LMFDB - Embedded newform 1224.2.l.c.1189.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1224,2,Mod(1189,1224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1224, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1224.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1224.l (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:	$9.77368920740$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{16} - 2x^{14} + 2x^{12} - 4x^{11} + 4x^{10} + 8x^{8} - 16x^{7} + 16x^{6} - 64x^{4} - 128x^{2} + 512 $ x^18 - x^16 - 2x^14 + 2x^12 - 4x^11 + 4x^10 + 8x^8 - 16x^7 + 16x^6 - 64x^4 - 128*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 408)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1189.13
Root			$0.937200 + 1.05908i$ of defining polynomial
Character	$\chi$	$=$	1224.1189
Dual form			1224.2.l.c.1189.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.937200 - 1.05908i) q^{2} +(-0.243310 - 1.98514i) q^{4} +4.06326 q^{5} -1.33474i q^{7} +(-2.33046 - 1.60279i) q^{8} +(3.80809 - 4.30332i) q^{10} -1.38281 q^{11} -2.52933i q^{13} +(-1.41360 - 1.25092i) q^{14} +(-3.88160 + 0.966013i) q^{16} +(-0.873177 - 4.02959i) q^{17} +4.60881i q^{19} +(-0.988633 - 8.06616i) q^{20} +(-1.29597 + 1.46451i) q^{22} -3.08302i q^{23} +11.5101 q^{25} +(-2.67877 - 2.37049i) q^{26} +(-2.64966 + 0.324757i) q^{28} -4.59613 q^{29} -2.64041i q^{31} +(-2.61475 + 5.01628i) q^{32} +(-5.08600 - 2.85176i) q^{34} -5.42340i q^{35} +7.56937 q^{37} +(4.88111 + 4.31938i) q^{38} +(-9.46927 - 6.51256i) q^{40} +1.67814i q^{41} +10.9014i q^{43} +(0.336451 + 2.74507i) q^{44} +(-3.26517 - 2.88941i) q^{46} +2.19704 q^{47} +5.21846 q^{49} +(10.7872 - 12.1901i) q^{50} +(-5.02110 + 0.615414i) q^{52} -3.93905i q^{53} -5.61870 q^{55} +(-2.13932 + 3.11057i) q^{56} +(-4.30749 + 4.86768i) q^{58} +12.8504i q^{59} +7.00079 q^{61} +(-2.79641 - 2.47459i) q^{62} +(2.86211 + 7.47050i) q^{64} -10.2773i q^{65} -2.01087i q^{67} +(-7.78686 + 2.71382i) q^{68} +(-5.74383 - 5.08281i) q^{70} -3.38152i q^{71} -12.6981i q^{73} +(7.09402 - 8.01658i) q^{74} +(9.14915 - 1.12137i) q^{76} +1.84569i q^{77} +10.0914i q^{79} +(-15.7719 + 3.92516i) q^{80} +(1.77729 + 1.57276i) q^{82} -13.3967i q^{83} +(-3.54794 - 16.3732i) q^{85} +(11.5455 + 10.2168i) q^{86} +(3.22258 + 2.21635i) q^{88} -10.8271 q^{89} -3.37601 q^{91} +(-6.12024 + 0.750131i) q^{92} +(2.05906 - 2.32684i) q^{94} +18.7268i q^{95} +11.8383i q^{97} +(4.89075 - 5.52678i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{4} - 4 q^{5} + 8 q^{10} - 6 q^{14} + 10 q^{16} + 2 q^{17} - 2 q^{20} - 2 q^{22} + 22 q^{25} - 2 q^{26} + 10 q^{28} + 12 q^{29} - 30 q^{34} + 16 q^{37} + 34 q^{38} + 10 q^{40} + 12 q^{44} - 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) $ 18 * q + 2 * q^4 - 4 * q^5 + 8 * q^10 - 6 * q^14 + 10 * q^16 + 2 * q^17 - 2 * q^20 - 2 * q^22 + 22 * q^25 - 2 * q^26 + 10 * q^28 + 12 * q^29 - 30 * q^34 + 16 * q^37 + 34 * q^38 + 10 * q^40 + 12 * q^44 - 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 - 14 * q^56 + 6 * q^58 + 16 * q^61 - 6 * q^62 + 2 * q^64 - 12 * q^68 - 32 * q^70 - 6 * q^74 - 62 * q^80 - 34 * q^82 - 16 * q^85 - 14 * q^86 - 16 * q^88 - 20 * q^89 - 2 * q^92 + 12 * q^94 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	0.937200	−	1.05908i	0.662701	−	0.748884i
$2$	0.937200	−	1.05908i	0.662701	−	0.748884i
$3$		0			0
$3$		0			0
$4$	−0.243310	−	1.98514i	−0.121655	−	0.992572i
$5$	4.06326			1.81714			0.908572	−	0.417728i	$-0.137173\pi$
$5$	4.06326			1.81714			0.908572	+	0.417728i	$0.137173\pi$
$6$		0			0
$7$		−	1.33474i		−	0.504485i	−0.967664	−	0.252243i	$-0.918832\pi$
$7$		−	1.33474i		−	0.504485i	0.967664	−	0.252243i	$-0.0811681\pi$
$8$	−2.33046	−	1.60279i	−0.823943	−	0.566673i
$9$		0			0
$10$	3.80809	−	4.30332i	1.20422	−	1.36083i
$11$	−1.38281			−0.416932			−0.208466	−	0.978030i	$-0.566847\pi$
$11$	−1.38281			−0.416932			−0.208466	+	0.978030i	$0.566847\pi$
$12$		0			0
$13$		−	2.52933i		−	0.701511i	−0.936467	−	0.350756i	$-0.885925\pi$
$13$		−	2.52933i		−	0.701511i	0.936467	−	0.350756i	$-0.114075\pi$
$14$	−1.41360	−	1.25092i	−0.377801	−	0.334323i
$15$		0			0
$16$	−3.88160	+	0.966013i	−0.970400	+	0.241503i
$17$	−0.873177	−	4.02959i	−0.211777	−	0.977318i
$17$	−0.873177	−	4.02959i	−0.211777	−	0.977318i
$18$		0			0
$19$			4.60881i			1.05733i	0.848830	+	0.528667i	$0.177308\pi$
$19$			4.60881i			1.05733i	−0.848830	+	0.528667i	$0.822692\pi$
$20$	−0.988633	−	8.06616i	−0.221065	−	1.80365i
$21$		0			0
$22$	−1.29597	+	1.46451i	−0.276301	+	0.312234i
$23$		−	3.08302i		−	0.642854i	−0.946934	−	0.321427i	$-0.895837\pi$
$23$		−	3.08302i		−	0.642854i	0.946934	−	0.321427i	$-0.104163\pi$
$24$		0			0
$25$	11.5101			2.30201
$26$	−2.67877	−	2.37049i	−0.525351	−	0.464892i
$27$		0			0
$28$	−2.64966	+	0.324757i	−0.500738	+	0.0613732i
$29$	−4.59613			−0.853479			−0.426740	−	0.904374i	$-0.640338\pi$
$29$	−4.59613			−0.853479			−0.426740	+	0.904374i	$0.640338\pi$
$30$		0			0
$31$		−	2.64041i		−	0.474231i	−0.971481	−	0.237116i	$-0.923798\pi$
$31$		−	2.64041i		−	0.474231i	0.971481	−	0.237116i	$-0.0762020\pi$
$32$	−2.61475	+	5.01628i	−0.462227	+	0.886762i
$33$		0			0
$34$	−5.08600	−	2.85176i	−0.872243	−	0.489073i
$35$		−	5.42340i		−	0.916722i
$36$		0			0
$37$	7.56937			1.24440			0.622198	−	0.782860i	$-0.286240\pi$
$37$	7.56937			1.24440			0.622198	+	0.782860i	$0.286240\pi$
$38$	4.88111	+	4.31938i	0.791820	+	0.700695i
$39$		0			0
$40$	−9.46927	−	6.51256i	−1.49722	−	1.02973i
$41$			1.67814i			0.262082i	0.991377	+	0.131041i	$0.0418320\pi$
$41$			1.67814i			0.262082i	−0.991377	+	0.131041i	$0.958168\pi$
$42$		0			0
$43$			10.9014i			1.66245i	0.555939	+	0.831223i	$0.312359\pi$
$43$			10.9014i			1.66245i	−0.555939	+	0.831223i	$0.687641\pi$
$44$	0.336451	+	2.74507i	0.0507219	+	0.413835i
$45$		0			0
$46$	−3.26517	−	2.88941i	−0.481423	−	0.426020i
$47$	2.19704			0.320471			0.160235	−	0.987079i	$-0.448775\pi$
$47$	2.19704			0.320471			0.160235	+	0.987079i	$0.448775\pi$
$48$		0			0
$49$	5.21846			0.745495
$50$	10.7872	−	12.1901i	1.52555	−	1.72394i
$51$		0			0
$52$	−5.02110	+	0.615414i	−0.696301	+	0.0853425i
$53$		−	3.93905i		−	0.541070i	−0.962710	−	0.270535i	$-0.912799\pi$
$53$		−	3.93905i		−	0.541070i	0.962710	−	0.270535i	$-0.0872006\pi$
$54$		0			0
$55$	−5.61870			−0.757625
$56$	−2.13932	+	3.11057i	−0.285878	+	0.415667i
$57$		0			0
$58$	−4.30749	+	4.86768i	−0.565602	+	0.639157i
$59$			12.8504i			1.67298i	0.547979	+	0.836492i	$0.315397\pi$
$59$			12.8504i			1.67298i	−0.547979	+	0.836492i	$0.684603\pi$
$60$		0			0
$61$	7.00079			0.896360			0.448180	−	0.893943i	$-0.352072\pi$
$61$	7.00079			0.896360			0.448180	+	0.893943i	$0.352072\pi$
$62$	−2.79641	−	2.47459i	−0.355144	−	0.314273i
$63$		0			0
$64$	2.86211	+	7.47050i	0.357764	+	0.933812i
$65$		−	10.2773i		−	1.27475i
$66$		0			0
$67$		−	2.01087i		−	0.245666i	−0.992427	−	0.122833i	$-0.960802\pi$
$67$		−	2.01087i		−	0.245666i	0.992427	−	0.122833i	$-0.0391980\pi$
$68$	−7.78686	+	2.71382i	−0.944295	+	0.329099i
$69$		0			0
$70$	−5.74383	−	5.08281i	−0.686519	−	0.607513i
$71$		−	3.38152i		−	0.401312i	−0.979662	−	0.200656i	$-0.935693\pi$
$71$		−	3.38152i		−	0.401312i	0.979662	−	0.200656i	$-0.0643074\pi$
$72$		0			0
$73$		−	12.6981i		−	1.48620i	−0.669179	−	0.743101i	$-0.733354\pi$
$73$		−	12.6981i		−	1.48620i	0.669179	−	0.743101i	$-0.266646\pi$
$74$	7.09402	−	8.01658i	0.824663	−	0.931909i
$75$		0			0
$76$	9.14915	−	1.12137i	1.04948	−	0.128630i
$77$			1.84569i			0.210336i
$78$		0			0
$79$			10.0914i			1.13537i	0.823244	+	0.567687i	$0.192162\pi$
$79$			10.0914i			1.13537i	−0.823244	+	0.567687i	$0.807838\pi$
$80$	−15.7719	+	3.92516i	−1.76336	+	0.438846i
$81$		0			0
$82$	1.77729	+	1.57276i	0.196269	+	0.173682i
$83$		−	13.3967i		−	1.47048i	−0.677808	−	0.735239i	$-0.737070\pi$
$83$		−	13.3967i		−	1.47048i	0.677808	−	0.735239i	$-0.262930\pi$
$84$		0			0
$85$	−3.54794	−	16.3732i	−0.384829	−	1.77593i
$86$	11.5455	+	10.2168i	1.24498	+	1.10170i
$87$		0			0
$88$	3.22258	+	2.21635i	0.343528	+	0.236264i
$89$	−10.8271			−1.14767			−0.573837	−	0.818970i	$-0.694546\pi$
$89$	−10.8271			−1.14767			−0.573837	+	0.818970i	$0.694546\pi$
$90$		0			0
$91$	−3.37601			−0.353902
$92$	−6.12024	+	0.750131i	−0.638079	+	0.0782066i
$93$		0			0
$94$	2.05906	−	2.32684i	0.212376	−	0.239996i
$95$			18.7268i			1.92133i
$96$		0			0
$97$			11.8383i			1.20200i	0.799248	+	0.601001i	$0.205231\pi$
$97$			11.8383i			1.20200i	−0.799248	+	0.601001i	$0.794769\pi$
$98$	4.89075	−	5.52678i	0.494040	−	0.558289i
$99$		0			0
$100$	−2.80052	−	22.8491i	−0.280052	−	2.28491i
$101$			19.2918i			1.91960i	0.280683	+	0.959801i	$0.409439\pi$
$101$			19.2918i			1.91960i	−0.280683	+	0.959801i	$0.590561\pi$
$102$		0			0
$103$	−11.3576			−1.11909			−0.559547	−	0.828799i	$-0.689025\pi$
$103$	−11.3576			−1.11909			−0.559547	+	0.828799i	$0.689025\pi$
$104$	−4.05400	+	5.89452i	−0.397527	+	0.578005i
$105$		0			0
$106$	−4.17178	−	3.69168i	−0.405199	−	0.358568i
$107$	−0.539159			−0.0521224			−0.0260612	−	0.999660i	$-0.508296\pi$
$107$	−0.539159			−0.0521224			−0.0260612	+	0.999660i	$0.508296\pi$
$108$		0			0
$109$	9.10216			0.871828			0.435914	−	0.899988i	$-0.356425\pi$
$109$	9.10216			0.871828			0.435914	+	0.899988i	$0.356425\pi$
$110$	−5.26585	+	5.95067i	−0.502079	+	0.567374i
$111$		0			0
$112$	1.28938	+	5.18094i	0.121835	+	0.489552i
$113$		−	6.53188i		−	0.614468i	−0.951634	−	0.307234i	$-0.900597\pi$
$113$		−	6.53188i		−	0.614468i	0.951634	−	0.307234i	$-0.0994034\pi$
$114$		0			0
$115$		−	12.5271i		−	1.16816i
$116$	1.11829	+	9.12398i	0.103830	+	0.847140i
$117$		0			0
$118$	13.6097	+	12.0434i	1.25287	+	1.10869i
$119$	−5.37846	+	1.16547i	−0.493042	+	0.106838i
$120$		0			0
$121$	−9.08785			−0.826168
$122$	6.56115	−	7.41442i	0.594018	−	0.671270i
$123$		0			0
$124$	−5.24159	+	0.642439i	−0.470709	+	0.0576927i
$125$	26.4521			2.36595
$126$		0			0
$127$	−12.5968			−1.11779			−0.558894	−	0.829239i	$-0.688774\pi$
$127$	−12.5968			−1.11779			−0.558894	+	0.829239i	$0.688774\pi$
$128$	10.5942	+	3.97014i	0.936408	+	0.350914i
$129$		0			0
$130$	−10.8845	−	9.63193i	−0.954638	−	0.844776i
$131$	−15.0923			−1.31862			−0.659311	−	0.751870i	$-0.729152\pi$
$131$	−15.0923			−1.31862			−0.659311	+	0.751870i	$0.729152\pi$
$132$		0			0
$133$	6.15157			0.533409
$134$	−2.12967	−	1.88459i	−0.183976	−	0.162803i
$135$		0			0
$136$	−4.42369	+	10.7903i	−0.379328	+	0.925262i
$137$	−1.12940			−0.0964912			−0.0482456	−	0.998836i	$-0.515363\pi$
$137$	−1.12940			−0.0964912			−0.0482456	+	0.998836i	$0.515363\pi$
$138$		0			0
$139$	10.6515			0.903450			0.451725	−	0.892157i	$-0.350809\pi$
$139$	10.6515			0.903450			0.451725	+	0.892157i	$0.350809\pi$
$140$	−10.7662	+	1.31957i	−0.909913	+	0.111524i
$141$		0			0
$142$	−3.58131	−	3.16916i	−0.300537	−	0.265950i
$143$			3.49758i			0.292482i
$144$		0			0
$145$	−18.6753			−1.55090
$146$	−13.4484	−	11.9007i	−1.11299	−	0.984908i
$147$		0			0
$148$	−1.84171	−	15.0263i	−0.151387	−	1.23515i
$149$		−	0.280184i		−	0.0229536i	−0.999934	−	0.0114768i	$-0.996347\pi$
$149$		−	0.280184i		−	0.0229536i	0.999934	−	0.0114768i	$-0.00365325\pi$
$150$		0			0
$151$	9.48355			0.771760			0.385880	−	0.922549i	$-0.373898\pi$
$151$	9.48355			0.771760			0.385880	+	0.922549i	$0.373898\pi$
$152$	7.38696	−	10.7407i	0.599162	−	0.871182i
$153$		0			0
$154$	1.95474	+	1.72978i	0.157517	+	0.139390i
$155$		−	10.7287i		−	0.861746i
$156$		0			0
$157$			23.6841i			1.89019i	0.326789	+	0.945097i	$0.394033\pi$
$157$			23.6841i			1.89019i	−0.326789	+	0.945097i	$0.605967\pi$
$158$	10.6877	+	9.45769i	0.850264	+	0.752414i
$159$		0			0
$160$	−10.6244	+	20.3824i	−0.839933	+	1.61137i
$161$	−4.11504			−0.324310
$162$		0			0
$163$	18.4216			1.44289			0.721446	−	0.692471i	$-0.243478\pi$
$163$	18.4216			1.44289			0.721446	+	0.692471i	$0.243478\pi$
$164$	3.33136	−	0.408310i	0.260135	−	0.0318837i
$165$		0			0
$166$	−14.1882	−	12.5554i	−1.10122	−	0.974487i
$167$		−	9.89324i		−	0.765562i	−0.923839	−	0.382781i	$-0.874966\pi$
$167$		−	9.89324i		−	0.765562i	0.923839	−	0.382781i	$-0.125034\pi$
$168$		0			0
$169$	6.60246			0.507882
$170$	−20.6658	−	11.5875i	−1.58499	−	0.888717i
$171$		0			0
$172$	21.6408	−	2.65242i	1.65010	−	0.202245i
$173$	18.5486			1.41022			0.705111	−	0.709097i	$-0.250897\pi$
$173$	18.5486			1.41022			0.705111	+	0.709097i	$0.250897\pi$
$174$		0			0
$175$		−	15.3630i		−	1.16133i
$176$	5.36750	−	1.33581i	0.404591	−	0.100690i
$177$		0			0
$178$	−10.1472	+	11.4668i	−0.760564	+	0.859475i
$179$		−	9.68489i		−	0.723883i	−0.932201	−	0.361941i	$-0.882114\pi$
$179$		−	9.68489i		−	0.723883i	0.932201	−	0.361941i	$-0.117886\pi$
$180$		0			0
$181$	−6.22823			−0.462941			−0.231470	−	0.972842i	$-0.574354\pi$
$181$	−6.22823			−0.462941			−0.231470	+	0.972842i	$0.574354\pi$
$182$	−3.16400	+	3.57547i	−0.234531	+	0.265032i
$183$		0			0
$184$	−4.94144	+	7.18486i	−0.364288	+	0.529675i
$185$	30.7563			2.26125
$186$		0			0
$187$	1.20743	+	5.57214i	0.0882964	+	0.407475i
$188$	−0.534562	−	4.36144i	−0.0389870	−	0.318091i
$189$		0			0
$190$	19.8332	+	17.5507i	1.43885	+	1.27326i
$191$	18.5765			1.34415			0.672074	−	0.740484i	$-0.265404\pi$
$191$	18.5765			1.34415			0.672074	+	0.740484i	$0.265404\pi$
$192$		0			0
$193$			13.6072i			0.979471i	0.871871	+	0.489736i	$0.162907\pi$
$193$			13.6072i			0.979471i	−0.871871	+	0.489736i	$0.837093\pi$
$194$	12.5378	+	11.0949i	0.900160	+	0.796568i
$195$		0			0
$196$	−1.26971	−	10.3594i	−0.0906933	−	0.739958i
$197$	−7.88624			−0.561871			−0.280936	−	0.959727i	$-0.590645\pi$
$197$	−7.88624			−0.561871			−0.280936	+	0.959727i	$0.590645\pi$
$198$		0			0
$199$			19.7275i			1.39844i	0.714906	+	0.699221i	$0.246470\pi$
$199$			19.7275i			1.39844i	−0.714906	+	0.699221i	$0.753530\pi$
$200$	−26.8238	−	18.4483i	−1.89673	−	1.30449i
$201$		0			0
$202$	20.4316	+	18.0802i	1.43756	+	1.27212i
$203$			6.13465i			0.430568i
$204$		0			0
$205$			6.81873i			0.476241i
$206$	−10.6443	+	12.0286i	−0.741624	+	0.838071i
$207$		0			0
$208$	2.44337	+	9.81787i	0.169417	+	0.680747i
$209$		−	6.37309i		−	0.440836i
$210$		0			0
$211$	−23.9727			−1.65035			−0.825175	−	0.564877i	$-0.808924\pi$
$211$	−23.9727			−1.65035			−0.825175	+	0.564877i	$0.808924\pi$
$212$	−7.81959	+	0.958412i	−0.537051	+	0.0658240i
$213$		0			0
$214$	−0.505300	+	0.571013i	−0.0345416	+	0.0390337i
$215$			44.2952i			3.02090i
$216$		0			0
$217$	−3.52426			−0.239243
$218$	8.53055	−	9.63993i	0.577761	−	0.652899i
$219$		0			0
$220$	1.36709	+	11.1539i	0.0921691	+	0.751998i
$221$	−10.1922	+	2.20856i	−0.685600	+	0.148564i
$222$		0			0
$223$	17.6208			1.17997			0.589987	−	0.807413i	$-0.299133\pi$
$223$	17.6208			1.17997			0.589987	+	0.807413i	$0.299133\pi$
$224$	6.69544	+	3.49002i	0.447358	+	0.233187i
$225$		0			0
$226$	−6.91780	−	6.12168i	−0.460165	−	0.407208i
$227$	14.7789			0.980911			0.490456	−	0.871466i	$-0.336830\pi$
$227$	14.7789			0.980911			0.490456	+	0.871466i	$0.336830\pi$
$228$		0			0
$229$			21.7445i			1.43692i	0.695569	+	0.718459i	$0.255152\pi$
$229$			21.7445i			1.43692i	−0.695569	+	0.718459i	$0.744848\pi$
$230$	−13.2672	−	11.7404i	−0.874816	−	0.774140i
$231$		0			0
$232$	10.7111	+	7.36664i	0.703218	+	0.483644i
$233$			10.4914i			0.687314i	0.939095	+	0.343657i	$0.111666\pi$
$233$			10.4914i			0.687314i	−0.939095	+	0.343657i	$0.888334\pi$
$234$		0			0
$235$	8.92713			0.582342
$236$	25.5100	−	3.12664i	1.66056	−	0.203527i
$237$		0			0
$238$	−3.80637	+	6.78850i	−0.246730	+	0.440033i
$239$	−14.7604			−0.954770			−0.477385	−	0.878694i	$-0.658415\pi$
$239$	−14.7604			−0.954770			−0.477385	+	0.878694i	$0.658415\pi$
$240$		0			0
$241$		−	21.7730i		−	1.40252i	−0.712903	−	0.701262i	$-0.752620\pi$
$241$		−	21.7730i		−	1.40252i	0.712903	−	0.701262i	$-0.247380\pi$
$242$	−8.51713	+	9.62478i	−0.547502	+	0.618704i
$243$		0			0
$244$	−1.70337	−	13.8976i	−0.109047	−	0.889702i
$245$	21.2040			1.35467
$246$		0			0
$247$	11.6572			0.741731
$248$	−4.23203	+	6.15337i	−0.268734	+	0.390739i
$249$		0			0
$250$	24.7909	−	28.0149i	1.56791	−	1.77182i
$251$			18.0029i			1.13634i	0.822913	+	0.568168i	$0.192347\pi$
$251$			18.0029i			1.13634i	−0.822913	+	0.568168i	$0.807653\pi$
$252$		0			0
$253$			4.26322i			0.268026i
$254$	−11.8058	+	13.3411i	−0.740759	+	0.837094i
$255$		0			0
$256$	14.1336	−	7.49935i	0.883352	−	0.468709i
$257$	−4.44516			−0.277281			−0.138641	−	0.990343i	$-0.544273\pi$
$257$	−4.44516			−0.277281			−0.138641	+	0.990343i	$0.544273\pi$
$258$		0			0
$259$		−	10.1032i		−	0.627780i
$260$	−20.4020	+	2.50058i	−1.26528	+	0.155080i
$261$		0			0
$262$	−14.1445	+	15.9840i	−0.873852	+	0.987495i
$263$	18.7200			1.15433			0.577163	−	0.816629i	$-0.304160\pi$
$263$	18.7200			1.15433			0.577163	+	0.816629i	$0.304160\pi$
$264$		0			0
$265$		−	16.0054i		−	0.983203i
$266$	5.76525	−	6.51502i	0.353490	−	0.399461i
$267$		0			0
$268$	−3.99186	+	0.489265i	−0.243842	+	0.0298866i
$269$	9.33536			0.569187			0.284594	−	0.958648i	$-0.408141\pi$
$269$	9.33536			0.569187			0.284594	+	0.958648i	$0.408141\pi$
$270$		0			0
$271$	12.0895			0.734388			0.367194	−	0.930144i	$-0.380319\pi$
$271$	12.0895			0.734388			0.367194	+	0.930144i	$0.380319\pi$
$272$	7.28196	+	14.7977i	0.441533	+	0.897245i
$273$		0			0
$274$	−1.05847	+	1.19613i	−0.0639448	+	0.0722607i
$275$	−15.9162			−0.959783
$276$		0			0
$277$	21.2973			1.27963			0.639816	−	0.768528i	$-0.279011\pi$
$277$	21.2973			1.27963			0.639816	+	0.768528i	$0.279011\pi$
$278$	9.98261	−	11.2808i	0.598717	−	0.676580i
$279$		0			0
$280$	−8.69259	+	12.6390i	−0.519482	+	0.755327i
$281$	−7.37238			−0.439799			−0.219900	−	0.975522i	$-0.570573\pi$
$281$	−7.37238			−0.439799			−0.219900	+	0.975522i	$0.570573\pi$
$282$		0			0
$283$	−22.3443			−1.32823			−0.664114	−	0.747631i	$-0.731191\pi$
$283$	−22.3443			−1.32823			−0.664114	+	0.747631i	$0.731191\pi$
$284$	−6.71280	+	0.822759i	−0.398332	+	0.0488217i
$285$		0			0
$286$	3.70423	+	3.27793i	0.219035	+	0.193828i
$287$	2.23989			0.132216
$288$		0			0
$289$	−15.4751	+	7.03708i	−0.910301	+	0.413946i
$290$	−17.5025	+	19.7786i	−1.02778	+	1.16144i
$291$		0			0
$292$	−25.2076	+	3.08959i	−1.47516	+	0.180804i
$293$		−	0.823580i		−	0.0481141i	−0.999711	−	0.0240570i	$-0.992342\pi$
$293$		−	0.823580i		−	0.0481141i	0.999711	−	0.0240570i	$-0.00765833\pi$
$294$		0			0
$295$			52.2146i			3.04005i
$296$	−17.6401	−	12.1321i	−1.02531	−	0.705166i
$297$		0			0
$298$	−0.296738	−	0.262588i	−0.0171896	−	0.0152113i
$299$	−7.79799			−0.450969
$300$		0			0
$301$	14.5505			0.838679
$302$	8.88799	−	10.0439i	0.511446	−	0.577959i
$303$		0			0
$304$	−4.45217	−	17.8895i	−0.255349	−	1.02604i
$305$	28.4460			1.62882
$306$		0			0
$307$		−	1.85701i		−	0.105985i	−0.998595	−	0.0529925i	$-0.983124\pi$
$307$		−	1.85701i		−	0.105985i	0.998595	−	0.0529925i	$-0.0168759\pi$
$308$	3.66396	−	0.449076i	0.208774	−	0.0255885i
$309$		0			0
$310$	−11.3625	−	10.0549i	−0.645348	−	0.571080i
$311$		−	4.96908i		−	0.281771i	−0.990026	−	0.140885i	$-0.955005\pi$
$311$		−	4.96908i		−	0.281771i	0.990026	−	0.140885i	$-0.0449949\pi$
$312$		0			0
$313$			4.54467i			0.256880i	0.991717	+	0.128440i	$0.0409969\pi$
$313$			4.54467i			0.256880i	−0.991717	+	0.128440i	$0.959003\pi$
$314$	25.0834	+	22.1967i	1.41554	+	1.25263i
$315$		0			0
$316$	20.0330	−	2.45535i	1.12694	−	0.138124i
$317$	−24.5554			−1.37917			−0.689585	−	0.724205i	$-0.742207\pi$
$317$	−24.5554			−1.37917			−0.689585	+	0.724205i	$0.742207\pi$
$318$		0			0
$319$	6.35556			0.355843
$320$	11.6295	+	30.3546i	0.650108	+	1.69687i
$321$		0			0
$322$	−3.85661	+	4.35816i	−0.214921	+	0.242871i
$323$	18.5716	−	4.02431i	1.03335	−	0.223918i
$324$		0			0
$325$		−	29.1128i		−	1.61489i
$326$	17.2647	−	19.5100i	0.956205	−	1.08056i
$327$		0			0
$328$	2.68972	−	3.91085i	0.148515	−	0.215941i
$329$		−	2.93248i		−	0.161673i
$330$		0			0
$331$		−	23.9681i		−	1.31740i	−0.752404	−	0.658702i	$-0.771106\pi$
$331$		−	23.9681i		−	1.31740i	0.752404	−	0.658702i	$-0.228894\pi$
$332$	−26.5944	+	3.25955i	−1.45956	+	0.178891i
$333$		0			0
$334$	−10.4778	−	9.27195i	−0.573317	−	0.507339i
$335$		−	8.17067i		−	0.446411i
$336$		0			0
$337$		−	31.1833i		−	1.69866i	−0.527861	−	0.849331i	$-0.677006\pi$
$337$		−	31.1833i		−	1.69866i	0.527861	−	0.849331i	$-0.322994\pi$
$338$	6.18783	−	6.99255i	0.336574	−	0.380345i
$339$		0			0
$340$	−31.6400	+	11.0270i	−1.71592	+	0.598021i
$341$			3.65117i			0.197722i
$342$		0			0
$343$		−	16.3085i		−	0.880576i
$344$	17.4727	−	25.4053i	0.942063	−	1.36976i
$345$		0			0
$346$	17.3837	−	19.6445i	0.934555	−	1.05609i
$347$	−29.7572			−1.59745			−0.798726	−	0.601695i	$-0.794492\pi$
$347$	−29.7572			−1.59745			−0.798726	+	0.601695i	$0.794492\pi$
$348$		0			0
$349$			17.3027i			0.926191i	0.886308	+	0.463095i	$0.153261\pi$
$349$			17.3027i			0.926191i	−0.886308	+	0.463095i	$0.846739\pi$
$350$	−16.2706	−	14.3982i	−0.869703	−	0.769615i
$351$		0			0
$352$	3.61569	−	6.93655i	0.192717	−	0.369719i
$353$	−16.4532			−0.875713			−0.437857	−	0.899045i	$-0.644262\pi$
$353$	−16.4532			−0.875713			−0.437857	+	0.899045i	$0.644262\pi$
$354$		0			0
$355$		−	13.7400i		−	0.729242i
$356$	2.63435	+	21.4934i	0.139621	+	1.13915i
$357$		0			0
$358$	−10.2571	−	9.07669i	−0.542104	−	0.479718i
$359$	−23.2851			−1.22894			−0.614472	−	0.788939i	$-0.710631\pi$
$359$	−23.2851			−1.22894			−0.614472	+	0.788939i	$0.710631\pi$
$360$		0			0
$361$	−2.24111			−0.117953
$362$	−5.83710	+	6.59621i	−0.306791	+	0.346689i
$363$		0			0
$364$	0.821419	+	6.70187i	0.0430540	+	0.351273i
$365$		−	51.5958i		−	2.70065i
$366$		0			0
$367$		−	4.59048i		−	0.239621i	−0.992797	−	0.119811i	$-0.961771\pi$
$367$		−	4.59048i		−	0.239621i	0.992797	−	0.119811i	$-0.0382287\pi$
$368$	2.97824	+	11.9671i	0.155251	+	0.623826i
$369$		0			0
$370$	28.8248	−	32.5735i	1.49853	−	1.69341i
$371$	−5.25762			−0.272962
$372$		0			0
$373$		−	15.3977i		−	0.797263i	−0.917111	−	0.398631i	$-0.869485\pi$
$373$		−	15.3977i		−	0.797263i	0.917111	−	0.398631i	$-0.130515\pi$
$374$	7.03296	+	3.94344i	0.363666	+	0.203910i
$375$		0			0
$376$	−5.12011	−	3.52140i	−0.264050	−	0.181602i
$377$			11.6251i			0.598726i
$378$		0			0
$379$	−1.84157			−0.0945951			−0.0472975	−	0.998881i	$-0.515061\pi$
$379$	−1.84157			−0.0945951			−0.0472975	+	0.998881i	$0.515061\pi$
$380$	37.1754	−	4.55642i	1.90706	−	0.233739i
$381$		0			0
$382$	17.4099	−	19.6740i	0.890768	−	1.00661i
$383$	−34.1856			−1.74680			−0.873401	−	0.487002i	$-0.838090\pi$
$383$	−34.1856			−1.74680			−0.873401	+	0.487002i	$0.838090\pi$
$384$		0			0
$385$			7.49952i			0.382211i
$386$	14.4112	+	12.7527i	0.733510	+	0.649096i
$387$		0			0
$388$	23.5008	−	2.88039i	1.19307	−	0.146230i
$389$			10.1711i			0.515693i	0.966186	+	0.257846i	$0.0830129\pi$
$389$			10.1711i			0.515693i	−0.966186	+	0.257846i	$0.916987\pi$
$390$		0			0
$391$	−12.4233	+	2.69202i	−0.628273	+	0.136141i
$392$	−12.1614	−	8.36412i	−0.614245	−	0.422452i
$393$		0			0
$394$	−7.39099	+	8.35218i	−0.372353	+	0.420777i
$395$			41.0041i			2.06314i
$396$		0			0
$397$	−24.1191			−1.21050			−0.605252	−	0.796034i	$-0.706928\pi$
$397$	−24.1191			−1.21050			−0.605252	+	0.796034i	$0.706928\pi$
$398$	20.8930	+	18.4886i	1.04727	+	0.926749i
$399$		0			0
$400$	−44.6775	+	11.1189i	−2.23387	+	0.555944i
$401$			12.1154i			0.605013i	0.953147	+	0.302506i	$0.0978234\pi$
$401$			12.1154i			0.605013i	−0.953147	+	0.302506i	$0.902177\pi$
$402$		0			0
$403$	−6.67847			−0.332678
$404$	38.2969	−	4.69389i	1.90534	−	0.233530i
$405$		0			0
$406$	6.49709	+	5.74939i	0.322445	+	0.285338i
$407$	−10.4670			−0.518829
$408$		0			0
$409$	5.35379			0.264728			0.132364	−	0.991201i	$-0.457743\pi$
$409$	5.35379			0.264728			0.132364	+	0.991201i	$0.457743\pi$
$410$	7.22160	+	6.39052i	0.356649	+	0.315605i
$411$		0			0
$412$	2.76341	+	22.5464i	0.136144	+	1.11078i
$413$	17.1520			0.843995
$414$		0			0
$415$		−	54.4342i		−	2.67207i
$416$	12.6879	+	6.61358i	0.622073	+	0.324257i
$417$		0			0
$418$	−6.74963	−	5.97286i	−0.330135	−	0.292142i
$419$	18.3063			0.894322			0.447161	−	0.894454i	$-0.352435\pi$
$419$	18.3063			0.894322			0.447161	+	0.894454i	$0.352435\pi$
$420$		0			0
$421$		−	2.57989i		−	0.125736i	−0.998022	−	0.0628682i	$-0.979975\pi$
$421$		−	2.57989i		−	0.125736i	0.998022	−	0.0628682i	$-0.0200248\pi$
$422$	−22.4673	+	25.3891i	−1.09369	+	1.23592i
$423$		0			0
$424$	−6.31348	+	9.17981i	−0.306610	+	0.445811i
$425$	−10.0503	−	46.3808i	−0.487512	−	2.24980i
$426$		0			0
$427$		−	9.34425i		−	0.452200i
$428$	0.131183	+	1.07031i	0.00634097	+	0.0517353i
$429$		0			0
$430$	46.9122	+	41.5134i	2.26231	+	2.00196i
$431$		−	23.8390i		−	1.14829i	−0.818755	−	0.574143i	$-0.805335\pi$
$431$		−	23.8390i		−	1.14829i	0.818755	−	0.574143i	$-0.194665\pi$
$432$		0			0
$433$	19.7075			0.947084			0.473542	−	0.880771i	$-0.342975\pi$
$433$	19.7075			0.947084			0.473542	+	0.880771i	$0.342975\pi$
$434$	−3.30294	+	3.73248i	−0.158546	+	0.179165i
$435$		0			0
$436$	−2.21465	−	18.0691i	−0.106062	−	0.865353i
$437$	14.2090			0.679711
$438$		0			0
$439$			11.3880i			0.543518i	0.962365	+	0.271759i	$0.0876054\pi$
$439$			11.3880i			0.543518i	−0.962365	+	0.271759i	$0.912395\pi$
$440$	13.0942	+	9.00561i	0.624240	+	0.429326i
$441$		0			0
$442$	−7.21307	+	12.8642i	−0.343091	+	0.611888i
$443$		−	3.77327i		−	0.179273i	−0.995975	−	0.0896367i	$-0.971429\pi$
$443$		−	3.77327i		−	0.179273i	0.995975	−	0.0896367i	$-0.0285706\pi$
$444$		0			0
$445$	−43.9934			−2.08549
$446$	16.5142	−	18.6618i	0.781970	−	0.883664i
$447$		0			0
$448$	9.97119	−	3.82018i	0.471094	−	0.180486i
$449$			16.5349i			0.780331i	0.920745	+	0.390165i	$0.127582\pi$
$449$			16.5349i			0.780331i	−0.920745	+	0.390165i	$0.872418\pi$
$450$		0			0
$451$		−	2.32055i		−	0.109270i
$452$	−12.9667	+	1.58927i	−0.609904	+	0.0747532i
$453$		0			0
$454$	13.8508	−	15.6521i	0.650051	−	0.734589i
$455$	−13.7176			−0.643091
$456$		0			0
$457$	−7.78148			−0.364002			−0.182001	−	0.983298i	$-0.558257\pi$
$457$	−7.78148			−0.364002			−0.182001	+	0.983298i	$0.558257\pi$
$458$	23.0292	+	20.3790i	1.07609	+	0.952247i
$459$		0			0
$460$	−24.8681	+	3.04798i	−1.15948	+	0.142113i
$461$		−	9.02457i		−	0.420316i	−0.977667	−	0.210158i	$-0.932602\pi$
$461$		−	9.02457i		−	0.420316i	0.977667	−	0.210158i	$-0.0673978\pi$
$462$		0			0
$463$	4.13029			0.191951			0.0959754	−	0.995384i	$-0.469403\pi$
$463$	4.13029			0.191951			0.0959754	+	0.995384i	$0.469403\pi$
$464$	17.8403	−	4.43992i	0.828217	−	0.206118i
$465$		0			0
$466$	11.1112	+	9.83253i	0.514718	+	0.455483i
$467$		−	26.5850i		−	1.23021i	−0.788447	−	0.615103i	$-0.789115\pi$
$467$		−	26.5850i		−	1.23021i	0.788447	−	0.615103i	$-0.210885\pi$
$468$		0			0
$469$	−2.68399			−0.123935
$470$	8.36651	−	9.45457i	0.385918	−	0.436107i
$471$		0			0
$472$	20.5966	−	29.9474i	0.948034	−	1.37844i
$473$		−	15.0745i		−	0.693127i
$474$		0			0
$475$			53.0477i			2.43399i
$476$	3.62225	+	10.3934i	0.166026	+	0.476383i
$477$		0			0
$478$	−13.8334	+	15.6325i	−0.632727	+	0.715012i
$479$			9.58908i			0.438136i	0.975710	+	0.219068i	$0.0703017\pi$
$479$			9.58908i			0.438136i	−0.975710	+	0.219068i	$0.929698\pi$
$480$		0			0
$481$		−	19.1455i		−	0.872958i
$482$	−23.0594	−	20.4057i	−1.05033	−	0.929454i
$483$		0			0
$484$	2.21117	+	18.0407i	0.100508	+	0.820031i
$485$			48.1023i			2.18421i
$486$		0			0
$487$			11.3135i			0.512663i	0.966589	+	0.256331i	$0.0825138\pi$
$487$			11.3135i			0.512663i	−0.966589	+	0.256331i	$0.917486\pi$
$488$	−16.3151	−	11.2208i	−0.738549	−	0.507943i
$489$		0			0
$490$	19.8724	−	22.4567i	0.897742	−	1.01449i
$491$			12.2851i			0.554421i	0.960809	+	0.277210i	$0.0894099\pi$
$491$			12.2851i			0.554421i	−0.960809	+	0.277210i	$0.910590\pi$
$492$		0			0
$493$	4.01323	+	18.5205i	0.180747	+	0.834121i
$494$	10.9252	−	12.3460i	0.491546	−	0.555471i
$495$		0			0
$496$	2.55067	+	10.2490i	0.114528	+	0.460194i
$497$	−4.51345			−0.202456
$498$		0			0
$499$	7.65944			0.342884			0.171442	−	0.985194i	$-0.445157\pi$
$499$	7.65944			0.342884			0.171442	+	0.985194i	$0.445157\pi$
$500$	−6.43607	−	52.5112i	−0.287830	−	2.34837i
$501$		0			0
$502$	19.0666	+	16.8724i	0.850983	+	0.753050i
$503$			39.8142i			1.77523i	0.460589	+	0.887614i	$0.347638\pi$
$503$			39.8142i			1.77523i	−0.460589	+	0.887614i	$0.652362\pi$
$504$		0			0
$505$			78.3874i			3.48819i
$506$	4.51510	+	3.99549i	0.200721	+	0.177621i
$507$		0			0
$508$	3.06494	+	25.0065i	0.135985	+	1.10949i
$509$		−	25.2357i		−	1.11855i	−0.828982	−	0.559275i	$-0.811079\pi$
$509$		−	25.2357i		−	1.11855i	0.828982	−	0.559275i	$-0.188921\pi$
$510$		0			0
$511$	−16.9487			−0.749767
$512$	5.30362	−	21.9971i	0.234389	−	0.972143i
$513$		0			0
$514$	−4.16600	+	4.70779i	−0.183755	+	0.207652i
$515$	−46.1487			−2.03355
$516$		0			0
$517$	−3.03808			−0.133615
$518$	−10.7001	−	9.46868i	−0.470134	−	0.416030i
$519$		0			0
$520$	−16.4724	+	23.9510i	−0.722365	+	1.05032i
$521$		−	25.5294i		−	1.11846i	−0.829012	−	0.559231i	$-0.811096\pi$
$521$		−	25.5294i		−	1.11846i	0.829012	−	0.559231i	$-0.188904\pi$
$522$		0			0
$523$			4.68453i			0.204840i	0.994741	+	0.102420i	$0.0326586\pi$
$523$			4.68453i			0.204840i	−0.994741	+	0.102420i	$0.967341\pi$
$524$	3.67212	+	29.9604i	0.160417	+	1.30883i
$525$		0			0
$526$	17.5444	−	19.8260i	0.764972	−	0.864456i
$527$	−10.6397	+	2.30554i	−0.463475	+	0.100431i
$528$		0			0
$529$	13.4950			0.586739
$530$	−16.9510	−	15.0002i	−0.736305	−	0.651569i
$531$		0			0
$532$	−1.49674	−	12.2118i	−0.0648920	−	0.529447i
$533$	4.24459			0.183854
$534$		0			0
$535$	−2.19074			−0.0947140
$536$	−3.22300	+	4.68625i	−0.139213	+	0.202415i
$537$		0			0
$538$	8.74911	−	9.88692i	0.377201	−	0.426255i
$539$	−7.21613			−0.310821
$540$		0			0
$541$	−30.5595			−1.31386			−0.656929	−	0.753953i	$-0.728145\pi$
$541$	−30.5595			−1.31386			−0.656929	+	0.753953i	$0.728145\pi$
$542$	11.3303	−	12.8038i	0.486679	−	0.549971i
$543$		0			0
$544$	22.4967	+	6.15626i	0.964537	+	0.263947i
$545$	36.9844			1.58424
$546$		0			0
$547$	−19.1292			−0.817904			−0.408952	−	0.912556i	$-0.634106\pi$
$547$	−19.1292			−0.817904			−0.408952	+	0.912556i	$0.634106\pi$
$548$	0.274795	+	2.24202i	0.0117387	+	0.0957745i
$549$		0			0
$550$	−14.9167	+	16.8566i	−0.636049	+	0.718766i
$551$		−	21.1827i		−	0.902412i
$552$		0			0
$553$	13.4695			0.572780
$554$	19.9599	−	22.5556i	0.848013	−	0.958296i
$555$		0			0
$556$	−2.59163	−	21.1448i	−0.109909	−	0.896740i
$557$		−	14.9766i		−	0.634581i	−0.948328	−	0.317290i	$-0.897227\pi$
$557$		−	14.9766i		−	0.634581i	0.948328	−	0.317290i	$-0.102773\pi$
$558$		0			0
$559$	27.5733			1.16622
$560$	5.23908	+	21.0515i	0.221391	+	0.889587i
$561$		0			0
$562$	−6.90940	+	7.80796i	−0.291455	+	0.329359i
$563$		−	16.9215i		−	0.713157i	−0.934265	−	0.356578i	$-0.883943\pi$
$563$		−	16.9215i		−	0.713157i	0.934265	−	0.356578i	$-0.116057\pi$
$564$		0			0
$565$		−	26.5407i		−	1.11658i
$566$	−20.9411	+	23.6644i	−0.880218	+	0.994690i
$567$		0			0
$568$	−5.41987	+	7.88050i	−0.227413	+	0.330658i
$569$	−2.45534			−0.102933			−0.0514667	−	0.998675i	$-0.516390\pi$
$569$	−2.45534			−0.102933			−0.0514667	+	0.998675i	$0.516390\pi$
$570$		0			0
$571$	−16.2429			−0.679744			−0.339872	−	0.940472i	$-0.610384\pi$
$571$	−16.2429			−0.679744			−0.339872	+	0.940472i	$0.610384\pi$
$572$	6.94321	−	0.850998i	0.290310	−	0.0355820i
$573$		0			0
$574$	2.09923	−	2.37223i	0.0876200	−	0.0990149i
$575$		−	35.4858i		−	1.47986i
$576$		0			0
$577$	−19.8321			−0.825619			−0.412810	−	0.910817i	$-0.635453\pi$
$577$	−19.8321			−0.825619			−0.412810	+	0.910817i	$0.635453\pi$
$578$	−7.05044	+	22.9846i	−0.293260	+	0.956033i
$579$		0			0
$580$	4.54388	+	37.0731i	0.188675	+	1.53938i
$581$	−17.8811			−0.741834
$582$		0			0
$583$			5.44695i			0.225589i
$584$	−20.3525	+	29.5925i	−0.842191	+	1.22455i
$585$		0			0
$586$	−0.872239	−	0.771860i	−0.0360319	−	0.0318852i
$587$			16.1112i			0.664982i	0.943106	+	0.332491i	$0.107889\pi$
$587$			16.1112i			0.664982i	−0.943106	+	0.332491i	$0.892111\pi$
$588$		0			0
$589$	12.1691			0.501420
$590$	55.2996	+	48.9356i	2.27665	+	2.01465i
$591$		0			0
$592$	−29.3813	+	7.31211i	−1.20756	+	0.300526i
$593$	−27.2516			−1.11909			−0.559544	−	0.828801i	$-0.689024\pi$
$593$	−27.2516			−1.11909			−0.559544	+	0.828801i	$0.689024\pi$
$594$		0			0
$595$	−21.8541	+	4.73559i	−0.895929	+	0.194140i
$596$	−0.556206	+	0.0681717i	−0.0227831	+	0.00279242i
$597$		0			0
$598$	−7.30828	+	8.25871i	−0.298858	+	0.337724i
$599$	−20.5532			−0.839780			−0.419890	−	0.907575i	$-0.637931\pi$
$599$	−20.5532			−0.839780			−0.419890	+	0.907575i	$0.637931\pi$
$600$		0			0
$601$		−	9.92222i		−	0.404736i	−0.979310	−	0.202368i	$-0.935136\pi$
$601$		−	9.92222i		−	0.404736i	0.979310	−	0.202368i	$-0.0648637\pi$
$602$	13.6368	−	15.4102i	0.555793	−	0.628074i
$603$		0			0
$604$	−2.30745	−	18.8262i	−0.0938887	−	0.766028i
$605$	−36.9263			−1.50127
$606$		0			0
$607$		−	21.2113i		−	0.860938i	−0.902605	−	0.430469i	$-0.858348\pi$
$607$		−	21.2113i		−	0.860938i	0.902605	−	0.430469i	$-0.141652\pi$
$608$	−23.1191	−	12.0509i	−0.937602	−	0.488728i
$609$		0			0
$610$	26.6596	−	30.1267i	1.07942	−	1.21979i
$611$		−	5.55704i		−	0.224814i
$612$		0			0
$613$			5.72825i			0.231362i	0.993286	+	0.115681i	$0.0369050\pi$
$613$			5.72825i			0.231362i	−0.993286	+	0.115681i	$0.963095\pi$
$614$	−1.96672	−	1.74039i	−0.0793705	−	0.0702364i
$615$		0			0
$616$	2.95826	−	4.30131i	0.119192	−	0.173305i
$617$			28.9519i			1.16556i	0.812631	+	0.582779i	$0.198035\pi$
$617$			28.9519i			1.16556i	−0.812631	+	0.582779i	$0.801965\pi$
$618$		0			0
$619$	−33.2069			−1.33470			−0.667349	−	0.744746i	$-0.732571\pi$
$619$	−33.2069			−1.33470			−0.667349	+	0.744746i	$0.732571\pi$
$620$	−21.2979	+	2.61039i	−0.855346	+	0.104836i
$621$		0			0
$622$	−5.26266	−	4.65702i	−0.211014	−	0.186730i
$623$			14.4514i			0.578984i
$624$		0			0
$625$	49.9313			1.99725
$626$	4.81317	+	4.25926i	0.192373	+	0.170234i
$627$		0			0
$628$	47.0163	−	5.76258i	1.87615	−	0.229952i
$629$	−6.60940	−	30.5014i	−0.263534	−	1.21617i
$630$		0			0
$631$	−9.18742			−0.365745			−0.182873	−	0.983137i	$-0.558540\pi$
$631$	−9.18742			−0.365745			−0.182873	+	0.983137i	$0.558540\pi$
$632$	16.1745	−	23.5177i	0.643386	−	0.935484i
$633$		0			0
$634$	−23.0133	+	26.0062i	−0.913977	+	1.03284i
$635$	−51.1842			−2.03118
$636$		0			0
$637$		−	13.1992i		−	0.522973i
$638$	5.95643	−	6.73106i	0.235817	−	0.266485i
$639$		0			0
$640$	43.0471	+	16.1317i	1.70159	+	0.637662i
$641$		−	1.98751i		−	0.0785019i	−0.999229	−	0.0392509i	$-0.987503\pi$
$641$		−	1.98751i		−	0.0785019i	0.999229	−	0.0392509i	$-0.0124972\pi$
$642$		0			0
$643$	15.6525			0.617274			0.308637	−	0.951180i	$-0.400127\pi$
$643$	15.6525			0.617274			0.308637	+	0.951180i	$0.400127\pi$
$644$	1.00123	+	8.16894i	0.0394540	+	0.321902i
$645$		0			0
$646$	13.1432	−	23.4404i	0.517113	−	0.922251i
$647$	50.3006			1.97752			0.988760	−	0.149512i	$-0.0477703\pi$
$647$	50.3006			1.97752			0.988760	+	0.149512i	$0.0477703\pi$
$648$		0			0
$649$		−	17.7697i		−	0.697520i
$650$	−30.8329	−	27.2845i	−1.20936	−	1.07019i
$651$		0			0
$652$	−4.48217	−	36.5696i	−0.175535	−	1.43217i
$653$	−9.17554			−0.359067			−0.179533	−	0.983752i	$-0.557459\pi$
$653$	−9.17554			−0.359067			−0.179533	+	0.983752i	$0.557459\pi$
$654$		0			0
$655$	−61.3240			−2.39613
$656$	−1.62111	−	6.51388i	−0.0632937	−	0.254324i
$657$		0			0
$658$	−3.10574	−	2.74832i	−0.121074	−	0.107141i
$659$		−	20.4499i		−	0.796616i	−0.917252	−	0.398308i	$-0.869597\pi$
$659$		−	20.4499i		−	0.796616i	0.917252	−	0.398308i	$-0.130403\pi$
$660$		0			0
$661$		−	41.2625i		−	1.60492i	−0.596703	−	0.802462i	$-0.703523\pi$
$661$		−	41.2625i		−	1.60492i	0.596703	−	0.802462i	$-0.296477\pi$
$662$	−25.3841	−	22.4629i	−0.986583	−	0.873044i
$663$		0			0
$664$	−21.4721	+	31.2205i	−0.833280	+	1.21159i
$665$	24.9954			0.969281
$666$		0			0
$667$			14.1700i			0.548663i
$668$	−19.6395	+	2.40713i	−0.759876	+	0.0931346i
$669$		0			0
$670$	−8.65341	−	7.65756i	−0.334310	−	0.295837i
$671$	−9.68074			−0.373721
$672$		0			0
$673$		−	23.7133i		−	0.914079i	−0.889446	−	0.457040i	$-0.848910\pi$
$673$		−	23.7133i		−	0.914079i	0.889446	−	0.457040i	$-0.151090\pi$
$674$	−33.0257	−	29.2250i	−1.27210	−	1.12570i
$675$		0			0
$676$	−1.60645	−	13.1068i	−0.0617865	−	0.504110i
$677$	−14.9173			−0.573317			−0.286659	−	0.958033i	$-0.592545\pi$
$677$	−14.9173			−0.573317			−0.286659	+	0.958033i	$0.592545\pi$
$678$		0			0
$679$	15.8011			0.606392
$680$	−17.9746	+	43.8439i	−0.689294	+	1.68134i
$681$		0			0
$682$	3.86689	+	3.42188i	0.148071	+	0.131031i
$683$	7.24088			0.277065			0.138532	−	0.990358i	$-0.455762\pi$
$683$	7.24088			0.277065			0.138532	+	0.990358i	$0.455762\pi$
$684$		0			0
$685$	−4.58905			−0.175338
$686$	−17.2720	−	15.2843i	−0.659450	−	0.583559i
$687$		0			0
$688$	−10.5309	−	42.3148i	−0.401486	−	1.61324i
$689$	−9.96318			−0.379567
$690$		0			0
$691$	17.5509			0.667666			0.333833	−	0.942632i	$-0.391658\pi$
$691$	17.5509			0.667666			0.333833	+	0.942632i	$0.391658\pi$
$692$	−4.51306	−	36.8216i	−0.171561	−	1.39975i
$693$		0			0
$694$	−27.8885	+	31.5154i	−1.05863	+	1.19631i
$695$	43.2799			1.64170
$696$		0			0
$697$	6.76223	−	1.46532i	0.256138	−	0.0555028i
$698$	18.3249	+	16.2161i	0.693610	+	0.613787i
$699$		0			0
$700$	−30.4977	+	3.73797i	−1.15271	+	0.141282i
$701$			22.1815i			0.837783i	0.908036	+	0.418891i	$0.137581\pi$
$701$			22.1815i			0.837783i	−0.908036	+	0.418891i	$0.862419\pi$
$702$		0			0
$703$			34.8858i			1.31574i
$704$	−3.95774	−	10.3303i	−0.149163	−	0.389336i
$705$		0			0
$706$	−15.4199	+	17.4253i	−0.580336	+	0.655808i
$707$	25.7495			0.968410
$708$		0			0
$709$	4.78270			0.179618			0.0898091	−	0.995959i	$-0.471374\pi$
$709$	4.78270			0.179618			0.0898091	+	0.995959i	$0.471374\pi$
$710$	−14.5518	−	12.8771i	−0.546118	−	0.483270i
$711$		0			0
$712$	25.2322	+	17.3537i	0.945618	+	0.650356i
$713$	−8.14043			−0.304861
$714$		0			0
$715$			14.2116i			0.531483i
$716$	−19.2259	+	2.35644i	−0.718506	+	0.0880641i
$717$		0			0
$718$	−21.8229	+	24.6609i	−0.814422	+	0.920336i
$719$		−	40.8961i		−	1.52517i	−0.646889	−	0.762584i	$-0.723930\pi$
$719$		−	40.8961i		−	1.52517i	0.646889	−	0.762584i	$-0.276070\pi$
$720$		0			0
$721$			15.1594i			0.564566i
$722$	−2.10037	+	2.37352i	−0.0781677	+	0.0883333i
$723$		0			0
$724$	1.51539	+	12.3639i	0.0563192	+	0.459502i
$725$	−52.9017			−1.96472
$726$		0			0
$727$	−10.7907			−0.400204			−0.200102	−	0.979775i	$-0.564127\pi$
$727$	−10.7907			−0.400204			−0.200102	+	0.979775i	$0.564127\pi$
$728$	7.86766	+	5.41104i	0.291595	+	0.200547i
$729$		0			0
$730$	−54.6441	−	48.3556i	−2.02247	−	1.78972i
$731$	43.9281	−	9.51884i	1.62474	−	0.352067i
$732$		0			0
$733$		−	8.86600i		−	0.327473i	−0.986504	−	0.163737i	$-0.947645\pi$
$733$		−	8.86600i		−	0.327473i	0.986504	−	0.163737i	$-0.0523547\pi$
$734$	−4.86170	−	4.30220i	−0.179449	−	0.158797i
$735$		0			0
$736$	15.4653	+	8.06133i	0.570058	+	0.297145i
$737$			2.78064i			0.102426i
$738$		0			0
$739$		−	14.2082i		−	0.522656i	−0.965250	−	0.261328i	$-0.915840\pi$
$739$		−	14.2082i		−	0.522656i	0.965250	−	0.261328i	$-0.0841604\pi$
$740$	−7.48333	−	61.0557i	−0.275093	−	2.24445i
$741$		0			0
$742$	−4.92744	+	5.56825i	−0.180892	+	0.204417i
$743$		−	33.9021i		−	1.24375i	−0.783118	−	0.621874i	$-0.786372\pi$
$743$		−	33.9021i		−	1.24375i	0.783118	−	0.621874i	$-0.213628\pi$
$744$		0			0
$745$		−	1.13846i		−	0.0417099i
$746$	−16.3074	−	14.4307i	−0.597057	−	0.528347i
$747$		0			0
$748$	10.7677	−	3.75269i	0.393707	−	0.137212i
$749$			0.719638i			0.0262950i
$750$		0			0
$751$		−	0.832425i		−	0.0303756i	−0.999885	−	0.0151878i	$-0.995165\pi$
$751$		−	0.832425i		−	0.0303756i	0.999885	−	0.0151878i	$-0.00483462\pi$
$752$	−8.52802	+	2.12237i	−0.310985	+	0.0773947i
$753$		0			0
$754$	12.3120	+	10.8951i	0.448376	+	0.396776i
$755$	38.5341			1.40240
$756$		0			0
$757$			26.1220i			0.949420i	0.880142	+	0.474710i	$0.157447\pi$
$757$			26.1220i			0.949420i	−0.880142	+	0.474710i	$0.842553\pi$
$758$	−1.72592	+	1.95037i	−0.0626882	+	0.0708408i
$759$		0			0
$760$	30.0151	−	43.6420i	1.08876	−	1.58306i
$761$	36.9537			1.33957			0.669784	−	0.742556i	$-0.266386\pi$
$761$	36.9537			1.33957			0.669784	+	0.742556i	$0.266386\pi$
$762$		0			0
$763$		−	12.1490i		−	0.439824i
$764$	−4.51985	−	36.8770i	−0.163523	−	1.33416i
$765$		0			0
$766$	−32.0387	+	36.2053i	−1.15761	+	1.30815i
$767$	32.5030			1.17362
$768$		0			0
$769$	−51.3629			−1.85219			−0.926097	−	0.377285i	$-0.876858\pi$
$769$	−51.3629			−1.85219			−0.926097	+	0.377285i	$0.876858\pi$
$770$	7.94260	+	7.02855i	0.286232	+	0.253291i
$771$		0			0
$772$	27.0124	−	3.31079i	0.972196	−	0.119158i
$773$			47.0804i			1.69336i	0.532100	+	0.846682i	$0.321403\pi$
$773$			47.0804i			1.69336i	−0.532100	+	0.846682i	$0.678597\pi$
$774$		0			0
$775$		−	30.3913i		−	1.09169i
$776$	18.9744	−	27.5888i	0.681142	−	0.990381i
$777$		0			0
$778$	10.7720	+	9.53232i	0.386194	+	0.341750i
$779$	−7.73424			−0.277108
$780$		0			0
$781$			4.67599i			0.167320i
$782$	−8.79205	+	15.6803i	−0.314403	+	0.560725i
$783$		0			0
$784$	−20.2560	+	5.04110i	−0.723428	+	0.180039i
$785$			96.2345i			3.43476i
$786$		0			0
$787$	21.2273			0.756671			0.378336	−	0.925669i	$-0.376497\pi$
$787$	21.2273			0.756671			0.378336	+	0.925669i	$0.376497\pi$
$788$	1.91880	+	15.6553i	0.0683546	+	0.557698i
$789$		0			0
$790$	43.4267	+	38.4291i	1.54505	+	1.36724i
$791$	−8.71838			−0.309990
$792$		0			0
$793$		−	17.7074i		−	0.628807i
$794$	−22.6044	+	25.5441i	−0.802202	+	0.906527i
$795$		0			0
$796$	39.1618	−	4.79989i	1.38805	−	0.170128i
$797$		−	1.24847i		−	0.0442232i	−0.999756	−	0.0221116i	$-0.992961\pi$
$797$		−	1.24847i		−	0.0442232i	0.999756	−	0.0221116i	$-0.00703891\pi$
$798$		0			0
$799$	−1.91840	−	8.85315i	−0.0678682	−	0.313202i
$800$	−30.0960	+	57.7377i	−1.06405	+	2.04134i
$801$		0			0
$802$	12.8312	+	11.3545i	0.453085	+	0.400943i
$803$			17.5591i			0.619645i
$804$		0			0
$805$	−16.7205			−0.589319
$806$	−6.25907	+	7.07305i	−0.220466	+	0.249138i
$807$		0			0
$808$	30.9207	−	44.9587i	1.08779	−	1.58164i
$809$		−	3.89688i		−	0.137007i	−0.997651	−	0.0685034i	$-0.978178\pi$
$809$		−	3.89688i		−	0.137007i	0.997651	−	0.0685034i	$-0.0218224\pi$
$810$		0			0
$811$	−39.7545			−1.39597			−0.697985	−	0.716112i	$-0.745920\pi$
$811$	−39.7545			−1.39597			−0.697985	+	0.716112i	$0.745920\pi$
$812$	12.1782	−	1.49262i	0.427370	−	0.0523808i
$813$		0			0
$814$	−9.80965	+	11.0854i	−0.343828	+	0.388543i
$815$	74.8517			2.62194
$816$		0			0
$817$	−50.2424			−1.75776
$818$	5.01757	−	5.67010i	0.175435	−	0.198250i
$819$		0			0
$820$	13.5362	−	1.65907i	0.472704	−	0.0579372i
$821$	−7.68119			−0.268076			−0.134038	−	0.990976i	$-0.542794\pi$
$821$	−7.68119			−0.268076			−0.134038	+	0.990976i	$0.542794\pi$
$822$		0			0
$823$		−	23.9730i		−	0.835647i	−0.908528	−	0.417824i	$-0.862793\pi$
$823$		−	23.9730i		−	0.835647i	0.908528	−	0.417824i	$-0.137207\pi$
$824$	26.4684	+	18.2038i	0.922069	+	0.634160i
$825$		0			0
$826$	16.0749	−	18.1654i	0.559316	−	0.632055i
$827$	53.2001			1.84995			0.924974	−	0.380030i	$-0.124086\pi$
$827$	53.2001			1.84995			0.924974	+	0.380030i	$0.124086\pi$
$828$		0			0
$829$			5.80159i			0.201498i	0.994912	+	0.100749i	$0.0321238\pi$
$829$			5.80159i			0.201498i	−0.994912	+	0.100749i	$0.967876\pi$
$830$	−57.6503	−	51.0158i	−2.00107	−	1.77078i
$831$		0			0
$832$	18.8954	−	7.23923i	0.655080	−	0.250975i
$833$	−4.55664	−	21.0282i	−0.157878	−	0.728586i
$834$		0			0
$835$		−	40.1988i		−	1.39114i
$836$	−12.6515	+	1.55064i	−0.437562	+	0.0536300i
$837$		0			0
$838$	17.1567	−	19.3879i	0.592668	−	0.669743i
$839$			21.8766i			0.755264i	0.925956	+	0.377632i	$0.123262\pi$
$839$			21.8766i			0.755264i	−0.925956	+	0.377632i	$0.876738\pi$
$840$		0			0
$841$	−7.87561			−0.271573
$842$	−2.73232	−	2.41788i	−0.0941620	−	0.0833256i
$843$		0			0
$844$	5.83282	+	47.5893i	0.200774	+	1.63809i
$845$	26.8275			0.922895
$846$		0			0
$847$			12.1299i			0.416789i
$848$	3.80517	+	15.2898i	0.130670	+	0.525055i
$849$		0			0
$850$	−58.5403	−	32.8240i	−2.00791	−	1.12585i
$851$		−	23.3365i		−	0.799966i
$852$		0			0
$853$	−13.3416			−0.456809			−0.228405	−	0.973566i	$-0.573351\pi$
$853$	−13.3416			−0.456809			−0.228405	+	0.973566i	$0.573351\pi$
$854$	−9.89633	−	8.75744i	−0.338646	−	0.299673i
$855$		0			0
$856$	1.25649	+	0.864160i	0.0429459	+	0.0295364i
$857$			0.322155i			0.0110046i	0.999985	+	0.00550230i	$0.00175145\pi$
$857$			0.322155i			0.0110046i	−0.999985	+	0.00550230i	$0.998249\pi$
$858$		0			0
$859$		−	28.0802i		−	0.958085i	−0.877792	−	0.479043i	$-0.840984\pi$
$859$		−	28.0802i		−	0.958085i	0.877792	−	0.479043i	$-0.159016\pi$
$860$	87.9323	−	10.7775i	2.99847	−	0.367509i
$861$		0			0
$862$	−25.2475	−	22.3419i	−0.859933	−	0.760970i
$863$	27.1517			0.924255			0.462127	−	0.886814i	$-0.347086\pi$
$863$	27.1517			0.924255			0.462127	+	0.886814i	$0.347086\pi$
$864$		0			0
$865$	75.3676			2.56258
$866$	18.4699	−	20.8719i	0.627633	−	0.709256i
$867$		0			0
$868$	0.857490	+	6.99617i	0.0291051	+	0.237466i
$869$		−	13.9545i		−	0.473374i
$870$		0			0
$871$	−5.08616			−0.172338
$872$	−21.2122	−	14.5889i	−0.718337	−	0.494042i
$873$		0			0
$874$	13.3167	−	15.0486i	0.450445	−	0.509025i
$875$		−	35.3067i		−	1.19358i
$876$		0			0
$877$	−25.4455			−0.859233			−0.429617	−	0.903011i	$-0.641351\pi$
$877$	−25.4455			−0.859233			−0.429617	+	0.903011i	$0.641351\pi$
$878$	12.0608	+	10.6728i	0.407032	+	0.360190i
$879$		0			0
$880$	21.8095	−	5.42774i	0.735200	−	0.182969i
$881$		−	15.2859i		−	0.514995i	−0.966279	−	0.257498i	$-0.917102\pi$
$881$		−	15.2859i		−	0.514995i	0.966279	−	0.257498i	$-0.0828979\pi$
$882$		0			0
$883$			13.6008i			0.457703i	0.973461	+	0.228852i	$0.0734970\pi$
$883$			13.6008i			0.457703i	−0.973461	+	0.228852i	$0.926503\pi$
$884$	6.86417	+	19.6956i	0.230867	+	0.662434i
$885$		0			0
$886$	−3.99620	−	3.53631i	−0.134255	−	0.118805i
$887$		−	22.2405i		−	0.746764i	−0.927678	−	0.373382i	$-0.878198\pi$
$887$		−	22.2405i		−	0.746764i	0.927678	−	0.373382i	$-0.121802\pi$
$888$		0			0
$889$			16.8135i			0.563908i
$890$	−41.2307	+	46.5927i	−1.38206	+	1.56179i
$891$		0			0
$892$	−4.28732	−	34.9798i	−0.143550	−	1.17121i
$893$			10.1257i			0.338844i
$894$		0			0
$895$		−	39.3522i		−	1.31540i
$896$	5.29912	−	14.1406i	0.177031	−	0.472404i
$897$		0			0
$898$	17.5118	+	15.4965i	0.584377	+	0.517126i
$899$			12.1356i			0.404747i
$900$		0			0
$901$	−15.8727	+	3.43949i	−0.528798	+	0.114586i
$902$	−2.45765	−	2.17482i	−0.0818309	−	0.0724136i
$903$		0			0
$904$	−10.4693	+	15.2223i	−0.348202	+	0.506286i
$905$	−25.3069			−0.841230
$906$		0			0
$907$	−1.22779			−0.0407680			−0.0203840	−	0.999792i	$-0.506489\pi$
$907$	−1.22779			−0.0407680			−0.0203840	+	0.999792i	$0.506489\pi$
$908$	−3.59587	−	29.3383i	−0.119333	−	0.973626i
$909$		0			0
$910$	−12.8561	+	14.5281i	−0.426177	+	0.481601i
$911$		−	4.50510i		−	0.149261i	−0.997211	−	0.0746304i	$-0.976222\pi$
$911$		−	4.50510i		−	0.149261i	0.997211	−	0.0746304i	$-0.0237777\pi$
$912$		0			0
$913$			18.5250i			0.613089i
$914$	−7.29281	+	8.24123i	−0.241225	+	0.272596i
$915$		0			0
$916$	43.1660	−	5.29067i	1.42625	−	0.174809i
$917$			20.1444i			0.665225i
$918$		0			0
$919$	24.2454			0.799781			0.399890	−	0.916563i	$-0.369048\pi$
$919$	24.2454			0.799781			0.399890	+	0.916563i	$0.369048\pi$
$920$	−20.0784	+	29.1940i	−0.661964	+	0.962496i
$921$		0			0
$922$	−9.55776	−	8.45783i	−0.314768	−	0.278544i
$923$	−8.55299			−0.281525
$924$		0			0
$925$	87.1239			2.86462
$926$	3.87091	−	4.37431i	0.127206	−	0.143749i
$927$		0			0
$928$	12.0177	−	23.0555i	0.394501	−	0.756833i
$929$		−	55.5044i		−	1.82104i	−0.413463	−	0.910521i	$-0.635681\pi$
$929$		−	55.5044i		−	1.82104i	0.413463	−	0.910521i	$-0.364319\pi$
$930$		0			0
$931$			24.0509i			0.788236i
$932$	20.8269	−	2.55266i	0.682209	−	0.0836153i
$933$		0			0
$934$	−28.1557	−	24.9154i	−0.921281	−	0.815258i
$935$	4.90612	+	22.6410i	0.160447	+	0.740441i
$936$		0			0
$937$	−18.5511			−0.606038			−0.303019	−	0.952985i	$-0.597995\pi$
$937$	−18.5511			−0.606038			−0.303019	+	0.952985i	$0.597995\pi$
$938$	−2.51544	+	2.84256i	−0.0821319	+	0.0928130i
$939$		0			0
$940$	−2.17206	−	17.7216i	−0.0708449	−	0.578016i
$941$	−35.9106			−1.17065			−0.585327	−	0.810798i	$-0.699034\pi$
$941$	−35.9106			−1.17065			−0.585327	+	0.810798i	$0.699034\pi$
$942$		0			0
$943$	5.17375			0.168481
$944$	−12.4137	−	49.8802i	−0.404031	−	1.62346i
$945$		0			0
$946$	−15.9651	−	14.1278i	−0.519072	−	0.459336i
$947$	13.4238			0.436216			0.218108	−	0.975925i	$-0.430012\pi$
$947$	13.4238			0.436216			0.218108	+	0.975925i	$0.430012\pi$
$948$		0			0
$949$	−32.1178			−1.04259
$950$	56.1819	+	49.7163i	1.82278	+	1.61301i
$951$		0			0
$952$	14.4023	+	5.90448i	0.466781	+	0.191365i
$953$	−52.8115			−1.71073			−0.855366	−	0.518024i	$-0.826668\pi$
$953$	−52.8115			−1.71073			−0.855366	+	0.518024i	$0.826668\pi$
$954$		0			0
$955$	75.4811			2.44251
$956$	3.59135	+	29.3015i	0.116153	+	0.947678i
$957$		0			0
$958$	10.1556	+	8.98689i	0.328113	+	0.290353i
$959$			1.50746i			0.0486784i
$960$		0			0
$961$	24.0282			0.775105
$962$	−20.2766	−	17.9431i	−0.653745	−	0.578510i
$963$		0			0
$964$	−43.2226	+	5.29761i	−1.39211	+	0.170624i
$965$			55.2898i			1.77984i
$966$		0			0
$967$	−7.20225			−0.231609			−0.115804	−	0.993272i	$-0.536945\pi$
$967$	−7.20225			−0.231609			−0.115804	+	0.993272i	$0.536945\pi$
$968$	21.1789	+	14.5659i	0.680715	+	0.468167i
$969$		0			0
$970$	50.9442	+	45.0815i	1.63572	+	1.44748i
$971$		−	53.5069i		−	1.71712i	−0.512715	−	0.858559i	$-0.671360\pi$
$971$		−	53.5069i		−	1.71712i	0.512715	−	0.858559i	$-0.328640\pi$
$972$		0			0
$973$		−	14.2170i		−	0.455777i
$974$	11.9819	+	10.6030i	0.383925	+	0.339742i
$975$		0			0
$976$	−27.1743	+	6.76286i	−0.869828	+	0.216474i
$977$	0.640518			0.0204920			0.0102460	−	0.999948i	$-0.496739\pi$
$977$	0.640518			0.0204920			0.0102460	+	0.999948i	$0.496739\pi$
$978$		0			0
$979$	14.9718			0.478502
$980$	−5.15915	−	42.0929i	−0.164803	−	1.34461i
$981$		0			0
$982$	13.0110	+	11.5136i	0.415197	+	0.367415i
$983$			16.1739i			0.515866i	0.966163	+	0.257933i	$0.0830414\pi$
$983$			16.1739i			0.515866i	−0.966163	+	0.257933i	$0.916959\pi$
$984$		0			0
$985$	−32.0438			−1.02100
$986$	23.3759	+	13.1071i	0.744441	+	0.417414i
$987$		0			0
$988$	−2.83632	−	23.1413i	−0.0902355	−	0.736222i
$989$	33.6092			1.06871
$990$		0			0
$991$		−	4.18546i		−	0.132955i	−0.997788	−	0.0664777i	$-0.978824\pi$
$991$		−	4.18546i		−	0.132955i	0.997788	−	0.0664777i	$-0.0211761\pi$
$992$	13.2450	+	6.90401i	0.420530	+	0.219202i
$993$		0			0
$994$	−4.23001	+	4.78012i	−0.134168	+	0.151616i
$995$			80.1577i			2.54117i
$996$		0			0
$997$	36.1353			1.14442			0.572209	−	0.820108i	$-0.306087\pi$
$997$	36.1353			1.14442			0.572209	+	0.820108i	$0.306087\pi$
$998$	7.17843	−	8.11198i	0.227229	−	0.256780i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.2.l.c.1189.13		18
3.2	odd	2		408.2.l.a.373.6	yes	18
4.3	odd	2		4896.2.l.c.3025.18		18
8.3	odd	2		4896.2.l.d.3025.2		18
8.5	even	2		1224.2.l.d.1189.14		18
12.11	even	2		1632.2.l.b.1393.2		18
17.16	even	2		1224.2.l.d.1189.13		18
24.5	odd	2		408.2.l.b.373.5	yes	18
24.11	even	2		1632.2.l.a.1393.18		18
51.50	odd	2		408.2.l.b.373.6	yes	18
68.67	odd	2		4896.2.l.d.3025.1		18
136.67	odd	2		4896.2.l.c.3025.17		18
136.101	even	2	inner	1224.2.l.c.1189.14		18
204.203	even	2		1632.2.l.a.1393.17		18
408.101	odd	2		408.2.l.a.373.5	✓	18
408.203	even	2		1632.2.l.b.1393.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
408.2.l.a.373.5	✓	18	408.101	odd	2
408.2.l.a.373.6	yes	18	3.2	odd	2
408.2.l.b.373.5	yes	18	24.5	odd	2
408.2.l.b.373.6	yes	18	51.50	odd	2
1224.2.l.c.1189.13		18	1.1	even	1	trivial
1224.2.l.c.1189.14		18	136.101	even	2	inner
1224.2.l.d.1189.13		18	17.16	even	2
1224.2.l.d.1189.14		18	8.5	even	2
1632.2.l.a.1393.17		18	204.203	even	2
1632.2.l.a.1393.18		18	24.11	even	2
1632.2.l.b.1393.1		18	408.203	even	2
1632.2.l.b.1393.2		18	12.11	even	2
4896.2.l.c.3025.17		18	136.67	odd	2
4896.2.l.c.3025.18		18	4.3	odd	2
4896.2.l.d.3025.1		18	68.67	odd	2
4896.2.l.d.3025.2		18	8.3	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:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1224.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.937200 - 1.05908i) q^{2} +(-0.243310 - 1.98514i) q^{4} +4.06326 q^{5} -1.33474i q^{7} +(-2.33046 - 1.60279i) q^{8} +(3.80809 - 4.30332i) q^{10} -1.38281 q^{11} -2.52933i q^{13} +(-1.41360 - 1.25092i) q^{14} +(-3.88160 + 0.966013i) q^{16} +(-0.873177 - 4.02959i) q^{17} +4.60881i q^{19} +(-0.988633 - 8.06616i) q^{20} +(-1.29597 + 1.46451i) q^{22} -3.08302i q^{23} +11.5101 q^{25} +(-2.67877 - 2.37049i) q^{26} +(-2.64966 + 0.324757i) q^{28} -4.59613 q^{29} -2.64041i q^{31} +(-2.61475 + 5.01628i) q^{32} +(-5.08600 - 2.85176i) q^{34} -5.42340i q^{35} +7.56937 q^{37} +(4.88111 + 4.31938i) q^{38} +(-9.46927 - 6.51256i) q^{40} +1.67814i q^{41} +10.9014i q^{43} +(0.336451 + 2.74507i) q^{44} +(-3.26517 - 2.88941i) q^{46} +2.19704 q^{47} +5.21846 q^{49} +(10.7872 - 12.1901i) q^{50} +(-5.02110 + 0.615414i) q^{52} -3.93905i q^{53} -5.61870 q^{55} +(-2.13932 + 3.11057i) q^{56} +(-4.30749 + 4.86768i) q^{58} +12.8504i q^{59} +7.00079 q^{61} +(-2.79641 - 2.47459i) q^{62} +(2.86211 + 7.47050i) q^{64} -10.2773i q^{65} -2.01087i q^{67} +(-7.78686 + 2.71382i) q^{68} +(-5.74383 - 5.08281i) q^{70} -3.38152i q^{71} -12.6981i q^{73} +(7.09402 - 8.01658i) q^{74} +(9.14915 - 1.12137i) q^{76} +1.84569i q^{77} +10.0914i q^{79} +(-15.7719 + 3.92516i) q^{80} +(1.77729 + 1.57276i) q^{82} -13.3967i q^{83} +(-3.54794 - 16.3732i) q^{85} +(11.5455 + 10.2168i) q^{86} +(3.22258 + 2.21635i) q^{88} -10.8271 q^{89} -3.37601 q^{91} +(-6.12024 + 0.750131i) q^{92} +(2.05906 - 2.32684i) q^{94} +18.7268i q^{95} +11.8383i q^{97} +(4.89075 - 5.52678i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{4} - 4 q^{5} + 8 q^{10} - 6 q^{14} + 10 q^{16} + 2 q^{17} - 2 q^{20} - 2 q^{22} + 22 q^{25} - 2 q^{26} + 10 q^{28} + 12 q^{29} - 30 q^{34} + 16 q^{37} + 34 q^{38} + 10 q^{40} + 12 q^{44} - 32 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) \) 18 * q + 2 * q^4 - 4 * q^5 + 8 * q^10 - 6 * q^14 + 10 * q^16 + 2 * q^17 - 2 * q^20 - 2 * q^22 + 22 * q^25 - 2 * q^26 + 10 * q^28 + 12 * q^29 - 30 * q^34 + 16 * q^37 + 34 * q^38 + 10 * q^40 + 12 * q^44 - 32 * q^46 - 18 * q^49 + 14 * q^50 + 8 * q^52 - 16 * q^55 - 14 * q^56 + 6 * q^58 + 16 * q^61 - 6 * q^62 + 2 * q^64 - 12 * q^68 - 32 * q^70 - 6 * q^74 - 62 * q^80 - 34 * q^82 - 16 * q^85 - 14 * q^86 - 16 * q^88 - 20 * q^89 - 2 * q^92 + 12 * q^94 + 60 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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