.168622 + 2.82340i) q^{56} +(-0.474342 - 0.860662i) q^{58} +12.8165i q^{59} +12.4829i q^{61} +(-2.07792 + 1.14522i) q^{62} +(7.94313 + 0.952173i) q^{64} -2.47815i q^{65} +0.634394 q^{67} +(-11.7873 - 7.44547i) q^{68} +(0.472408 - 0.260361i) q^{70} +5.79187 q^{71} +8.13772 q^{73} +(9.99136 - 5.50660i) q^{74} +(-6.61399 + 10.4710i) q^{76} -2.13458 q^{77} -14.1354i q^{79} +(-0.655443 - 1.37770i) q^{80} +(-1.62406 + 0.895079i) q^{82} -3.36133i q^{83} +2.65883i q^{85} +(-5.23772 - 9.50350i) q^{86} +(-0.359936 + 6.02676i) q^{88} +15.9304i q^{89} +6.49722 q^{91} +(1.94920 - 3.08588i) q^{92} +(-4.65790 - 8.45146i) q^{94} +2.36190 q^{95} +10.8796 q^{97} +(0.682616 + 1.23856i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4}+O(q^{10}) $ 48 * q - 4 * q^4	$ 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.682616	−	1.23856i	−0.482682	−	0.875796i
$2$	−0.682616	−	1.23856i	−0.482682	−	0.875796i
$3$		0			0
$3$		0			0
$4$	−1.06807	+	1.69092i	−0.534036	+	0.845462i
$5$	0.381416			0.170575			0.0852873	−	0.996356i	$-0.472819\pi$
$5$	0.381416			0.170575			0.0852873	+	0.996356i	$0.472819\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.82340	+	0.168622i	0.998221	+	0.0596169i
$9$		0			0
$10$	−0.260361	−	0.472408i	−0.0823333	−	0.149388i
$11$			2.13458i			0.643599i	0.946808	+	0.321799i	$0.104288\pi$
$11$			2.13458i			0.643599i	−0.946808	+	0.321799i	$0.895712\pi$
$12$		0			0
$13$		−	6.49722i		−	1.80201i	−0.433813	−	0.901003i	$-0.642832\pi$
$13$		−	6.49722i		−	1.80201i	0.433813	−	0.901003i	$-0.357168\pi$
$14$	1.23856	−	0.682616i	0.331020	−	0.182437i
$15$		0			0
$16$	−1.71845	−	3.61206i	−0.429611	−	0.903014i
$17$			6.97095i			1.69070i	0.534211	+	0.845351i	$0.320609\pi$
$17$			6.97095i			1.69070i	−0.534211	+	0.845351i	$0.679391\pi$
$18$		0			0
$19$	6.19245			1.42065			0.710323	−	0.703876i	$-0.248549\pi$
$19$	6.19245			1.42065			0.710323	+	0.703876i	$0.248549\pi$
$20$	−0.407380	+	0.644946i	−0.0910929	+	0.144214i
$21$		0			0
$22$	2.64381	−	1.45710i	0.563661	−	0.310654i
$23$	−1.82497			−0.380533			−0.190266	−	0.981733i	$-0.560935\pi$
$23$	−1.82497			−0.380533			−0.190266	+	0.981733i	$0.560935\pi$
$24$		0			0
$25$	−4.85452			−0.970904
$26$	−8.04722	+	4.43511i	−1.57819	+	0.869796i
$27$		0			0
$28$	−1.69092	−	1.06807i	−0.319555	−	0.201847i
$29$	0.694888			0.129038			0.0645188	−	0.997916i	$-0.479449\pi$
$29$	0.694888			0.129038			0.0645188	+	0.997916i	$0.479449\pi$
$30$		0			0
$31$		−	1.67769i		−	0.301322i	−0.988585	−	0.150661i	$-0.951860\pi$
$31$		−	1.67769i		−	0.301322i	0.988585	−	0.150661i	$-0.0481402\pi$
$32$	−3.30072	+	4.59405i	−0.583490	+	0.812121i
$33$		0			0
$34$	8.63395	−	4.75848i	1.48071	−	0.816072i
$35$			0.381416i			0.0644711i
$36$		0			0
$37$			8.06690i			1.32619i	0.748535	+	0.663095i	$0.230758\pi$
$37$			8.06690i			1.32619i	−0.748535	+	0.663095i	$0.769242\pi$
$38$	−4.22707	−	7.66974i	−0.685721	−	1.24420i
$39$		0			0
$40$	1.07689	+	0.0643151i	0.170271	+	0.0101691i
$41$		−	1.31125i		−	0.204783i	−0.994744	−	0.102391i	$-0.967351\pi$
$41$		−	1.31125i		−	0.204783i	0.994744	−	0.102391i	$-0.0326494\pi$
$42$		0			0
$43$	7.67301			1.17012			0.585061	−	0.810989i	$-0.301070\pi$
$43$	7.67301			1.17012			0.585061	+	0.810989i	$0.301070\pi$
$44$	−3.60941	−	2.27988i	−0.544138	−	0.343705i
$45$		0			0
$46$	1.24575	+	2.26034i	0.183676	+	0.333269i
$47$	6.82360			0.995325			0.497662	−	0.867371i	$-0.334192\pi$
$47$	6.82360			0.995325			0.497662	+	0.867371i	$0.334192\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	3.31377	+	6.01263i	0.468638	+	0.850314i
$51$		0			0
$52$	10.9863	+	6.93950i	1.52353	+	0.962336i
$53$	−0.954792			−0.131151			−0.0655754	−	0.997848i	$-0.520888\pi$
$53$	−0.954792			−0.131151			−0.0655754	+	0.997848i	$0.520888\pi$
$54$		0			0
$55$			0.814162i			0.109782i
$56$	−0.168622	+	2.82340i	−0.0225331	+	0.377292i
$57$		0			0
$58$	−0.474342	−	0.860662i	−0.0622841	−	0.113010i
$59$			12.8165i			1.66856i	0.551341	+	0.834280i	$0.314116\pi$
$59$			12.8165i			1.66856i	−0.551341	+	0.834280i	$0.685884\pi$
$60$		0			0
$61$			12.4829i			1.59827i	0.601149	+	0.799137i	$0.294710\pi$
$61$			12.4829i			1.59827i	−0.601149	+	0.799137i	$0.705290\pi$
$62$	−2.07792	+	1.14522i	−0.263896	+	0.145443i
$63$		0			0
$64$	7.94313	+	0.952173i	0.992892	+	0.119022i
$65$		−	2.47815i		−	0.307376i
$66$		0			0
$67$	0.634394			0.0775036			0.0387518	−	0.999249i	$-0.487662\pi$
$67$	0.634394			0.0775036			0.0387518	+	0.999249i	$0.487662\pi$
$68$	−11.7873	−	7.44547i	−1.42942	−	0.902896i
$69$		0			0
$70$	0.472408	−	0.260361i	0.0564635	−	0.0311191i
$71$	5.79187			0.687368			0.343684	−	0.939085i	$-0.388325\pi$
$71$	5.79187			0.687368			0.343684	+	0.939085i	$0.388325\pi$
$72$		0			0
$73$	8.13772			0.952448			0.476224	−	0.879324i	$-0.342005\pi$
$73$	8.13772			0.952448			0.476224	+	0.879324i	$0.342005\pi$
$74$	9.99136	−	5.50660i	1.16147	−	0.640129i
$75$		0			0
$76$	−6.61399	+	10.4710i	−0.758676	+	1.20110i
$77$	−2.13458			−0.243258
$78$		0			0
$79$		−	14.1354i		−	1.59036i	−0.606377	−	0.795178i	$-0.707378\pi$
$79$		−	14.1354i		−	1.59036i	0.606377	−	0.795178i	$-0.292622\pi$
$80$	−0.655443	−	1.37770i	−0.0732808	−	0.154031i
$81$		0			0
$82$	−1.62406	+	0.895079i	−0.179348	+	0.0988450i
$83$		−	3.36133i		−	0.368954i	−0.982837	−	0.184477i	$-0.940941\pi$
$83$		−	3.36133i		−	0.368954i	0.982837	−	0.184477i	$-0.0590591\pi$
$84$		0			0
$85$			2.65883i			0.288391i
$86$	−5.23772	−	9.50350i	−0.564797	−	1.02479i
$87$		0			0
$88$	−0.359936	+	6.02676i	−0.0383694	+	0.642454i
$89$			15.9304i			1.68862i	0.535858	+	0.844308i	$0.319988\pi$
$89$			15.9304i			1.68862i	−0.535858	+	0.844308i	$0.680012\pi$
$90$		0			0
$91$	6.49722			0.681094
$92$	1.94920	−	3.08588i	0.203218	−	0.321726i
$93$		0			0
$94$	−4.65790	−	8.45146i	−0.480426	−	0.871701i
$95$	2.36190			0.242326
$96$		0			0
$97$	10.8796			1.10465			0.552326	−	0.833628i	$-0.313740\pi$
$97$	10.8796			1.10465			0.552326	+	0.833628i	$0.313740\pi$
$98$	0.682616	+	1.23856i	0.0689546	+	0.125114i
$99$		0			0
$100$	5.18498	−	8.20863i	0.518498	−	0.820863i
$101$	11.1758			1.11203			0.556016	−	0.831171i	$-0.312329\pi$
$101$	11.1758			1.11203			0.556016	+	0.831171i	$0.312329\pi$
$102$		0			0
$103$		−	4.65366i		−	0.458539i	−0.973363	−	0.229270i	$-0.926366\pi$
$103$		−	4.65366i		−	0.458539i	0.973363	−	0.229270i	$-0.0736337\pi$
$104$	1.09557	−	18.3442i	0.107430	−	1.79880i
$105$		0			0
$106$	0.651756	+	1.18257i	0.0633041	+	0.114861i
$107$			17.4916i			1.69098i	0.533993	+	0.845489i	$0.320691\pi$
$107$			17.4916i			1.69098i	−0.533993	+	0.845489i	$0.679309\pi$
$108$		0			0
$109$			1.55555i			0.148994i	0.997221	+	0.0744972i	$0.0237352\pi$
$109$			1.55555i			0.148994i	−0.997221	+	0.0744972i	$0.976265\pi$
$110$	1.00839	−	0.555760i	0.0961462	−	0.0529896i
$111$		0			0
$112$	3.61206	−	1.71845i	0.341307	−	0.162378i
$113$			10.7024i			1.00679i	0.864055	+	0.503397i	$0.167917\pi$
$113$			10.7024i			1.00679i	−0.864055	+	0.503397i	$0.832083\pi$
$114$		0			0
$115$	−0.696073			−0.0649092
$116$	−0.742191	+	1.17500i	−0.0689107	+	0.109096i
$117$		0			0
$118$	15.8740	−	8.74871i	1.46132	−	0.805384i
$119$	−6.97095			−0.639026
$120$		0			0
$121$	6.44358			0.585780
$122$	15.4609	−	8.52103i	1.39976	−	0.771458i
$123$		0			0
$124$	2.83684	+	1.79189i	0.254756	+	0.160917i
$125$	−3.75867			−0.336186
$126$		0			0
$127$		−	19.8483i		−	1.76125i	−0.473814	−	0.880625i	$-0.657123\pi$
$127$		−	19.8483i		−	1.76125i	0.473814	−	0.880625i	$-0.342877\pi$
$128$	−4.24278	−	10.4880i	−0.375012	−	0.927020i
$129$		0			0
$130$	−3.06934	+	1.69162i	−0.269199	+	0.148365i
$131$		−	16.8474i		−	1.47197i	−0.677000	−	0.735983i	$-0.736720\pi$
$131$		−	16.8474i		−	1.47197i	0.677000	−	0.735983i	$-0.263280\pi$
$132$		0			0
$133$			6.19245i			0.536954i
$134$	−0.433048	−	0.785737i	−0.0374096	−	0.0678773i
$135$		0			0
$136$	−1.17545	+	19.6817i	−0.100794	+	1.68770i
$137$		−	8.76935i		−	0.749216i	−0.927183	−	0.374608i	$-0.877777\pi$
$137$		−	8.76935i		−	0.749216i	0.927183	−	0.374608i	$-0.122223\pi$
$138$		0			0
$139$	−0.920814			−0.0781024			−0.0390512	−	0.999237i	$-0.512434\pi$
$139$	−0.920814			−0.0781024			−0.0390512	+	0.999237i	$0.512434\pi$
$140$	−0.644946	−	0.407380i	−0.0545079	−	0.0344299i
$141$		0			0
$142$	−3.95362	−	7.17359i	−0.331780	−	0.601994i
$143$	13.8688			1.15977
$144$		0			0
$145$	0.265042			0.0220105
$146$	−5.55494	−	10.0791i	−0.459730	−	0.834150i
$147$		0			0
$148$	−13.6405	−	8.61603i	−1.12124	−	0.708233i
$149$	14.7098			1.20507			0.602537	−	0.798091i	$-0.294157\pi$
$149$	14.7098			1.20507			0.602537	+	0.798091i	$0.294157\pi$
$150$		0			0
$151$			15.1404i			1.23211i	0.787704	+	0.616054i	$0.211270\pi$
$151$			15.1404i			1.23211i	−0.787704	+	0.616054i	$0.788730\pi$
$152$	17.4838	+	1.04418i	1.41812	+	0.0846945i
$153$		0			0
$154$	1.45710	+	2.64381i	0.117416	+	0.213044i
$155$		−	0.639898i		−	0.0513978i
$156$		0			0
$157$			5.91486i			0.472057i	0.971746	+	0.236029i	$0.0758460\pi$
$157$			5.91486i			0.472057i	−0.971746	+	0.236029i	$0.924154\pi$
$158$	−17.5076	+	9.64904i	−1.39283	+	0.767636i
$159$		0			0
$160$	−1.25895	+	1.75224i	−0.0995285	+	0.138527i
$161$		−	1.82497i		−	0.143828i
$162$		0			0
$163$	0.494679			0.0387462			0.0193731	−	0.999812i	$-0.493833\pi$
$163$	0.494679			0.0387462			0.0193731	+	0.999812i	$0.493833\pi$
$164$	2.21722	+	1.40051i	0.173136	+	0.109361i
$165$		0			0
$166$	−4.16322	+	2.29450i	−0.323128	+	0.178088i
$167$	−16.8984			−1.30764			−0.653820	−	0.756650i	$-0.726835\pi$
$167$	−16.8984			−1.30764			−0.653820	+	0.756650i	$0.726835\pi$
$168$		0			0
$169$	−29.2139			−2.24723
$170$	3.29313	−	1.81496i	0.252571	−	0.139201i
$171$		0			0
$172$	−8.19532	+	12.9745i	−0.624888	+	0.989294i
$173$	−13.5249			−1.02828			−0.514141	−	0.857705i	$-0.671889\pi$
$173$	−13.5249			−1.02828			−0.514141	+	0.857705i	$0.671889\pi$
$174$		0			0
$175$		−	4.85452i		−	0.366967i
$176$	7.71021	−	3.66815i	0.581179	−	0.276498i
$177$		0			0
$178$	19.7308	−	10.8743i	1.47888	−	0.815065i
$179$			1.44357i			0.107897i	0.998544	+	0.0539487i	$0.0171807\pi$
$179$			1.44357i			0.107897i	−0.998544	+	0.0539487i	$0.982819\pi$
$180$		0			0
$181$		−	6.40425i		−	0.476024i	−0.971262	−	0.238012i	$-0.923504\pi$
$181$		−	6.40425i		−	0.476024i	0.971262	−	0.238012i	$-0.0764958\pi$
$182$	−4.43511	−	8.04722i	−0.328752	−	0.596499i
$183$		0			0
$184$	−5.15261	−	0.307730i	−0.379856	−	0.0226862i
$185$			3.07685i			0.226214i
$186$		0			0
$187$	−14.8800			−1.08813
$188$	−7.28810	+	11.5382i	−0.531539	+	0.841509i
$189$		0			0
$190$	−1.61227	−	2.92536i	−0.116966	−	0.212228i
$191$	2.60609			0.188570			0.0942850	−	0.995545i	$-0.469944\pi$
$191$	2.60609			0.188570			0.0942850	+	0.995545i	$0.469944\pi$
$192$		0			0
$193$	−11.5433			−0.830904			−0.415452	−	0.909615i	$-0.636377\pi$
$193$	−11.5433			−0.830904			−0.415452	+	0.909615i	$0.636377\pi$
$194$	−7.42656	−	13.4750i	−0.533196	−	0.967450i
$195$		0			0
$196$	1.06807	−	1.69092i	0.0762908	−	0.120780i
$197$	15.6718			1.11657			0.558285	−	0.829650i	$-0.311460\pi$
$197$	15.6718			1.11657			0.558285	+	0.829650i	$0.311460\pi$
$198$		0			0
$199$			2.80803i			0.199056i	0.995035	+	0.0995278i	$0.0317332\pi$
$199$			2.80803i			0.199056i	−0.995035	+	0.0995278i	$0.968267\pi$
$200$	−13.7062	−	0.818579i	−0.969177	−	0.0578823i
$201$		0			0
$202$	−7.62877	−	13.8419i	−0.536758	−	0.973913i
$203$			0.694888i			0.0487716i
$204$		0			0
$205$		−	0.500132i		−	0.0349307i
$206$	−5.76385	+	3.17666i	−0.401586	+	0.221329i
$207$		0			0
$208$	−23.4683	+	11.1651i	−1.62724	+	0.774162i
$209$			13.2183i			0.914327i
$210$		0			0
$211$	22.7609			1.56692			0.783462	−	0.621440i	$-0.213452\pi$
$211$	22.7609			1.56692			0.783462	+	0.621440i	$0.213452\pi$
$212$	1.01979	−	1.61448i	0.0700392	−	0.110883i
$213$		0			0
$214$	21.6644	−	11.9400i	1.48095	−	0.816205i
$215$	2.92661			0.199593
$216$		0			0
$217$	1.67769			0.113889
$218$	1.92664	−	1.06184i	0.130489	−	0.0719170i
$219$		0			0
$220$	−1.37669	−	0.869583i	−0.0928161	−	0.0586273i
$221$	45.2918			3.04666
$222$		0			0
$223$		−	7.34083i		−	0.491578i	−0.969323	−	0.245789i	$-0.920953\pi$
$223$		−	7.34083i		−	0.491578i	0.969323	−	0.245789i	$-0.0790471\pi$
$224$	−4.59405	−	3.30072i	−0.306953	−	0.220538i
$225$		0			0
$226$	13.2555	−	7.30560i	0.881745	−	0.485961i
$227$		−	5.96015i		−	0.395589i	−0.980244	−	0.197794i	$-0.936622\pi$
$227$		−	5.96015i		−	0.395589i	0.980244	−	0.197794i	$-0.0633778\pi$
$228$		0			0
$229$			20.0338i			1.32387i	0.749561	+	0.661935i	$0.230264\pi$
$229$			20.0338i			1.32387i	−0.749561	+	0.661935i	$0.769736\pi$
$230$	0.475150	+	0.862130i	0.0313305	+	0.0568472i
$231$		0			0
$232$	1.96195	+	0.117173i	0.128808	+	0.00769281i
$233$		−	19.0205i		−	1.24608i	−0.782192	−	0.623038i	$-0.785898\pi$
$233$		−	19.0205i		−	1.24608i	0.782192	−	0.623038i	$-0.214102\pi$
$234$		0			0
$235$	2.60263			0.169777
$236$	−21.6716	−	13.6889i	−1.41070	−	0.891071i
$237$		0			0
$238$	4.75848	+	8.63395i	0.308446	+	0.559656i
$239$	9.44700			0.611076			0.305538	−	0.952180i	$-0.401164\pi$
$239$	9.44700			0.611076			0.305538	+	0.952180i	$0.401164\pi$
$240$		0			0
$241$	−16.0144			−1.03158			−0.515789	−	0.856716i	$-0.672501\pi$
$241$	−16.0144			−1.03158			−0.515789	+	0.856716i	$0.672501\pi$
$242$	−4.39849	−	7.98078i	−0.282746	−	0.513024i
$243$		0			0
$244$	−21.1077	−	13.3326i	−1.35128	−	0.853535i
$245$	−0.381416			−0.0243678
$246$		0			0
$247$		−	40.2338i		−	2.56001i
$248$	0.282895	−	4.73678i	0.0179639	−	0.300786i
$249$		0			0
$250$	2.56573	+	4.65535i	0.162271	+	0.294430i
$251$			17.8027i			1.12370i	0.827240	+	0.561849i	$0.189910\pi$
$251$			17.8027i			1.12370i	−0.827240	+	0.561849i	$0.810090\pi$
$252$		0			0
$253$		−	3.89554i		−	0.244910i
$254$	−24.5833	+	13.5487i	−1.54249	+	0.850124i
$255$		0			0
$256$	−10.0939	+	12.4142i	−0.630868	+	0.775890i
$257$		−	11.2136i		−	0.699486i	−0.936846	−	0.349743i	$-0.886269\pi$
$257$		−	11.2136i		−	0.699486i	0.936846	−	0.349743i	$-0.113731\pi$
$258$		0			0
$259$	−8.06690			−0.501253
$260$	4.19036	+	2.64684i	0.259875	+	0.164150i
$261$		0			0
$262$	−20.8666	+	11.5003i	−1.28914	+	0.710492i
$263$	30.8071			1.89965			0.949825	−	0.312782i	$-0.101261\pi$
$263$	30.8071			1.89965			0.949825	+	0.312782i	$0.101261\pi$
$264$		0			0
$265$	−0.364173			−0.0223710
$266$	7.66974	−	4.22707i	0.470262	−	0.259178i
$267$		0			0
$268$	−0.677579	+	1.07271i	−0.0413897	+	0.0655263i
$269$	−26.9698			−1.64438			−0.822188	−	0.569216i	$-0.807247\pi$
$269$	−26.9698			−1.64438			−0.822188	+	0.569216i	$0.807247\pi$
$270$		0			0
$271$		−	4.91487i		−	0.298557i	−0.988795	−	0.149279i	$-0.952305\pi$
$271$		−	4.91487i		−	0.298557i	0.988795	−	0.149279i	$-0.0476951\pi$
$272$	25.1794	−	11.9792i	1.52673	−	0.726345i
$273$		0			0
$274$	−10.8614	+	5.98609i	−0.656160	+	0.361633i
$275$		−	10.3623i		−	0.624873i
$276$		0			0
$277$			17.3250i			1.04096i	0.853874	+	0.520480i	$0.174247\pi$
$277$			17.3250i			1.04096i	−0.853874	+	0.520480i	$0.825753\pi$
$278$	0.628562	+	1.14049i	0.0376986	+	0.0684018i
$279$		0			0
$280$	−0.0643151	+	1.07689i	−0.00384357	+	0.0643564i
$281$			14.5958i			0.870712i	0.900258	+	0.435356i	$0.143377\pi$
$281$			14.5958i			0.870712i	−0.900258	+	0.435356i	$0.856623\pi$
$282$		0			0
$283$	17.2643			1.02625			0.513127	−	0.858313i	$-0.328487\pi$
$283$	17.2643			1.02625			0.513127	+	0.858313i	$0.328487\pi$
$284$	−6.18613	+	9.79360i	−0.367079	+	0.581144i
$285$		0			0
$286$	−9.46708	−	17.1774i	−0.559800	−	1.01572i
$287$	1.31125			0.0774006
$288$		0			0
$289$	−31.5941			−1.85848
$290$	−0.180922	−	0.328271i	−0.0106241	−	0.0192767i
$291$		0			0
$292$	−8.69167	+	13.7603i	−0.508642	+	0.805259i
$293$	−24.2206			−1.41498			−0.707491	−	0.706722i	$-0.750173\pi$
$293$	−24.2206			−1.41498			−0.707491	+	0.706722i	$0.750173\pi$
$294$		0			0
$295$			4.88840i			0.284614i
$296$	−1.36026	+	22.7761i	−0.0790633	+	1.32383i
$297$		0			0
$298$	−10.0411	−	18.2190i	−0.581667	−	1.05540i
$299$			11.8572i			0.685722i
$300$		0			0
$301$			7.67301i			0.442265i
$302$	18.7523	−	10.3351i	1.07907	−	0.594716i
$303$		0			0
$304$	−10.6414	−	22.3675i	−0.610326	−	1.28286i
$305$			4.76119i			0.272625i
$306$		0			0
$307$	−0.805392			−0.0459662			−0.0229831	−	0.999736i	$-0.507316\pi$
$307$	−0.805392			−0.0459662			−0.0229831	+	0.999736i	$0.507316\pi$
$308$	2.27988	−	3.60941i	0.129908	−	0.205665i
$309$		0			0
$310$	−0.792553	+	0.436804i	−0.0450140	+	0.0248088i
$311$	−17.5723			−0.996432			−0.498216	−	0.867053i	$-0.666011\pi$
$311$	−17.5723			−0.996432			−0.498216	+	0.867053i	$0.666011\pi$
$312$		0			0
$313$	−12.6581			−0.715477			−0.357739	−	0.933822i	$-0.616452\pi$
$313$	−12.6581			−0.715477			−0.357739	+	0.933822i	$0.616452\pi$
$314$	7.32593	−	4.03758i	0.413426	−	0.227854i
$315$		0			0
$316$	23.9019	+	15.0976i	1.34458	+	0.849307i
$317$	−21.9610			−1.23345			−0.616725	−	0.787178i	$-0.711541\pi$
$317$	−21.9610			−1.23345			−0.616725	+	0.787178i	$0.711541\pi$
$318$		0			0
$319$			1.48329i			0.0830484i
$320$	3.02964	+	0.363174i	0.169362	+	0.0203021i
$321$		0			0
$322$	−2.26034	+	1.24575i	−0.125964	+	0.0694231i
$323$			43.1673i			2.40189i
$324$		0			0
$325$			31.5409i			1.74958i
$326$	−0.337676	−	0.612691i	−0.0187021	−	0.0339338i
$327$		0			0
$328$	0.221105	−	3.70218i	0.0122085	−	0.204418i
$329$			6.82360i			0.376197i
$330$		0			0
$331$	−3.55541			−0.195423			−0.0977115	−	0.995215i	$-0.531152\pi$
$331$	−3.55541			−0.195423			−0.0977115	+	0.995215i	$0.531152\pi$
$332$	5.68375	+	3.59014i	0.311937	+	0.197035i
$333$		0			0
$334$	11.5351	+	20.9298i	0.631175	+	1.14523i
$335$	0.241968			0.0132201
$336$		0			0
$337$	−3.54995			−0.193378			−0.0966890	−	0.995315i	$-0.530825\pi$
$337$	−3.54995			−0.193378			−0.0966890	+	0.995315i	$0.530825\pi$
$338$	19.9419	+	36.1833i	1.08470	+	1.96811i
$339$		0			0
$340$	−4.49588	−	2.83982i	−0.243823	−	0.154011i
$341$	3.58116			0.193930
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	21.6639	+	1.29384i	1.16804	+	0.0697591i
$345$		0			0
$346$	9.23234	+	16.7515i	0.496334	+	0.900565i
$347$		−	23.7798i		−	1.27657i	−0.769801	−	0.638284i	$-0.779644\pi$
$347$		−	23.7798i		−	1.27657i	0.769801	−	0.638284i	$-0.220356\pi$
$348$		0			0
$349$			13.9749i			0.748058i	0.927417	+	0.374029i	$0.122024\pi$
$349$			13.9749i			0.748058i	−0.927417	+	0.374029i	$0.877976\pi$
$350$	−6.01263	+	3.31377i	−0.321388	+	0.177129i
$351$		0			0
$352$	−9.80634	−	7.04563i	−0.522680	−	0.375533i
$353$		−	10.3186i		−	0.549203i	−0.961558	−	0.274602i	$-0.911454\pi$
$353$		−	10.3186i		−	0.549203i	0.961558	−	0.274602i	$-0.0885460\pi$
$354$		0			0
$355$	2.20911			0.117247
$356$	−26.9370	−	17.0148i	−1.42766	−	0.901782i
$357$		0			0
$358$	1.78795	−	0.985402i	0.0944960	−	0.0520801i
$359$	−7.36947			−0.388945			−0.194473	−	0.980908i	$-0.562300\pi$
$359$	−7.36947			−0.388945			−0.194473	+	0.980908i	$0.562300\pi$
$360$		0			0
$361$	19.3465			1.01824
$362$	−7.93206	+	4.37164i	−0.416900	+	0.229768i
$363$		0			0
$364$	−6.93950	+	10.9863i	−0.363729	+	0.575839i
$365$	3.10386			0.162463
$366$		0			0
$367$			15.2286i			0.794928i	0.917618	+	0.397464i	$0.130110\pi$
$367$			15.2286i			0.794928i	−0.917618	+	0.397464i	$0.869890\pi$
$368$	3.13611	+	6.59189i	0.163481	+	0.343626i
$369$		0			0
$370$	3.81087	−	2.10030i	0.198118	−	0.109190i
$371$		−	0.954792i		−	0.0495703i
$372$		0			0
$373$		−	24.7361i		−	1.28079i	−0.768047	−	0.640394i	$-0.778771\pi$
$373$		−	24.7361i		−	1.28079i	0.768047	−	0.640394i	$-0.221229\pi$
$374$	10.1573	+	18.4298i	0.525223	+	0.952983i
$375$		0			0
$376$	19.2657	+	1.15061i	0.993555	+	0.0593382i
$377$		−	4.51485i		−	0.232526i
$378$		0			0
$379$	−2.09123			−0.107419			−0.0537096	−	0.998557i	$-0.517105\pi$
$379$	−2.09123			−0.107419			−0.0537096	+	0.998557i	$0.517105\pi$
$380$	−2.52268	+	3.99380i	−0.129411	+	0.204877i
$381$		0			0
$382$	−1.77896	−	3.22780i	−0.0910193	−	0.165149i
$383$	−21.9617			−1.12219			−0.561094	−	0.827752i	$-0.689619\pi$
$383$	−21.9617			−1.12219			−0.561094	+	0.827752i	$0.689619\pi$
$384$		0			0
$385$	−0.814162			−0.0414935
$386$	7.87963	+	14.2971i	0.401062	+	0.727702i
$387$		0			0
$388$	−11.6202	+	18.3965i	−0.589924	+	0.933942i
$389$	−19.7874			−1.00326			−0.501631	−	0.865082i	$-0.667266\pi$
$389$	−19.7874			−1.00326			−0.501631	+	0.865082i	$0.667266\pi$
$390$		0			0
$391$		−	12.7218i		−	0.643367i
$392$	−2.82340	−	0.168622i	−0.142603	−	0.00851669i
$393$		0			0
$394$	−10.6978	−	19.4105i	−0.538948	−	0.977886i
$395$		−	5.39147i		−	0.271274i
$396$		0			0
$397$			2.02424i			0.101593i	0.998709	+	0.0507967i	$0.0161761\pi$
$397$			2.02424i			0.101593i	−0.998709	+	0.0507967i	$0.983824\pi$
$398$	3.47791	−	1.91680i	0.174332	−	0.0960806i
$399$		0			0
$400$	8.34223	+	17.5348i	0.417112	+	0.876740i
$401$			22.5494i			1.12606i	0.826436	+	0.563031i	$0.190365\pi$
$401$			22.5494i			1.12606i	−0.826436	+	0.563031i	$0.809635\pi$
$402$		0			0
$403$	−10.9003			−0.542984
$404$	−11.9365	+	18.8974i	−0.593865	+	0.940181i
$405$		0			0
$406$	0.860662	−	0.474342i	0.0427140	−	0.0235412i
$407$	−17.2194			−0.853535
$408$		0			0
$409$	−20.6609			−1.02161			−0.510807	−	0.859695i	$-0.670653\pi$
$409$	−20.6609			−1.02161			−0.510807	+	0.859695i	$0.670653\pi$
$410$	−0.619444	+	0.341398i	−0.0305922	+	0.0168604i
$411$		0			0
$412$	7.86899	+	4.97045i	0.387677	+	0.244876i
$413$	−12.8165			−0.630656
$414$		0			0
$415$		−	1.28207i		−	0.0629341i
$416$	29.8486	+	21.4455i	1.46345	+	1.05145i
$417$		0			0
$418$	16.3716	−	9.02300i	0.800763	−	0.441329i
$419$			12.3671i			0.604171i	0.953281	+	0.302086i	$0.0976829\pi$
$419$			12.3671i			0.604171i	−0.953281	+	0.302086i	$0.902317\pi$
$420$		0			0
$421$			3.03328i			0.147833i	0.997264	+	0.0739165i	$0.0235498\pi$
$421$			3.03328i			0.147833i	−0.997264	+	0.0739165i	$0.976450\pi$
$422$	−15.5369	−	28.1908i	−0.756326	−	1.37230i
$423$		0			0
$424$	−2.69576	−	0.160999i	−0.130918	−	0.00781880i
$425$		−	33.8406i		−	1.64151i
$426$		0			0
$427$	−12.4829			−0.604091
$428$	−29.5770	−	18.6823i	−1.42966	−	0.903043i
$429$		0			0
$430$	−1.99775	−	3.62479i	−0.0963401	−	0.174803i
$431$	15.8066			0.761378			0.380689	−	0.924703i	$-0.375687\pi$
$431$	15.8066			0.761378			0.380689	+	0.924703i	$0.375687\pi$
$432$		0			0
$433$	−3.30149			−0.158659			−0.0793297	−	0.996848i	$-0.525278\pi$
$433$	−3.30149			−0.158659			−0.0793297	+	0.996848i	$0.525278\pi$
$434$	−1.14522	−	2.07792i	−0.0549722	−	0.0997435i
$435$		0			0
$436$	−2.63031	−	1.66144i	−0.125969	−	0.0795684i
$437$	−11.3010			−0.540602
$438$		0			0
$439$		−	10.8506i		−	0.517871i	−0.965895	−	0.258936i	$-0.916628\pi$
$439$		−	10.8506i		−	0.517871i	0.965895	−	0.258936i	$-0.0833717\pi$
$440$	−0.137286	+	2.29870i	−0.00654483	+	0.109586i
$441$		0			0
$442$	−30.9169	−	56.0967i	−1.47057	−	2.66825i
$443$		−	12.1061i		−	0.575177i	−0.957754	−	0.287589i	$-0.907146\pi$
$443$		−	12.1061i		−	0.575177i	0.957754	−	0.287589i	$-0.0928536\pi$
$444$		0			0
$445$			6.07610i			0.288035i
$446$	−9.09207	+	5.01096i	−0.430522	+	0.237276i
$447$		0			0
$448$	−0.952173	+	7.94313i	−0.0449860	+	0.375278i
$449$			1.10578i			0.0521848i	0.999660	+	0.0260924i	$0.00830640\pi$
$449$			1.10578i			0.0521848i	−0.999660	+	0.0260924i	$0.991694\pi$
$450$		0			0
$451$	2.79896			0.131798
$452$	−18.0969	−	11.4309i	−0.851205	−	0.537664i
$453$		0			0
$454$	−7.38201	+	4.06849i	−0.346455	+	0.190944i
$455$	2.47815			0.116177
$456$		0			0
$457$	−2.60091			−0.121665			−0.0608327	−	0.998148i	$-0.519376\pi$
$457$	−2.60091			−0.121665			−0.0608327	+	0.998148i	$0.519376\pi$
$458$	24.8131	−	13.6754i	1.15944	−	0.639008i
$459$		0			0
$460$	0.743456	−	1.17701i	0.0346638	−	0.0548782i
$461$	25.7622			1.19987			0.599933	−	0.800050i	$-0.295194\pi$
$461$	25.7622			1.19987			0.599933	+	0.800050i	$0.295194\pi$
$462$		0			0
$463$			9.73328i			0.452344i	0.974087	+	0.226172i	$0.0726211\pi$
$463$			9.73328i			0.452344i	−0.974087	+	0.226172i	$0.927379\pi$
$464$	−1.19413	−	2.50998i	−0.0554360	−	0.116523i
$465$		0			0
$466$	−23.5581	+	12.9837i	−1.09131	+	0.601459i
$467$		−	8.70336i		−	0.402743i	−0.979515	−	0.201372i	$-0.935460\pi$
$467$		−	8.70336i		−	0.402743i	0.979515	−	0.201372i	$-0.0645399\pi$
$468$		0			0
$469$			0.634394i			0.0292936i
$470$	−1.77660	−	3.22352i	−0.0819484	−	0.148690i
$471$		0			0
$472$	−2.16114	+	36.1859i	−0.0994743	+	1.66559i
$473$			16.3786i			0.753090i
$474$		0			0
$475$	−30.0614			−1.37931
$476$	7.44547	−	11.7873i	0.341263	−	0.540272i
$477$		0			0
$478$	−6.44867	−	11.7007i	−0.294955	−	0.535177i
$479$	−13.7878			−0.629983			−0.314991	−	0.949095i	$-0.602002\pi$
$479$	−13.7878			−0.629983			−0.314991	+	0.949095i	$0.602002\pi$
$480$		0			0
$481$	52.4125			2.38980
$482$	10.9317	+	19.8348i	0.497924	+	0.903451i
$483$		0			0
$484$	−6.88221	+	10.8956i	−0.312828	+	0.495255i
$485$	4.14964			0.188426
$486$		0			0
$487$		−	28.1191i		−	1.27420i	−0.770783	−	0.637098i	$-0.780135\pi$
$487$		−	28.1191i		−	1.27420i	0.770783	−	0.637098i	$-0.219865\pi$
$488$	−2.10489	+	35.2442i	−0.0952841	+	1.59543i
$489$		0			0
$490$	0.260361	+	0.472408i	0.0117619	+	0.0213412i
$491$		−	22.2021i		−	1.00197i	−0.865457	−	0.500983i	$-0.832972\pi$
$491$		−	22.2021i		−	1.00197i	0.865457	−	0.500983i	$-0.167028\pi$
$492$		0			0
$493$			4.84403i			0.218164i
$494$	−49.8320	+	27.4642i	−2.24205	+	1.23567i
$495$		0			0
$496$	−6.05991	+	2.88302i	−0.272098	+	0.129451i
$497$			5.79187i			0.259801i
$498$		0			0
$499$	4.17365			0.186838			0.0934192	−	0.995627i	$-0.470220\pi$
$499$	4.17365			0.186838			0.0934192	+	0.995627i	$0.470220\pi$
$500$	4.01453	−	6.35563i	0.179535	−	0.284232i
$501$		0			0
$502$	22.0498	−	12.1524i	0.984129	−	0.542389i
$503$	−15.7948			−0.704256			−0.352128	−	0.935952i	$-0.614542\pi$
$503$	−15.7948			−0.704256			−0.352128	+	0.935952i	$0.614542\pi$
$504$		0			0
$505$	4.26263			0.189684
$506$	−4.82487	+	2.65916i	−0.214491	+	0.118214i
$507$		0			0
$508$	33.5619	+	21.1994i	1.48907	+	0.940570i
$509$	36.0454			1.59769			0.798843	−	0.601540i	$-0.205446\pi$
$509$	36.0454			1.59769			0.798843	+	0.601540i	$0.205446\pi$
$510$		0			0
$511$			8.13772i			0.359992i
$512$	22.2661	+	4.02775i	0.984030	+	0.178003i
$513$		0			0
$514$	−13.8888	+	7.65459i	−0.612607	+	0.337630i
$515$		−	1.77498i		−	0.0782151i
$516$		0			0
$517$			14.5655i			0.640590i
$518$	5.50660	+	9.99136i	0.241946	+	0.438995i
$519$		0			0
$520$	0.417870	−	6.99679i	0.0183248	−	0.306830i
$521$			15.7116i			0.688336i	0.938908	+	0.344168i	$0.111839\pi$
$521$			15.7116i			0.688336i	−0.938908	+	0.344168i	$0.888161\pi$
$522$		0			0
$523$	5.96881			0.260998			0.130499	−	0.991448i	$-0.458342\pi$
$523$	5.96881			0.260998			0.130499	+	0.991448i	$0.458342\pi$
$524$	28.4877	+	17.9942i	1.24449	+	0.786082i
$525$		0			0
$526$	−21.0294	−	38.1566i	−0.916927	−	1.66371i
$527$	11.6951			0.509446
$528$		0			0
$529$	−19.6695			−0.855195
$530$	0.248590	+	0.451051i	0.0107981	+	0.0195924i
$531$		0			0
$532$	−10.4710	−	6.61399i	−0.453974	−	0.286753i
$533$	−8.51948			−0.369020
$534$		0			0
$535$			6.67158i			0.288438i
$536$	1.79115	+	0.106973i	0.0773657	+	0.00462052i
$537$		0			0
$538$	18.4100	+	33.4037i	0.793711	+	1.44014i
$539$		−	2.13458i		−	0.0919427i
$540$		0			0
$541$		−	24.3780i		−	1.04809i	−0.851690	−	0.524047i	$-0.824422\pi$
$541$		−	24.3780i		−	1.04809i	0.851690	−	0.524047i	$-0.175578\pi$
$542$	−6.08737	+	3.35497i	−0.261475	+	0.144108i
$543$		0			0
$544$	−32.0249	−	23.0091i	−1.37305	−	0.986508i
$545$			0.593311i			0.0254147i
$546$		0			0
$547$	4.69571			0.200774			0.100387	−	0.994948i	$-0.467992\pi$
$547$	4.69571			0.200774			0.100387	+	0.994948i	$0.467992\pi$
$548$	14.8283	+	9.36629i	0.633433	+	0.400108i
$549$		0			0
$550$	−12.8344	+	7.07350i	−0.547261	+	0.301615i
$551$	4.30306			0.183317
$552$		0			0
$553$	14.1354			0.601098
$554$	21.4581	−	11.8263i	0.911669	−	0.502453i
$555$		0			0
$556$	0.983495	−	1.55703i	0.0417095	−	0.0660326i
$557$	23.4437			0.993340			0.496670	−	0.867939i	$-0.334556\pi$
$557$	23.4437			0.993340			0.496670	+	0.867939i	$0.334556\pi$
$558$		0			0
$559$		−	49.8533i		−	2.10857i
$560$	1.37770	−	0.655443i	0.0582183	−	0.0276975i
$561$		0			0
$562$	18.0778	−	9.96331i	0.762566	−	0.420277i
$563$		−	12.1216i		−	0.510865i	−0.966827	−	0.255433i	$-0.917782\pi$
$563$		−	12.1216i		−	0.510865i	0.966827	−	0.255433i	$-0.0822179\pi$
$564$		0			0
$565$			4.08205i			0.171733i
$566$	−11.7849	−	21.3829i	−0.495355	−	0.898789i
$567$		0			0
$568$	16.3527	+	0.976636i	0.686146	+	0.0409787i
$569$		−	13.9834i		−	0.586215i	−0.956079	−	0.293108i	$-0.905311\pi$
$569$		−	13.9834i		−	0.586215i	0.956079	−	0.293108i	$-0.0946894\pi$
$570$		0			0
$571$	30.9600			1.29564			0.647819	−	0.761795i	$-0.275681\pi$
$571$	30.9600			1.29564			0.647819	+	0.761795i	$0.275681\pi$
$572$	−14.8129	+	23.4511i	−0.619358	+	0.980541i
$573$		0			0
$574$	−0.895079	−	1.62406i	−0.0373599	−	0.0677871i
$575$	8.85936			0.369461
$576$		0			0
$577$	−25.9858			−1.08180			−0.540901	−	0.841087i	$-0.681916\pi$
$577$	−25.9858			−1.08180			−0.540901	+	0.841087i	$0.681916\pi$
$578$	21.5666	+	39.1312i	0.897053	+	1.62764i
$579$		0			0
$580$	−0.283084	+	0.448165i	−0.0117544	+	0.0186090i
$581$	3.36133			0.139451
$582$		0			0
$583$		−	2.03808i		−	0.0844085i
$584$	22.9760	+	1.37220i	0.950754	+	0.0567820i
$585$		0			0
$586$	16.5334	+	29.9987i	0.682987	+	1.23924i
$587$		−	18.2153i		−	0.751828i	−0.926655	−	0.375914i	$-0.877329\pi$
$587$		−	18.2153i		−	0.751828i	0.926655	−	0.375914i	$-0.122671\pi$
$588$		0			0
$589$		−	10.3890i		−	0.428072i
$590$	6.05459	−	3.33690i	0.249264	−	0.137378i
$591$		0			0
$592$	29.1381	−	13.8625i	1.19757	−	0.569747i
$593$		−	37.4912i		−	1.53958i	−0.638297	−	0.769790i	$-0.720361\pi$
$593$		−	37.4912i		−	1.53958i	0.638297	−	0.769790i	$-0.279639\pi$
$594$		0			0
$595$	−2.65883			−0.109001
$596$	−15.7111	+	24.8731i	−0.643552	+	1.01884i
$597$		0			0
$598$	14.6859	−	8.09394i	0.600552	−	0.330986i
$599$	−38.3963			−1.56883			−0.784416	−	0.620235i	$-0.787037\pi$
$599$	−38.3963			−1.56883			−0.784416	+	0.620235i	$0.787037\pi$
$600$		0			0
$601$	−25.6236			−1.04521			−0.522604	−	0.852576i	$-0.675039\pi$
$601$	−25.6236			−1.04521			−0.522604	+	0.852576i	$0.675039\pi$
$602$	9.50350	−	5.23772i	0.387334	−	0.213473i
$603$		0			0
$604$	−25.6013	−	16.1710i	−1.04170	−	0.657990i
$605$	2.45769			0.0999192
$606$		0			0
$607$			24.6445i			1.00029i	0.865942	+	0.500145i	$0.166720\pi$
$607$			24.6445i			1.00029i	−0.865942	+	0.500145i	$0.833280\pi$
$608$	−20.4395	+	28.4484i	−0.828933	+	1.15374i
$609$		0			0
$610$	5.89702	−	3.25006i	0.238764	−	0.131591i
$611$		−	44.3345i		−	1.79358i
$612$		0			0
$613$			11.3317i			0.457685i	0.973463	+	0.228842i	$0.0734941\pi$
$613$			11.3317i			0.457685i	−0.973463	+	0.228842i	$0.926506\pi$
$614$	0.549773	+	0.997528i	0.0221870	+	0.0402570i
$615$		0			0
$616$	−6.02676	−	0.359936i	−0.242825	−	0.0145023i
$617$		−	34.6800i		−	1.39616i	−0.716018	−	0.698082i	$-0.754037\pi$
$617$		−	34.6800i		−	1.39616i	0.716018	−	0.698082i	$-0.245963\pi$
$618$		0			0
$619$	24.6276			0.989866			0.494933	−	0.868931i	$-0.335193\pi$
$619$	24.6276			0.989866			0.494933	+	0.868931i	$0.335193\pi$
$620$	1.08202	+	0.683457i	0.0434549	+	0.0274483i
$621$		0			0
$622$	11.9951	+	21.7644i	0.480960	+	0.872671i
$623$	−15.9304			−0.638237
$624$		0			0
$625$	22.8390			0.913560
$626$	8.64061	+	15.6778i	0.345348	+	0.626612i
$627$		0			0
$628$	−10.0016	−	6.31750i	−0.399107	−	0.252096i
$629$	−56.2340			−2.24219
$630$		0			0
$631$			10.8695i			0.432708i	0.976315	+	0.216354i	$0.0694166\pi$
$631$			10.8695i			0.432708i	−0.976315	+	0.216354i	$0.930583\pi$
$632$	2.38354	−	39.9098i	0.0948120	−	1.58753i
$633$		0			0
$634$	14.9909	+	27.2000i	0.595365	+	1.08025i
$635$		−	7.57045i		−	0.300424i
$636$		0			0
$637$			6.49722i			0.257429i
$638$	1.83715	−	1.01252i	0.0727334	−	0.0400860i
$639$		0			0
$640$	−1.61827	−	4.00031i	−0.0639676	−	0.158126i
$641$		−	38.7871i		−	1.53200i	−0.642842	−	0.765999i	$-0.722245\pi$
$641$		−	38.7871i		−	1.53200i	0.642842	−	0.765999i	$-0.277755\pi$
$642$		0			0
$643$	15.8941			0.626801			0.313400	−	0.949621i	$-0.398532\pi$
$643$	15.8941			0.626801			0.313400	+	0.949621i	$0.398532\pi$
$644$	3.08588	+	1.94920i	0.121601	+	0.0768092i
$645$		0			0
$646$	53.4653	−	29.4667i	2.10357	−	1.15935i
$647$	−0.857423			−0.0337088			−0.0168544	−	0.999858i	$-0.505365\pi$
$647$	−0.857423			−0.0337088			−0.0168544	+	0.999858i	$0.505365\pi$
$648$		0			0
$649$	−27.3577			−1.07388
$650$	39.0654	−	21.5303i	1.53227	−	0.844489i
$651$		0			0
$652$	−0.528353	+	0.836464i	−0.0206919	+	0.0327585i
$653$	5.35844			0.209692			0.104846	−	0.994488i	$-0.466565\pi$
$653$	5.35844			0.209692			0.104846	+	0.994488i	$0.466565\pi$
$654$		0			0
$655$		−	6.42588i		−	0.251080i
$656$	−4.73630	+	2.25331i	−0.184922	+	0.0879770i
$657$		0			0
$658$	8.45146	−	4.65790i	0.329472	−	0.181584i
$659$		−	3.84388i		−	0.149736i	−0.997193	−	0.0748681i	$-0.976146\pi$
$659$		−	3.84388i		−	0.149736i	0.997193	−	0.0748681i	$-0.0238536\pi$
$660$		0			0
$661$		−	38.4840i		−	1.49685i	−0.663218	−	0.748426i	$-0.730810\pi$
$661$		−	38.4840i		−	1.49685i	0.663218	−	0.748426i	$-0.269190\pi$
$662$	2.42698	+	4.40360i	0.0943272	+	0.171151i
$663$		0			0
$664$	0.566794	−	9.49037i	0.0219959	−	0.368298i
$665$			2.36190i			0.0915907i
$666$		0			0
$667$	−1.26815			−0.0491030
$668$	18.0487	−	28.5740i	0.698327	−	1.10556i
$669$		0			0
$670$	−0.165171	−	0.299693i	−0.00638113	−	0.0115781i
$671$	−26.6457			−1.02865
$672$		0			0
$673$	−19.3543			−0.746055			−0.373027	−	0.927820i	$-0.621680\pi$
$673$	−19.3543			−0.746055			−0.373027	+	0.927820i	$0.621680\pi$
$674$	2.42325	+	4.39683i	0.0933401	+	0.169360i
$675$		0			0
$676$	31.2026	−	49.3985i	1.20010	−	1.89994i
$677$	16.5044			0.634315			0.317157	−	0.948373i	$-0.397272\pi$
$677$	16.5044			0.634315			0.317157	+	0.948373i	$0.397272\pi$
$678$		0			0
$679$			10.8796i			0.417520i
$680$	−0.448337	+	7.50694i	−0.0171930	+	0.287878i
$681$		0			0
$682$	−2.44455	−	4.43548i	−0.0936068	−	0.169843i
$683$		−	45.3881i		−	1.73673i	−0.495929	−	0.868363i	$-0.665172\pi$
$683$		−	45.3881i		−	1.73673i	0.495929	−	0.868363i	$-0.334828\pi$
$684$		0			0
$685$		−	3.34477i		−	0.127797i
$686$	−1.23856	+	0.682616i	−0.0472885	+	0.0260624i
$687$		0			0
$688$	−13.1856	−	27.7153i	−0.502698	−	1.05664i
$689$			6.20350i			0.236335i
$690$		0			0
$691$	−21.0358			−0.800239			−0.400119	−	0.916463i	$-0.631031\pi$
$691$	−21.0358			−0.800239			−0.400119	+	0.916463i	$0.631031\pi$
$692$	14.4456	−	22.8697i	0.549140	−	0.869374i
$693$		0			0
$694$	−29.4528	+	16.2325i	−1.11801	+	0.616177i
$695$	−0.351213			−0.0133223
$696$		0			0
$697$	9.14065			0.346227
$698$	17.3087	−	9.53947i	0.655146	−	0.361074i
$699$		0			0
$700$	8.20863	+	5.18498i	0.310257	+	0.195974i
$701$	−44.0611			−1.66417			−0.832083	−	0.554652i	$-0.812852\pi$
$701$	−44.0611			−1.66417			−0.832083	+	0.554652i	$0.812852\pi$
$702$		0			0
$703$			49.9539i			1.88405i
$704$	−2.03249	+	16.9552i	−0.0766022	+	0.639024i
$705$		0			0
$706$	−12.7802	+	7.04363i	−0.480990	+	0.265091i
$707$			11.1758i			0.420309i
$708$		0			0
$709$		−	14.8620i		−	0.558152i	−0.960269	−	0.279076i	$-0.909972\pi$
$709$		−	14.8620i		−	0.558152i	0.960269	−	0.279076i	$-0.0900282\pi$
$710$	−1.50797	−	2.73612i	−0.0565933	−	0.102685i
$711$		0			0
$712$	−2.68621	+	44.9778i	−0.100670	+	1.68561i
$713$			3.06173i			0.114663i
$714$		0			0
$715$	5.28979			0.197827
$716$	−2.44096	−	1.54183i	−0.0912231	−	0.0576210i
$717$		0			0
$718$	5.03051	+	9.12754i	0.187737	+	0.340637i
$719$	52.1512			1.94491			0.972455	−	0.233090i	$-0.0748838\pi$
$719$	52.1512			1.94491			0.972455	+	0.233090i	$0.0748838\pi$
$720$		0			0
$721$	4.65366			0.173311
$722$	−13.2062	−	23.9618i	−0.491485	−	0.891767i
$723$		0			0
$724$	10.8291	+	6.84020i	0.402460	+	0.254214i
$725$	−3.37335			−0.125283
$726$		0			0
$727$		−	32.4943i		−	1.20515i	−0.798063	−	0.602574i	$-0.794142\pi$
$727$		−	32.4943i		−	1.20515i	0.798063	−	0.602574i	$-0.205858\pi$
$728$	18.3442	+	1.09557i	0.679883	+	0.0406047i
$729$		0			0
$730$	−2.11874	−	3.84432i	−0.0784182	−	0.142285i
$731$			53.4881i			1.97833i
$732$		0			0
$733$			29.8758i			1.10349i	0.834014	+	0.551744i	$0.186037\pi$
$733$			29.8758i			1.10349i	−0.834014	+	0.551744i	$0.813963\pi$
$734$	18.8616	−	10.3953i	0.696194	−	0.383698i
$735$		0			0
$736$	6.02371	−	8.38400i	0.222037	−	0.309038i
$737$			1.35416i			0.0498812i
$738$		0			0
$739$	37.0819			1.36408			0.682040	−	0.731315i	$-0.261093\pi$
$739$	37.0819			1.36408			0.682040	+	0.731315i	$0.261093\pi$
$740$	−5.20272	−	3.28629i	−0.191256	−	0.120807i
$741$		0			0
$742$	−1.18257	+	0.651756i	−0.0434135	+	0.0239267i
$743$	−42.7019			−1.56658			−0.783290	−	0.621657i	$-0.786460\pi$
$743$	−42.7019			−1.56658			−0.783290	+	0.621657i	$0.786460\pi$
$744$		0			0
$745$	5.61055			0.205555
$746$	−30.6372	+	16.8853i	−1.12171	+	0.618213i
$747$		0			0
$748$	15.8929	−	25.1610i	0.581103	−	0.919976i
$749$	−17.4916			−0.639130
$750$		0			0
$751$		−	1.04931i		−	0.0382897i	−0.999817	−	0.0191449i	$-0.993906\pi$
$751$		−	1.04931i		−	0.0382897i	0.999817	−	0.0191449i	$-0.00609437\pi$
$752$	−11.7260	−	24.6472i	−0.427603	−	0.898792i
$753$		0			0
$754$	−5.59192	+	3.08190i	−0.203646	+	0.112236i
$755$			5.77479i			0.210166i
$756$		0			0
$757$		−	42.8516i		−	1.55747i	−0.627354	−	0.778734i	$-0.715862\pi$
$757$		−	42.8516i		−	1.55747i	0.627354	−	0.778734i	$-0.284138\pi$
$758$	1.42750	+	2.59011i	0.0518493	+	0.0940772i
$759$		0			0
$760$	6.66859	+	0.398269i	0.241895	+	0.0144467i
$761$			16.6457i			0.603408i	0.953402	+	0.301704i	$0.0975554\pi$
$761$			16.6457i			0.603408i	−0.953402	+	0.301704i	$0.902445\pi$
$762$		0			0
$763$	−1.55555			−0.0563146
$764$	−2.78349	+	4.40670i	−0.100703	+	0.159429i
$765$		0			0
$766$	14.9914	+	27.2009i	0.541660	+	0.982807i
$767$	83.2714			3.00675
$768$		0			0
$769$	23.0100			0.829763			0.414881	−	0.909876i	$-0.363823\pi$
$769$	23.0100			0.829763			0.414881	+	0.909876i	$0.363823\pi$
$770$	0.555760	+	1.00839i	0.0200282	+	0.0363399i
$771$		0			0
$772$	12.3291	−	19.5188i	0.443732	−	0.702497i
$773$	−40.5801			−1.45956			−0.729782	−	0.683680i	$-0.760378\pi$
$773$	−40.5801			−1.45956			−0.729782	+	0.683680i	$0.760378\pi$
$774$		0			0
$775$			8.14438i			0.292555i
$776$	30.7173	+	1.83453i	1.10269	+	0.0658559i
$777$		0			0
$778$	13.5072	+	24.5079i	0.484257	+	0.878652i
$779$		−	8.11985i		−	0.290924i
$780$		0			0
$781$			12.3632i			0.442389i
$782$	−15.7567	+	8.68408i	−0.563458	+	0.310542i
$783$		0			0
$784$	1.71845	+	3.61206i	0.0613731	+	0.129002i
$785$			2.25602i			0.0805210i
$786$		0			0
$787$	14.8449			0.529162			0.264581	−	0.964363i	$-0.414766\pi$
$787$	14.8449			0.529162			0.264581	+	0.964363i	$0.414766\pi$
$788$	−16.7386	+	26.4998i	−0.596288	+	0.944017i
$789$		0			0
$790$	−6.67766	+	3.68030i	−0.237581	+	0.130939i
$791$	−10.7024			−0.380532
$792$		0			0
$793$	81.1043			2.88010
$794$	2.50714	−	1.38178i	0.0889751	−	0.0490374i
$795$		0			0
$796$	−4.74816	−	2.99917i	−0.168294	−	0.106303i
$797$	1.99972			0.0708337			0.0354169	−	0.999373i	$-0.488724\pi$
$797$	1.99972			0.0708337			0.0354169	+	0.999373i	$0.488724\pi$
$798$		0			0
$799$			47.5670i			1.68280i
$800$	16.0234	−	22.3019i	0.566513	−	0.788491i
$801$		0			0
$802$	27.9288	−	15.3925i	0.986199	−	0.543530i
$803$			17.3706i			0.612995i
$804$		0			0
$805$		−	0.696073i		−	0.0245334i
$806$	7.44073	+	13.5007i	0.262089	+	0.475543i
$807$		0			0
$808$	31.5537	+	1.88448i	1.11005	+	0.0662959i
$809$		−	53.9508i		−	1.89681i	−0.317065	−	0.948404i	$-0.602697\pi$
$809$		−	53.9508i		−	1.89681i	0.317065	−	0.948404i	$-0.397303\pi$
$810$		0			0
$811$	−15.4358			−0.542025			−0.271012	−	0.962576i	$-0.587358\pi$
$811$	−15.4358			−0.542025			−0.271012	+	0.962576i	$0.587358\pi$
$812$	−1.17500	−	0.742191i	−0.0412345	−	0.0260458i
$813$		0			0
$814$	11.7542	+	21.3273i	0.411986	+	0.747522i
$815$	0.188679			0.00660912
$816$		0			0
$817$	47.5148			1.66233
$818$	14.1034	+	25.5898i	0.493115	+	0.894725i
$819$		0			0
$820$	0.845685	+	0.534176i	0.0295326	+	0.0186543i
$821$	−15.2354			−0.531720			−0.265860	−	0.964012i	$-0.585656\pi$
$821$	−15.2354			−0.531720			−0.265860	+	0.964012i	$0.585656\pi$
$822$		0			0
$823$		−	22.8119i		−	0.795173i	−0.917565	−	0.397586i	$-0.869848\pi$
$823$		−	22.8119i		−	0.795173i	0.917565	−	0.397586i	$-0.130152\pi$
$824$	0.784710	−	13.1391i	0.0273367	−	0.457723i
$825$		0			0
$826$	8.74871	+	15.8740i	0.304407	+	0.552326i
$827$		−	35.8221i		−	1.24565i	−0.782359	−	0.622827i	$-0.785984\pi$
$827$		−	35.8221i		−	1.24565i	0.782359	−	0.622827i	$-0.214016\pi$
$828$		0			0
$829$			26.6357i			0.925094i	0.886595	+	0.462547i	$0.153064\pi$
$829$			26.6357i			0.925094i	−0.886595	+	0.462547i	$0.846936\pi$
$830$	−1.58792	+	0.875158i	−0.0551175	+	0.0303772i
$831$		0			0
$832$	6.18648	−	51.6083i	0.214478	−	1.78920i
$833$		−	6.97095i		−	0.241529i
$834$		0			0
$835$	−6.44534			−0.223050
$836$	−22.3511	−	14.1181i	−0.773028	−	0.488283i
$837$		0			0
$838$	15.3174	−	8.44196i	0.529131	−	0.291623i
$839$	0.200994			0.00693908			0.00346954	−	0.999994i	$-0.498896\pi$
$839$	0.200994			0.00693908			0.00346954	+	0.999994i	$0.498896\pi$
$840$		0			0
$841$	−28.5171			−0.983349
$842$	3.75690	−	2.07056i	0.129471	−	0.0713563i
$843$		0			0
$844$	−24.3102	+	38.4869i	−0.836793	+	1.32477i
$845$	−11.1427			−0.383319
$846$		0			0
$847$			6.44358i			0.221404i
$848$	1.64076	+	3.44876i	0.0563439	+	0.118431i
$849$		0			0
$850$	−41.9137	+	23.1001i	−1.43763	+	0.792328i
$851$		−	14.7219i		−	0.504659i
$852$		0			0
$853$			23.4171i			0.801787i	0.916125	+	0.400893i	$0.131300\pi$
$853$			23.4171i			0.801787i	−0.916125	+	0.400893i	$0.868700\pi$
$854$	8.52103	+	15.4609i	0.291584	+	0.529060i
$855$		0			0
$856$	−2.94947	+	49.3858i	−0.100811	+	1.68797i
$857$			4.65764i			0.159102i	0.996831	+	0.0795509i	$0.0253486\pi$
$857$			4.65764i			0.159102i	−0.996831	+	0.0795509i	$0.974651\pi$
$858$		0			0
$859$	1.56210			0.0532980			0.0266490	−	0.999645i	$-0.491516\pi$
$859$	1.56210			0.0532980			0.0266490	+	0.999645i	$0.491516\pi$
$860$	−3.12583	+	4.94867i	−0.106590	+	0.168748i
$861$		0			0
$862$	−10.7898	−	19.5775i	−0.367504	−	0.666812i
$863$	54.8529			1.86721			0.933607	−	0.358300i	$-0.116643\pi$
$863$	54.8529			1.86721			0.933607	+	0.358300i	$0.116643\pi$
$864$		0			0
$865$	−5.15863			−0.175399
$866$	2.25365	+	4.08910i	0.0765821	+	0.138953i
$867$		0			0
$868$	−1.79189	+	2.83684i	−0.0608208	+	0.0962888i
$869$	30.1731			1.02355
$870$		0			0
$871$		−	4.12180i		−	0.139662i
$872$	−0.262299	+	4.39193i	−0.00888258	+	0.148729i
$873$		0			0
$874$	7.71427	+	13.9970i	0.260939	+	0.473457i
$875$		−	3.75867i		−	0.127066i
$876$		0			0
$877$		−	2.53416i		−	0.0855724i	−0.999084	−	0.0427862i	$-0.986377\pi$
$877$		−	2.53416i		−	0.0855724i	0.999084	−	0.0427862i	$-0.0136234\pi$
$878$	−13.4391	+	7.40679i	−0.453549	+	0.249967i
$879$		0			0
$880$	2.94080	−	1.39909i	0.0991343	−	0.0471634i
$881$		−	21.8861i		−	0.737361i	−0.929556	−	0.368680i	$-0.879810\pi$
$881$		−	21.8861i		−	0.737361i	0.929556	−	0.368680i	$-0.120190\pi$
$882$		0			0
$883$	49.1420			1.65376			0.826880	−	0.562378i	$-0.190113\pi$
$883$	49.1420			1.65376			0.826880	+	0.562378i	$0.190113\pi$
$884$	−48.3749	+	76.5850i	−1.62702	+	2.57583i
$885$		0			0
$886$	−14.9941	+	8.26380i	−0.503738	+	0.277628i
$887$	−21.2007			−0.711849			−0.355924	−	0.934515i	$-0.615834\pi$
$887$	−21.2007			−0.711849			−0.355924	+	0.934515i	$0.615834\pi$
$888$		0			0
$889$	19.8483			0.665690
$890$	7.52563	−	4.14764i	0.252260	−	0.139029i
$891$		0			0
$892$	12.4128	+	7.84053i	0.415611	+	0.262520i
$893$	42.2549			1.41400
$894$		0			0
$895$			0.550600i			0.0184045i
$896$	10.4880	−	4.24278i	0.350381	−	0.141741i
$897$		0			0
$898$	1.36957	−	0.754819i	0.0457032	−	0.0251887i
$899$		−	1.16581i		−	0.0388818i
$900$		0			0
$901$		−	6.65580i		−	0.221737i
$902$	−1.91061	−	3.46669i	−0.0636165	−	0.115428i
$903$		0			0
$904$	−1.80465	+	30.2170i	−0.0600219	+	1.00500i
$905$		−	2.44268i		−	0.0811976i
$906$		0			0
$907$	15.8245			0.525443			0.262722	−	0.964872i	$-0.415380\pi$
$907$	15.8245			0.525443			0.262722	+	0.964872i	$0.415380\pi$
$908$	10.0782	+	6.36586i	0.334455	+	0.211259i
$909$		0			0
$910$	−1.69162	−	3.06934i	−0.0560767	−	0.101748i
$911$	−34.8223			−1.15372			−0.576858	−	0.816845i	$-0.695721\pi$
$911$	−34.8223			−1.15372			−0.576858	+	0.816845i	$0.695721\pi$
$912$		0			0
$913$	7.17502			0.237458
$914$	1.77542	+	3.22138i	0.0587257	+	0.106554i
$915$		0			0
$916$	−33.8756	−	21.3975i	−1.11928	−	0.706994i
$917$	16.8474			0.556351
$918$		0			0
$919$			7.23491i			0.238658i	0.992855	+	0.119329i	$0.0380743\pi$
$919$			7.23491i			0.238658i	−0.992855	+	0.119329i	$0.961926\pi$
$920$	−1.96529	−	0.117373i	−0.0647937	−	0.00386968i
$921$		0			0
$922$	−17.5857	−	31.9081i	−0.579154	−	1.05084i
$923$		−	37.6311i		−	1.23864i
$924$		0			0
$925$		−	39.1610i		−	1.28760i
$926$	12.0553	−	6.64409i	0.396161	−	0.218338i
$927$		0			0
$928$	−2.29363	+	3.19235i	−0.0752921	+	0.104794i
$929$			16.7468i			0.549445i	0.961524	+	0.274722i	$0.0885859\pi$
$929$			16.7468i			0.549445i	−0.961524	+	0.274722i	$0.911414\pi$
$930$		0			0
$931$	−6.19245			−0.202950
$932$	32.1622	+	20.3153i	1.05351	+	0.665449i
$933$		0			0
$934$	−10.7796	+	5.94105i	−0.352721	+	0.194397i
$935$	−5.67548			−0.185608
$936$		0			0
$937$	48.8065			1.59444			0.797220	−	0.603689i	$-0.206303\pi$
$937$	48.8065			1.59444			0.797220	+	0.603689i	$0.206303\pi$
$938$	0.785737	−	0.433048i	0.0256552	−	0.0141395i
$939$		0			0
$940$	−2.77980	+	4.40085i	−0.0906670	+	0.143540i
$941$	19.4343			0.633540			0.316770	−	0.948502i	$-0.397402\pi$
$941$	19.4343			0.633540			0.316770	+	0.948502i	$0.397402\pi$
$942$		0			0
$943$			2.39299i			0.0779265i
$944$	46.2937	−	22.0244i	1.50673	−	0.716832i
$945$		0			0
$946$	20.2859	−	11.1803i	0.659553	−	0.363503i
$947$			31.5298i			1.02458i	0.858812	+	0.512290i	$0.171203\pi$
$947$			31.5298i			1.02458i	−0.858812	+	0.512290i	$0.828797\pi$
$948$		0			0
$949$		−	52.8726i		−	1.71632i
$950$	20.5204	+	37.2329i	0.665769	+	1.20800i
$951$		0			0
$952$	−19.6817	−	1.17545i	−0.637889	−	0.0380967i
$953$		−	37.0260i		−	1.19939i	−0.800228	−	0.599696i	$-0.795288\pi$
$953$		−	37.0260i		−	1.19939i	0.800228	−	0.599696i	$-0.204712\pi$
$954$		0			0
$955$	0.994004			0.0321652
$956$	−10.0901	+	15.9742i	−0.326336	+	0.516641i
$957$		0			0
$958$	9.41180	+	17.0771i	0.304081	+	0.551736i
$959$	8.76935			0.283177
$960$		0			0
$961$	28.1854			0.909205
$962$	−35.7776	−	64.9161i	−1.15352	−	2.09298i
$963$		0			0
$964$	17.1045	−	27.0791i	0.550899	−	0.872159i
$965$	−4.40280			−0.141731
$966$		0			0
$967$			29.1641i			0.937854i	0.883237	+	0.468927i	$0.155359\pi$
$967$			29.1641i			0.937854i	−0.883237	+	0.468927i	$0.844641\pi$
$968$	18.1928	+	1.08653i	0.584738	+	0.0349224i
$969$		0			0
$970$	−2.83261	−	5.13959i	−0.0909497	−	0.165022i
$971$			10.8284i			0.347500i	0.984790	+	0.173750i	$0.0555885\pi$
$971$			10.8284i			0.347500i	−0.984790	+	0.173750i	$0.944412\pi$
$972$		0			0
$973$		−	0.920814i		−	0.0295199i
$974$	−34.8272	+	19.1945i	−1.11594	+	0.615032i
$975$		0			0
$976$	45.0890	−	21.4512i	1.44326	−	0.686637i
$977$		−	2.12012i		−	0.0678285i	−0.999425	−	0.0339142i	$-0.989203\pi$
$977$		−	2.12012i		−	0.0678285i	0.999425	−	0.0339142i	$-0.0107973\pi$
$978$		0			0
$979$	−34.0046			−1.08679
$980$	0.407380	−	0.644946i	0.0130133	−	0.0206020i
$981$		0			0
$982$	−27.4987	+	15.1555i	−0.877518	+	0.483631i
$983$	−38.6019			−1.23121			−0.615605	−	0.788055i	$-0.711088\pi$
$983$	−38.6019			−1.23121			−0.615605	+	0.788055i	$0.711088\pi$
$984$		0			0
$985$	5.97748			0.190458
$986$	5.99963	−	3.30661i	0.191067	−	0.105304i
$987$		0			0
$988$	68.0322	+	42.9726i	2.16439	+	1.36714i
$989$	−14.0030			−0.445270
$990$		0			0
$991$			61.3104i			1.94759i	0.227431	+	0.973794i	$0.426967\pi$
$991$			61.3104i			1.94759i	−0.227431	+	0.973794i	$0.573033\pi$
$992$	7.70738	+	5.53758i	0.244710	+	0.175818i
$993$		0			0
$994$	7.17359	−	3.95362i	0.227532	−	0.125401i
$995$			1.07103i			0.0339538i
$996$		0			0
$997$		−	11.0697i		−	0.350582i	−0.984517	−	0.175291i	$-0.943913\pi$
$997$		−	11.0697i		−	0.350582i	0.984517	−	0.175291i	$-0.0560866\pi$
$998$	−2.84900	−	5.16933i	−0.0901836	−	0.163632i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.d.323.17	✓	48
3.2	odd	2	inner	1512.2.j.d.323.32	yes	48
4.3	odd	2		6048.2.j.d.5615.26		48
8.3	odd	2	inner	1512.2.j.d.323.31	yes	48
8.5	even	2		6048.2.j.d.5615.24		48
12.11	even	2		6048.2.j.d.5615.23		48
24.5	odd	2		6048.2.j.d.5615.25		48
24.11	even	2	inner	1512.2.j.d.323.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.d.323.17	✓	48	1.1	even	1	trivial
1512.2.j.d.323.18	yes	48	24.11	even	2	inner
1512.2.j.d.323.31	yes	48	8.3	odd	2	inner
1512.2.j.d.323.32	yes	48	3.2	odd	2	inner
6048.2.j.d.5615.23		48	12.11	even	2
6048.2.j.d.5615.24		48	8.5	even	2
6048.2.j.d.5615.25		48	24.5	odd	2
6048.2.j.d.5615.26		48	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.682616 - 1.23856i) q^{2} +(-1.06807 + 1.69092i) q^{4} +0.381416 q^{5} +1.00000i q^{7} +(2.82340 + 0.168622i) q^{8} +O(q^{10})\)	\(q+(-0.682616 - 1.23856i) q^{2} +(-1.06807 + 1.69092i) q^{4} +0.381416 q^{5} +1.00000i q^{7} +(2.82340 + 0.168622i) q^{8} +(-0.260361 - 0.472408i) q^{10} +2.13458i q^{11} -6.49722i q^{13} +(1.23856 - 0.682616i) q^{14} +(-1.71845 - 3.61206i) q^{16} +6.97095i q^{17} +6.19245 q^{19} +(-0.407380 + 0.644946i) q^{20} +(2.64381 - 1.45710i) q^{22} -1.82497 q^{23} -4.85452 q^{25} +(-8.04722 + 4.43511i) q^{26} +(-1.69092 - 1.06807i) q^{28} +0.694888 q^{29} -1.67769i q^{31} +(-3.30072 + 4.59405i) q^{32} +(8.63395 - 4.75848i) q^{34} +0.381416i q^{35} +8.06690i q^{37} +(-4.22707 - 7.66974i) q^{38} +(1.07689 + 0.0643151i) q^{40} -1.31125i q^{41} +7.67301 q^{43} +(-3.60941 - 2.27988i) q^{44} +(1.24575 + 2.26034i) q^{46} +6.82360 q^{47} -1.00000 q^{49} +(3.31377 + 6.01263i) q^{50} +(10.9863 + 6.93950i) q^{52} -0.954792 q^{53} +0.814162i q^{55} +(-0.168622 + 2.82340i) q^{56} +(-0.474342 - 0.860662i) q^{58} +12.8165i q^{59} +12.4829i q^{61} +(-2.07792 + 1.14522i) q^{62} +(7.94313 + 0.952173i) q^{64} -2.47815i q^{65} +0.634394 q^{67} +(-11.7873 - 7.44547i) q^{68} +(0.472408 - 0.260361i) q^{70} +5.79187 q^{71} +8.13772 q^{73} +(9.99136 - 5.50660i) q^{74} +(-6.61399 + 10.4710i) q^{76} -2.13458 q^{77} -14.1354i q^{79} +(-0.655443 - 1.37770i) q^{80} +(-1.62406 + 0.895079i) q^{82} -3.36133i q^{83} +2.65883i q^{85} +(-5.23772 - 9.50350i) q^{86} +(-0.359936 + 6.02676i) q^{88} +15.9304i q^{89} +6.49722 q^{91} +(1.94920 - 3.08588i) q^{92} +(-4.65790 - 8.45146i) q^{94} +2.36190 q^{95} +10.8796 q^{97} +(0.682616 + 1.23856i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4}+O(q^{10}) \) 48 * q - 4 * q^4	\( 48 q - 4 q^{4} - 12 q^{10} - 12 q^{16} + 16 q^{19} - 24 q^{22} + 48 q^{25} + 8 q^{28} + 12 q^{34} + 32 q^{40} + 64 q^{43} + 60 q^{46} - 48 q^{49} + 16 q^{52} + 36 q^{58} - 4 q^{64} + 32 q^{67} + 12 q^{70} - 32 q^{76} + 36 q^{82} + 24 q^{88} - 60 q^{94}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^10 - 12 * q^16 + 16 * q^19 - 24 * q^22 + 48 * q^25 + 8 * q^28 + 12 * q^34 + 32 * q^40 + 64 * q^43 + 60 * q^46 - 48 * q^49 + 16 * q^52 + 36 * q^58 - 4 * q^64 + 32 * q^67 + 12 * q^70 - 32 * q^76 + 36 * q^82 + 24 * q^88 - 60 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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