LMFDB - Embedded newform 1368.2.e.g.379.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1368,2,Mod(379,1368)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1368, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("1368.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.e (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:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.6
Character	$\chi$	$=$	1368.379
Dual form			1368.2.e.g.379.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33983 + 0.452615i) q^{2} +(1.59028 - 1.21285i) q^{4} +0.393257i q^{5} -1.35370i q^{7} +(-1.58175 + 2.34480i) q^{8} +O(q^{10})$	\(q+(-1.33983 + 0.452615i) q^{2} +(1.59028 - 1.21285i) q^{4} +0.393257i q^{5} -1.35370i q^{7} +(-1.58175 + 2.34480i) q^{8} +(-0.177994 - 0.526897i) q^{10} -1.21598 q^{11} -3.30636 q^{13} +(0.612703 + 1.81372i) q^{14} +(1.05798 - 3.85755i) q^{16} +0.00555711 q^{17} +(2.48659 + 3.58007i) q^{19} +(0.476963 + 0.625388i) q^{20} +(1.62920 - 0.550370i) q^{22} -0.677182i q^{23} +4.84535 q^{25} +(4.42996 - 1.49651i) q^{26} +(-1.64183 - 2.15275i) q^{28} +5.04174 q^{29} +4.84195 q^{31} +(0.328479 + 5.64731i) q^{32} +(-0.00744557 + 0.00251523i) q^{34} +0.532350 q^{35} -4.23826 q^{37} +(-4.95199 - 3.67121i) q^{38} +(-0.922108 - 0.622032i) q^{40} +1.96739i q^{41} +4.59845 q^{43} +(-1.93374 + 1.47480i) q^{44} +(0.306503 + 0.907308i) q^{46} -10.9421i q^{47} +5.16751 q^{49} +(-6.49194 + 2.19308i) q^{50} +(-5.25804 + 4.01013i) q^{52} +4.67945 q^{53} -0.478192i q^{55} +(3.17414 + 2.14120i) q^{56} +(-6.75507 + 2.28197i) q^{58} -9.88941i q^{59} +4.99390i q^{61} +(-6.48738 + 2.19154i) q^{62} +(-2.99616 - 7.41775i) q^{64} -1.30025i q^{65} -2.46296i q^{67} +(0.00883735 - 0.00673995i) q^{68} +(-0.713258 + 0.240950i) q^{70} -0.424001 q^{71} -1.23201 q^{73} +(5.67855 - 1.91830i) q^{74} +(8.29646 + 2.67744i) q^{76} +1.64606i q^{77} +11.1012 q^{79} +(1.51701 + 0.416056i) q^{80} +(-0.890470 - 2.63596i) q^{82} +7.42465 q^{83} +0.00218537i q^{85} +(-6.16114 + 2.08133i) q^{86} +(1.92337 - 2.85122i) q^{88} -11.9802i q^{89} +4.47581i q^{91} +(-0.821323 - 1.07691i) q^{92} +(4.95256 + 14.6605i) q^{94} +(-1.40789 + 0.977868i) q^{95} -2.05436i q^{97} +(-6.92357 + 2.33889i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4}+O(q^{10}) $ 40 * q - 4 * q^4	$ 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) $ 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.33983	+	0.452615i	−0.947402	+	0.320047i
$2$	−1.33983	+	0.452615i	−0.947402	+	0.320047i
$3$		0			0
$3$		0			0
$4$	1.59028	−	1.21285i	0.795140	−	0.606426i
$5$			0.393257i			0.175870i	0.996126	+	0.0879349i	$0.0280268\pi$
$5$			0.393257i			0.175870i	−0.996126	+	0.0879349i	$0.971973\pi$
$6$		0			0
$7$		−	1.35370i		−	0.511649i	−0.966723	−	0.255824i	$-0.917653\pi$
$7$		−	1.35370i		−	0.511649i	0.966723	−	0.255824i	$-0.0823469\pi$
$8$	−1.58175	+	2.34480i	−0.559231	+	0.829012i
$9$		0			0
$10$	−0.177994	−	0.526897i	−0.0562866	−	0.166619i
$11$	−1.21598			−0.366631			−0.183316	−	0.983054i	$-0.558683\pi$
$11$	−1.21598			−0.366631			−0.183316	+	0.983054i	$0.558683\pi$
$12$		0			0
$13$	−3.30636			−0.917020			−0.458510	−	0.888689i	$-0.651617\pi$
$13$	−3.30636			−0.917020			−0.458510	+	0.888689i	$0.651617\pi$
$14$	0.612703	+	1.81372i	0.163752	+	0.484737i
$15$		0			0
$16$	1.05798	−	3.85755i	0.264494	−	0.964387i
$17$	0.00555711			0.00134780			0.000673898	−	1.00000i	$-0.499785\pi$
$17$	0.00555711			0.00134780			0.000673898		1.00000i	$0.499785\pi$
$18$		0			0
$19$	2.48659	+	3.58007i	0.570462	+	0.821324i
$19$	2.48659	+	3.58007i	0.570462	+	0.821324i
$20$	0.476963	+	0.625388i	0.106652	+	0.139841i
$21$		0			0
$22$	1.62920	−	0.550370i	0.347347	−	0.117339i
$23$		−	0.677182i		−	0.141202i	−0.997505	−	0.0706011i	$-0.977508\pi$
$23$		−	0.677182i		−	0.141202i	0.997505	−	0.0706011i	$-0.0224918\pi$
$24$		0			0
$25$	4.84535			0.969070
$26$	4.42996	−	1.49651i	0.868786	−	0.293490i
$27$		0			0
$28$	−1.64183	−	2.15275i	−0.310277	−	0.406832i
$29$	5.04174			0.936228			0.468114	−	0.883668i	$-0.344934\pi$
$29$	5.04174			0.936228			0.468114	+	0.883668i	$0.344934\pi$
$30$		0			0
$31$	4.84195			0.869639			0.434820	−	0.900518i	$-0.356812\pi$
$31$	4.84195			0.869639			0.434820	+	0.900518i	$0.356812\pi$
$32$	0.328479	+	5.64731i	0.0580674	+	0.998313i
$33$		0			0
$34$	−0.00744557	+	0.00251523i	−0.00127690	+	0.000431358i
$35$	0.532350			0.0899836
$36$		0			0
$37$	−4.23826			−0.696766			−0.348383	−	0.937352i	$-0.613269\pi$
$37$	−4.23826			−0.696766			−0.348383	+	0.937352i	$0.613269\pi$
$38$	−4.95199	−	3.67121i	−0.803319	−	0.595549i
$39$		0			0
$40$	−0.922108	−	0.622032i	−0.145798	−	0.0983519i
$41$			1.96739i			0.307254i	0.988129	+	0.153627i	$0.0490955\pi$
$41$			1.96739i			0.307254i	−0.988129	+	0.153627i	$0.950905\pi$
$42$		0			0
$43$	4.59845			0.701257			0.350629	−	0.936515i	$-0.385968\pi$
$43$	4.59845			0.701257			0.350629	+	0.936515i	$0.385968\pi$
$44$	−1.93374	+	1.47480i	−0.291523	+	0.222335i
$45$		0			0
$46$	0.306503	+	0.907308i	0.0451914	+	0.133775i
$47$		−	10.9421i		−	1.59607i	−0.602612	−	0.798034i	$-0.705873\pi$
$47$		−	10.9421i		−	1.59607i	0.602612	−	0.798034i	$-0.294127\pi$
$48$		0			0
$49$	5.16751			0.738215
$50$	−6.49194	+	2.19308i	−0.918098	+	0.310148i
$51$		0			0
$52$	−5.25804	+	4.01013i	−0.729159	+	0.556105i
$53$	4.67945			0.642772			0.321386	−	0.946948i	$-0.395851\pi$
$53$	4.67945			0.642772			0.321386	+	0.946948i	$0.395851\pi$
$54$		0			0
$55$		−	0.478192i		−	0.0644793i
$56$	3.17414	+	2.14120i	0.424163	+	0.286130i
$57$		0			0
$58$	−6.75507	+	2.28197i	−0.886984	+	0.299637i
$59$		−	9.88941i		−	1.28749i	−0.765240	−	0.643745i	$-0.777380\pi$
$59$		−	9.88941i		−	1.28749i	0.765240	−	0.643745i	$-0.222620\pi$
$60$		0			0
$61$			4.99390i			0.639403i	0.947518	+	0.319701i	$0.103583\pi$
$61$			4.99390i			0.639403i	−0.947518	+	0.319701i	$0.896417\pi$
$62$	−6.48738	+	2.19154i	−0.823897	+	0.278326i
$63$		0			0
$64$	−2.99616	−	7.41775i	−0.374520	−	0.927219i
$65$		−	1.30025i		−	0.161276i
$66$		0			0
$67$		−	2.46296i		−	0.300899i	−0.988618	−	0.150450i	$-0.951928\pi$
$67$		−	2.46296i		−	0.300899i	0.988618	−	0.150450i	$-0.0480721\pi$
$68$	0.00883735	−	0.00673995i	0.00107169	−	0.000817339i
$69$		0			0
$70$	−0.713258	+	0.240950i	−0.0852506	+	0.0287990i
$71$	−0.424001			−0.0503197			−0.0251598	−	0.999683i	$-0.508009\pi$
$71$	−0.424001			−0.0503197			−0.0251598	+	0.999683i	$0.508009\pi$
$72$		0			0
$73$	−1.23201			−0.144196			−0.0720978	−	0.997398i	$-0.522969\pi$
$73$	−1.23201			−0.144196			−0.0720978	+	0.997398i	$0.522969\pi$
$74$	5.67855	−	1.91830i	0.660118	−	0.222998i
$75$		0			0
$76$	8.29646	+	2.67744i	0.951670	+	0.307124i
$77$			1.64606i			0.187586i
$78$		0			0
$79$	11.1012			1.24899			0.624494	−	0.781030i	$-0.285305\pi$
$79$	11.1012			1.24899			0.624494	+	0.781030i	$0.285305\pi$
$80$	1.51701	+	0.416056i	0.169607	+	0.0465165i
$81$		0			0
$82$	−0.890470	−	2.63596i	−0.0983359	−	0.291093i
$83$	7.42465			0.814961			0.407481	−	0.913214i	$-0.366407\pi$
$83$	7.42465			0.814961			0.407481	+	0.913214i	$0.366407\pi$
$84$		0			0
$85$			0.00218537i			0.000237037i
$86$	−6.16114	+	2.08133i	−0.664372	+	0.224435i
$87$		0			0
$88$	1.92337	−	2.85122i	0.205032	−	0.303941i
$89$		−	11.9802i		−	1.26990i	−0.772552	−	0.634952i	$-0.781020\pi$
$89$		−	11.9802i		−	1.26990i	0.772552	−	0.634952i	$-0.218980\pi$
$90$		0			0
$91$			4.47581i			0.469192i
$92$	−0.821323	−	1.07691i	−0.0856288	−	0.112276i
$93$		0			0
$94$	4.95256	+	14.6605i	0.510817	+	1.51212i
$95$	−1.40789	+	0.977868i	−0.144446	+	0.100327i
$96$		0			0
$97$		−	2.05436i		−	0.208589i	−0.994546	−	0.104295i	$-0.966742\pi$
$97$		−	2.05436i		−	0.208589i	0.994546	−	0.104295i	$-0.0332585\pi$
$98$	−6.92357	+	2.33889i	−0.699386	+	0.236264i
$99$		0			0
$100$	7.70546	−	5.87670i	0.770546	−	0.587670i
$101$			8.75636i			0.871291i	0.900118	+	0.435645i	$0.143480\pi$
$101$			8.75636i			0.871291i	−0.900118	+	0.435645i	$0.856520\pi$
$102$		0			0
$103$	9.60437			0.946346			0.473173	−	0.880969i	$-0.343108\pi$
$103$	9.60437			0.946346			0.473173	+	0.880969i	$0.343108\pi$
$104$	5.22982	−	7.75275i	0.512826	−	0.760220i
$105$		0			0
$106$	−6.26966	+	2.11799i	−0.608964	+	0.205718i
$107$		−	7.32145i		−	0.707791i	−0.935285	−	0.353896i	$-0.884857\pi$
$107$		−	7.32145i		−	0.707791i	0.935285	−	0.353896i	$-0.115143\pi$
$108$		0			0
$109$	−6.70281			−0.642013			−0.321006	−	0.947077i	$-0.604021\pi$
$109$	−6.70281			−0.642013			−0.321006	+	0.947077i	$0.604021\pi$
$110$	0.216437	+	0.640695i	0.0206364	+	0.0610878i
$111$		0			0
$112$	−5.22195	−	1.43218i	−0.493428	−	0.135328i
$113$			2.04224i			0.192118i	0.995376	+	0.0960588i	$0.0306237\pi$
$113$			2.04224i			0.192118i	−0.995376	+	0.0960588i	$0.969376\pi$
$114$		0			0
$115$	0.266307			0.0248332
$116$	8.01778	−	6.11489i	0.744432	−	0.567753i
$117$		0			0
$118$	4.47609	+	13.2501i	0.412058	+	1.21977i
$119$		−	0.00752263i		−	0.000689598i
$120$		0			0
$121$	−9.52140			−0.865582
$122$	−2.26031	−	6.69096i	−0.204639	−	0.605771i
$123$		0			0
$124$	7.70005	−	5.87257i	0.691484	−	0.527372i
$125$			3.87175i			0.346300i
$126$		0			0
$127$	−5.00649			−0.444254			−0.222127	−	0.975018i	$-0.571300\pi$
$127$	−5.00649			−0.444254			−0.222127	+	0.975018i	$0.571300\pi$
$128$	7.37173	+	8.58240i	0.651575	+	0.758584i
$129$		0			0
$130$	0.588513	+	1.74211i	0.0516160	+	0.152793i
$131$	16.6424			1.45406			0.727028	−	0.686608i	$-0.240901\pi$
$131$	16.6424			1.45406			0.727028	+	0.686608i	$0.240901\pi$
$132$		0			0
$133$	4.84632	−	3.36608i	0.420229	−	0.291876i
$134$	1.11477	+	3.29995i	0.0963019	+	0.285072i
$135$		0			0
$136$	−0.00878993	+	0.0130303i	−0.000753730	+	0.00111734i
$137$	13.3028			1.13653			0.568267	−	0.822844i	$-0.307614\pi$
$137$	13.3028			1.13653			0.568267	+	0.822844i	$0.307614\pi$
$138$		0			0
$139$	14.9252			1.26594			0.632968	−	0.774178i	$-0.281836\pi$
$139$	14.9252			1.26594			0.632968	+	0.774178i	$0.281836\pi$
$140$	0.846585	−	0.645662i	0.0715495	−	0.0545684i
$141$		0			0
$142$	0.568089	−	0.191909i	0.0476729	−	0.0161047i
$143$	4.02046			0.336208
$144$		0			0
$145$			1.98270i			0.164654i
$146$	1.65068	−	0.557625i	0.136611	−	0.0461494i
$147$		0			0
$148$	−6.74002	+	5.14039i	−0.554027	+	0.422538i
$149$			19.2617i			1.57798i	0.614408	+	0.788989i	$0.289395\pi$
$149$			19.2617i			1.57798i	−0.614408	+	0.788989i	$0.710605\pi$
$150$		0			0
$151$	19.3294			1.57300			0.786501	−	0.617589i	$-0.211890\pi$
$151$	19.3294			1.57300			0.786501	+	0.617589i	$0.211890\pi$
$152$	−12.3277	+	0.167793i	−0.999907	+	0.0136098i
$153$		0			0
$154$	−0.745033	−	2.20544i	−0.0600365	−	0.177720i
$155$			1.90413i			0.152943i
$156$		0			0
$157$			2.56382i			0.204615i	0.994753	+	0.102307i	$0.0326226\pi$
$157$			2.56382i			0.204615i	−0.994753	+	0.102307i	$0.967377\pi$
$158$	−14.8738	+	5.02459i	−1.18329	+	0.399735i
$159$		0			0
$160$	−2.22084	+	0.129177i	−0.175573	+	0.0102123i
$161$	−0.916699			−0.0722460
$162$		0			0
$163$	−16.0963			−1.26076			−0.630378	−	0.776288i	$-0.717100\pi$
$163$	−16.0963			−1.26076			−0.630378	+	0.776288i	$0.717100\pi$
$164$	2.38615	+	3.12870i	0.186327	+	0.244310i
$165$		0			0
$166$	−9.94775	+	3.36051i	−0.772096	+	0.260826i
$167$	16.5107			1.27764			0.638818	−	0.769358i	$-0.279424\pi$
$167$	16.5107			1.27764			0.638818	+	0.769358i	$0.279424\pi$
$168$		0			0
$169$	−2.06797			−0.159075
$170$	−0.000989132	−	0.00292802i	−7.58629e−5	−	0.000224569i
$171$		0			0
$172$	7.31282	−	5.57725i	0.557598	−	0.425261i
$173$	13.8251			1.05110			0.525550	−	0.850763i	$-0.323860\pi$
$173$	13.8251			1.05110			0.525550	+	0.850763i	$0.323860\pi$
$174$		0			0
$175$		−	6.55913i		−	0.495823i
$176$	−1.28648	+	4.69069i	−0.0969717	+	0.353574i
$177$		0			0
$178$	5.42244	+	16.0515i	0.406429	+	1.20311i
$179$			9.07865i			0.678570i	0.940684	+	0.339285i	$0.110185\pi$
$179$			9.07865i			0.678570i	−0.940684	+	0.339285i	$0.889815\pi$
$180$		0			0
$181$	−4.43828			−0.329895			−0.164947	−	0.986302i	$-0.552745\pi$
$181$	−4.43828			−0.329895			−0.164947	+	0.986302i	$0.552745\pi$
$182$	−2.02582	−	5.99681i	−0.150164	−	0.444513i
$183$		0			0
$184$	1.58786	+	1.07113i	0.117058	+	0.0789648i
$185$		−	1.66673i		−	0.122540i
$186$		0			0
$187$	−0.00675732			−0.000494144
$188$	−13.2712	−	17.4010i	−0.967898	−	1.26910i
$189$		0			0
$190$	1.44373	−	1.94741i	0.104739	−	0.141280i
$191$			10.7380i			0.776976i	0.921454	+	0.388488i	$0.127003\pi$
$191$			10.7380i			0.776976i	−0.921454	+	0.388488i	$0.872997\pi$
$192$		0			0
$193$		−	24.4529i		−	1.76016i	−0.474826	−	0.880080i	$-0.657489\pi$
$193$		−	24.4529i		−	1.76016i	0.474826	−	0.880080i	$-0.342511\pi$
$194$	0.929836	+	2.75250i	0.0667584	+	0.197618i
$195$		0			0
$196$	8.21778	−	6.26743i	0.586984	−	0.447673i
$197$			0.602544i			0.0429295i	0.999770	+	0.0214647i	$0.00683297\pi$
$197$			0.602544i			0.0429295i	−0.999770	+	0.0214647i	$0.993167\pi$
$198$		0			0
$199$			1.82192i			0.129152i	0.997913	+	0.0645761i	$0.0205695\pi$
$199$			1.82192i			0.129152i	−0.997913	+	0.0645761i	$0.979430\pi$
$200$	−7.66411	+	11.3614i	−0.541934	+	0.803370i
$201$		0			0
$202$	−3.96326	−	11.7320i	−0.278854	−	0.825462i
$203$		−	6.82498i		−	0.479020i
$204$		0			0
$205$	−0.773689			−0.0540368
$206$	−12.8682	+	4.34708i	−0.896570	+	0.302875i
$207$		0			0
$208$	−3.49805	+	12.7545i	−0.242546	+	0.884362i
$209$	−3.02364	−	4.35328i	−0.209149	−	0.301123i
$210$		0			0
$211$		−	5.00976i		−	0.344886i	−0.985020	−	0.172443i	$-0.944834\pi$
$211$		−	5.00976i		−	0.344886i	0.985020	−	0.172443i	$-0.0551660\pi$
$212$	7.44164	−	5.67549i	0.511094	−	0.389794i
$213$		0			0
$214$	3.31380	+	9.80948i	0.226527	+	0.670563i
$215$			1.80837i			0.123330i
$216$		0			0
$217$		−	6.55452i		−	0.444950i
$218$	8.98061	−	3.03379i	0.608244	−	0.205474i
$219$		0			0
$220$	−0.579976	−	0.760458i	−0.0391020	−	0.0512701i
$221$	−0.0183738			−0.00123596
$222$		0			0
$223$	−6.38809			−0.427778			−0.213889	−	0.976858i	$-0.568613\pi$
$223$	−6.38809			−0.427778			−0.213889	+	0.976858i	$0.568613\pi$
$224$	7.64474	−	0.444661i	0.510786	−	0.0297101i
$225$		0			0
$226$	−0.924347	−	2.73625i	−0.0614867	−	0.182012i
$227$			12.2227i			0.811248i	0.914040	+	0.405624i	$0.132946\pi$
$227$			12.2227i			0.811248i	−0.914040	+	0.405624i	$0.867054\pi$
$228$		0			0
$229$			22.2874i			1.47280i	0.676549	+	0.736398i	$0.263475\pi$
$229$			22.2874i			1.47280i	−0.676549	+	0.736398i	$0.736525\pi$
$230$	−0.356805	+	0.120534i	−0.0235270	+	0.00794780i
$231$		0			0
$232$	−7.97475	+	11.8219i	−0.523568	+	0.776144i
$233$	−6.96654			−0.456393			−0.228197	−	0.973615i	$-0.573283\pi$
$233$	−6.96654			−0.456393			−0.228197	+	0.973615i	$0.573283\pi$
$234$		0			0
$235$	4.30306			0.280700
$236$	−11.9944	−	15.7269i	−0.780769	−	1.02374i
$237$		0			0
$238$	0.00340486	+	0.0100790i	0.000220704	+	0.000653327i
$239$		−	9.25488i		−	0.598648i	−0.954151	−	0.299324i	$-0.903239\pi$
$239$		−	9.25488i		−	0.598648i	0.954151	−	0.299324i	$-0.0967612\pi$
$240$		0			0
$241$		−	7.83870i		−	0.504935i	−0.967605	−	0.252468i	$-0.918758\pi$
$241$		−	7.83870i		−	0.504935i	0.967605	−	0.252468i	$-0.0812421\pi$
$242$	12.7570	−	4.30953i	0.820053	−	0.277027i
$243$		0			0
$244$	6.05686	+	7.94169i	0.387751	+	0.508414i
$245$			2.03216i			0.129830i
$246$		0			0
$247$	−8.22156	−	11.8370i	−0.523125	−	0.753170i
$248$	−7.65873	+	11.3534i	−0.486330	+	0.720941i
$249$		0			0
$250$	−1.75241	−	5.18748i	−0.110832	−	0.328085i
$251$	8.09717			0.511089			0.255544	−	0.966797i	$-0.417745\pi$
$251$	8.09717			0.511089			0.255544	+	0.966797i	$0.417745\pi$
$252$		0			0
$253$			0.823439i			0.0517691i
$254$	6.70784	−	2.26601i	0.420887	−	0.142182i
$255$		0			0
$256$	−13.7614	−	8.16239i	−0.860086	−	0.510149i
$257$		−	4.42157i		−	0.275810i	−0.990445	−	0.137905i	$-0.955963\pi$
$257$		−	4.42157i		−	0.275810i	0.990445	−	0.137905i	$-0.0440369\pi$
$258$		0			0
$259$			5.73732i			0.356500i
$260$	−1.57701	−	2.06776i	−0.0978021	−	0.128237i
$261$		0			0
$262$	−22.2980	+	7.53262i	−1.37758	+	0.465367i
$263$		−	0.798438i		−	0.0492338i	−0.999697	−	0.0246169i	$-0.992163\pi$
$263$		−	0.798438i		−	0.0492338i	0.999697	−	0.0246169i	$-0.00783660\pi$
$264$		0			0
$265$			1.84023i			0.113044i
$266$	−4.96970	+	6.70349i	−0.304712	+	0.411017i
$267$		0			0
$268$	−2.98721	−	3.91680i	−0.182473	−	0.239257i
$269$	−14.3823			−0.876903			−0.438451	−	0.898755i	$-0.644473\pi$
$269$	−14.3823			−0.876903			−0.438451	+	0.898755i	$0.644473\pi$
$270$		0			0
$271$		−	29.7531i		−	1.80737i	−0.428197	−	0.903686i	$-0.640851\pi$
$271$		−	29.7531i		−	1.80737i	0.428197	−	0.903686i	$-0.359149\pi$
$272$	0.00587928	−	0.0214368i	0.000356484	−	0.00129980i
$273$		0			0
$274$	−17.8235	+	6.02105i	−1.07675	+	0.363745i
$275$	−5.89184			−0.355291
$276$		0			0
$277$			26.7252i			1.60576i	0.596138	+	0.802882i	$0.296701\pi$
$277$			26.7252i			1.60576i	−0.596138	+	0.802882i	$0.703299\pi$
$278$	−19.9972	+	6.75536i	−1.19935	+	0.405159i
$279$		0			0
$280$	−0.842042	+	1.24825i	−0.0503217	+	0.0745974i
$281$			9.71220i			0.579381i	0.957120	+	0.289690i	$0.0935524\pi$
$281$			9.71220i			0.579381i	−0.957120	+	0.289690i	$0.906448\pi$
$282$		0			0
$283$	−0.279927			−0.0166399			−0.00831995	−	0.999965i	$-0.502648\pi$
$283$	−0.279927			−0.0166399			−0.00831995	+	0.999965i	$0.502648\pi$
$284$	−0.674280	+	0.514251i	−0.0400112	+	0.0305152i
$285$		0			0
$286$	−5.38673	+	1.81972i	−0.318524	+	0.107602i
$287$	2.66325			0.157206
$288$		0			0
$289$	−17.0000			−0.999998
$290$	−0.897400	−	2.65648i	−0.0526971	−	0.155994i
$291$		0			0
$292$	−1.95923	+	1.49424i	−0.114656	+	0.0874440i
$293$	−26.6739			−1.55831			−0.779154	−	0.626833i	$-0.784351\pi$
$293$	−26.6739			−1.55831			−0.779154	+	0.626833i	$0.784351\pi$
$294$		0			0
$295$	3.88908			0.226431
$296$	6.70386	−	9.93788i	0.389654	−	0.577627i
$297$		0			0
$298$	−8.71812	−	25.8073i	−0.505027	−	1.49498i
$299$			2.23901i			0.129485i
$300$		0			0
$301$		−	6.22491i		−	0.358798i
$302$	−25.8980	+	8.74877i	−1.49026	+	0.503435i
$303$		0			0
$304$	16.4410	−	5.80451i	0.942958	−	0.332911i
$305$	−1.96388			−0.112452
$306$		0			0
$307$		−	18.0033i		−	1.02750i	−0.857939	−	0.513751i	$-0.828256\pi$
$307$		−	18.0033i		−	1.02750i	0.857939	−	0.513751i	$-0.171744\pi$
$308$	1.99643	+	2.61770i	0.113757	+	0.149157i
$309$		0			0
$310$	−0.861837	−	2.55121i	−0.0489491	−	0.144899i
$311$			19.2359i			1.09077i	0.838186	+	0.545385i	$0.183616\pi$
$311$			19.2359i			1.09077i	−0.838186	+	0.545385i	$0.816384\pi$
$312$		0			0
$313$	−20.0287			−1.13209			−0.566044	−	0.824375i	$-0.691527\pi$
$313$	−20.0287			−1.13209			−0.566044	+	0.824375i	$0.691527\pi$
$314$	−1.16042	−	3.43507i	−0.0654864	−	0.193852i
$315$		0			0
$316$	17.6541	−	13.4642i	0.993119	−	0.757419i
$317$	−11.0972			−0.623283			−0.311642	−	0.950200i	$-0.600879\pi$
$317$	−11.0972			−0.623283			−0.311642	+	0.950200i	$0.600879\pi$
$318$		0			0
$319$	−6.13065			−0.343250
$320$	2.91708	−	1.17826i	0.163070	−	0.0658668i
$321$		0			0
$322$	1.22822	−	0.414912i	0.0684460	−	0.0231221i
$323$	0.0138182	+	0.0198948i	0.000768867	+	0.00110698i
$324$		0			0
$325$	−16.0205			−0.888656
$326$	21.5662	−	7.28541i	1.19444	−	0.403502i
$327$		0			0
$328$	−4.61313	−	3.11191i	−0.254718	−	0.171826i
$329$	−14.8123			−0.816627
$330$		0			0
$331$		−	23.0048i		−	1.26446i	−0.774781	−	0.632230i	$-0.782140\pi$
$331$		−	23.0048i		−	1.26446i	0.774781	−	0.632230i	$-0.217860\pi$
$332$	11.8073	−	9.00501i	0.648008	−	0.494214i
$333$		0			0
$334$	−22.1215	+	7.47299i	−1.21044	+	0.408904i
$335$	0.968578			0.0529191
$336$		0			0
$337$		−	14.7725i		−	0.804710i	−0.915484	−	0.402355i	$-0.868192\pi$
$337$		−	14.7725i		−	0.804710i	0.915484	−	0.402355i	$-0.131808\pi$
$338$	2.77073	−	0.935995i	0.150708	−	0.0509114i
$339$		0			0
$340$	0.00265053	+	0.00347535i	0.000143745	+	0.000188477i
$341$	−5.88770			−0.318837
$342$		0			0
$343$		−	16.4711i		−	0.889356i
$344$	−7.27358	+	10.7824i	−0.392165	+	0.581351i
$345$		0			0
$346$	−18.5232	+	6.25743i	−0.995813	+	0.336401i
$347$	−32.3507			−1.73668			−0.868338	−	0.495973i	$-0.834811\pi$
$347$	−32.3507			−1.73668			−0.868338	+	0.495973i	$0.834811\pi$
$348$		0			0
$349$			28.8848i			1.54617i	0.634303	+	0.773084i	$0.281287\pi$
$349$			28.8848i			1.54617i	−0.634303	+	0.773084i	$0.718713\pi$
$350$	2.96876	+	8.78810i	0.158687	+	0.469744i
$351$		0			0
$352$	−0.399423	−	6.86700i	−0.0212893	−	0.366012i
$353$	22.1629			1.17961			0.589806	−	0.807545i	$-0.299204\pi$
$353$	22.1629			1.17961			0.589806	+	0.807545i	$0.299204\pi$
$354$		0			0
$355$		−	0.166741i		−	0.00884971i
$356$	−14.5303	−	19.0519i	−0.770103	−	1.00975i
$357$		0			0
$358$	−4.10913	−	12.1638i	−0.217174	−	0.642878i
$359$		−	21.0084i		−	1.10878i	−0.832256	−	0.554391i	$-0.812951\pi$
$359$		−	21.0084i		−	1.10878i	0.832256	−	0.554391i	$-0.187049\pi$
$360$		0			0
$361$	−6.63376	+	17.8043i	−0.349145	+	0.937069i
$362$	5.94653	−	2.00883i	0.312543	−	0.105582i
$363$		0			0
$364$	5.42850	+	7.11778i	0.284531	+	0.373073i
$365$		−	0.484495i		−	0.0253596i
$366$		0			0
$367$			4.90961i			0.256280i	0.991756	+	0.128140i	$0.0409007\pi$
$367$			4.90961i			0.256280i	−0.991756	+	0.128140i	$0.959099\pi$
$368$	−2.61226	−	0.716443i	−0.136174	−	0.0373472i
$369$		0			0
$370$	0.754386	+	2.23313i	0.0392186	+	0.116095i
$371$		−	6.33456i		−	0.328874i
$372$		0			0
$373$	−16.5859			−0.858784			−0.429392	−	0.903118i	$-0.641272\pi$
$373$	−16.5859			−0.858784			−0.429392	+	0.903118i	$0.641272\pi$
$374$	0.00905365	−	0.00305846i	0.000468153	−	0.000158149i
$375$		0			0
$376$	25.6570	+	17.3076i	1.32316	+	0.892572i
$377$	−16.6698			−0.858540
$378$		0			0
$379$			25.6241i			1.31622i	0.752920	+	0.658112i	$0.228644\pi$
$379$			25.6241i			1.31622i	−0.752920	+	0.658112i	$0.771356\pi$
$380$	−1.05292	+	3.26264i	−0.0540138	+	0.167370i
$381$		0			0
$382$	−4.86019	−	14.3871i	−0.248669	−	0.736108i
$383$	−24.1194			−1.23245			−0.616223	−	0.787572i	$-0.711338\pi$
$383$	−24.1194			−1.23245			−0.616223	+	0.787572i	$0.711338\pi$
$384$		0			0
$385$	−0.647326			−0.0329908
$386$	11.0678	+	32.7627i	0.563334	+	1.66758i
$387$		0			0
$388$	−2.49164	−	3.26701i	−0.126494	−	0.165857i
$389$		−	26.1872i		−	1.32774i	−0.747847	−	0.663871i	$-0.768913\pi$
$389$		−	26.1872i		−	1.32774i	0.747847	−	0.663871i	$-0.231087\pi$
$390$		0			0
$391$		−	0.00376317i		−	0.000190312i
$392$	−8.17368	+	12.1168i	−0.412833	+	0.611989i
$393$		0			0
$394$	−0.272721	−	0.807306i	−0.0137395	−	0.0406715i
$395$			4.36564i			0.219659i
$396$		0			0
$397$		−	5.83861i		−	0.293032i	−0.989208	−	0.146516i	$-0.953194\pi$
$397$		−	5.83861i		−	0.293032i	0.989208	−	0.146516i	$-0.0468059\pi$
$398$	−0.824627	−	2.44106i	−0.0413348	−	0.122359i
$399$		0			0
$400$	5.12626	−	18.6912i	0.256313	−	0.934559i
$401$		−	10.8439i		−	0.541519i	−0.962647	−	0.270759i	$-0.912725\pi$
$401$		−	10.8439i		−	0.541519i	0.962647	−	0.270759i	$-0.0872748\pi$
$402$		0			0
$403$	−16.0092			−0.797476
$404$	10.6202	+	13.9251i	0.528374	+	0.692798i
$405$		0			0
$406$	3.08909	+	9.14431i	0.153309	+	0.453824i
$407$	5.15364			0.255456
$408$		0			0
$409$			23.8663i			1.18011i	0.807363	+	0.590055i	$0.200894\pi$
$409$			23.8663i			1.18011i	−0.807363	+	0.590055i	$0.799106\pi$
$410$	1.03661	−	0.350183i	0.0511945	−	0.0172943i
$411$		0			0
$412$	15.2736	−	11.6487i	0.752477	−	0.573889i
$413$	−13.3872			−0.658743
$414$		0			0
$415$			2.91979i			0.143327i
$416$	−1.08607	−	18.6720i	−0.0532490	−	0.915472i
$417$		0			0
$418$	6.02151	+	4.46411i	0.294522	+	0.218347i
$419$	−10.0928			−0.493064			−0.246532	−	0.969135i	$-0.579291\pi$
$419$	−10.0928			−0.493064			−0.246532	+	0.969135i	$0.579291\pi$
$420$		0			0
$421$	21.2013			1.03329			0.516645	−	0.856200i	$-0.327181\pi$
$421$	21.2013			1.03329			0.516645	+	0.856200i	$0.327181\pi$
$422$	2.26749	+	6.71221i	0.110380	+	0.326745i
$423$		0			0
$424$	−7.40171	+	10.9724i	−0.359459	+	0.532866i
$425$	0.0269261			0.00130611
$426$		0			0
$427$	6.76021			0.327150
$428$	−8.87984	−	11.6431i	−0.429223	−	0.562793i
$429$		0			0
$430$	−0.818497	−	2.42291i	−0.0394714	−	0.116843i
$431$	29.6252			1.42700			0.713498	−	0.700657i	$-0.247110\pi$
$431$	29.6252			1.42700			0.713498	+	0.700657i	$0.247110\pi$
$432$		0			0
$433$			37.6370i			1.80872i	0.426770	+	0.904360i	$0.359651\pi$
$433$			37.6370i			1.80872i	−0.426770	+	0.904360i	$0.640349\pi$
$434$	2.96667	+	8.78193i	0.142405	+	0.421546i
$435$		0			0
$436$	−10.6593	+	8.12952i	−0.510490	+	0.389333i
$437$	2.42436	−	1.68387i	0.115973	−	0.0805506i
$438$		0			0
$439$	−4.58779			−0.218963			−0.109482	−	0.993989i	$-0.534919\pi$
$439$	−4.58779			−0.218963			−0.109482	+	0.993989i	$0.534919\pi$
$440$	1.12126	+	0.756377i	0.0534541	+	0.0360589i
$441$		0			0
$442$	0.0246177	−	0.00831626i	0.00117095	−	0.000395564i
$443$	2.78642			0.132387			0.0661935	−	0.997807i	$-0.478915\pi$
$443$	2.78642			0.132387			0.0661935	+	0.997807i	$0.478915\pi$
$444$		0			0
$445$	4.71131			0.223338
$446$	8.55894	−	2.89135i	0.405278	−	0.136909i
$447$		0			0
$448$	−10.0414	+	4.05589i	−0.474410	+	0.191623i
$449$		−	25.9258i		−	1.22352i	−0.791045	−	0.611758i	$-0.790463\pi$
$449$		−	25.9258i		−	1.22352i	0.791045	−	0.611758i	$-0.209537\pi$
$450$		0			0
$451$		−	2.39230i		−	0.112649i
$452$	2.47693	+	3.24773i	0.116505	+	0.152760i
$453$		0			0
$454$	−5.53217	−	16.3763i	−0.259638	−	0.768577i
$455$	−1.76014			−0.0825167
$456$		0			0
$457$	11.1120			0.519798			0.259899	−	0.965636i	$-0.416311\pi$
$457$	11.1120			0.519798			0.259899	+	0.965636i	$0.416311\pi$
$458$	−10.0876	−	29.8613i	−0.471364	−	1.39533i
$459$		0			0
$460$	0.423502	−	0.322991i	0.0197459	−	0.0150595i
$461$		−	40.3495i		−	1.87927i	−0.342185	−	0.939633i	$-0.611167\pi$
$461$		−	40.3495i		−	1.87927i	0.342185	−	0.939633i	$-0.388833\pi$
$462$		0			0
$463$			3.44187i			0.159957i	0.996797	+	0.0799787i	$0.0254852\pi$
$463$			3.44187i			0.159957i	−0.996797	+	0.0799787i	$0.974515\pi$
$464$	5.33404	−	19.4488i	0.247627	−	0.902886i
$465$		0			0
$466$	9.33397	−	3.15316i	0.432388	−	0.146067i
$467$	31.1938			1.44348			0.721738	−	0.692166i	$-0.243344\pi$
$467$	31.1938			1.44348			0.721738	+	0.692166i	$0.243344\pi$
$468$		0			0
$469$	−3.33410			−0.153955
$470$	−5.76535	+	1.94763i	−0.265936	+	0.0898374i
$471$		0			0
$472$	23.1887	+	15.6425i	1.06734	+	0.720005i
$473$	−5.59162			−0.257103
$474$		0			0
$475$	12.0484	+	17.3467i	0.552818	+	0.795920i
$476$	−0.00912384	−	0.0119631i	−0.000418191	−	0.000548327i
$477$		0			0
$478$	4.18890	+	12.3999i	0.191596	+	0.567160i
$479$			0.844102i			0.0385680i	0.999814	+	0.0192840i	$0.00613867\pi$
$479$			0.844102i			0.0385680i	−0.999814	+	0.0192840i	$0.993861\pi$
$480$		0			0
$481$	14.0132			0.638949
$482$	3.54791	+	10.5025i	0.161603	+	0.478376i
$483$		0			0
$484$	−15.1417	+	11.5481i	−0.688258	+	0.524912i
$485$	0.807893			0.0366845
$486$		0			0
$487$	−31.4332			−1.42437			−0.712186	−	0.701990i	$-0.752295\pi$
$487$	−31.4332			−1.42437			−0.712186	+	0.701990i	$0.752295\pi$
$488$	−11.7097	−	7.89907i	−0.530072	−	0.357574i
$489$		0			0
$490$	−0.919785	−	2.72274i	−0.0415517	−	0.123001i
$491$	−33.2319			−1.49974			−0.749868	−	0.661588i	$-0.769883\pi$
$491$	−33.2319			−1.49974			−0.749868	+	0.661588i	$0.769883\pi$
$492$		0			0
$493$	0.0280175			0.00126184
$494$	16.3731	+	12.1383i	0.736660	+	0.546130i
$495$		0			0
$496$	5.12266	−	18.6780i	0.230014	−	0.838669i
$497$			0.573969i			0.0257460i
$498$		0			0
$499$	−1.07956			−0.0483275			−0.0241638	−	0.999708i	$-0.507692\pi$
$499$	−1.07956			−0.0483275			−0.0241638	+	0.999708i	$0.507692\pi$
$500$	4.69586	+	6.15717i	0.210005	+	0.275357i
$501$		0			0
$502$	−10.8488	+	3.66490i	−0.484206	+	0.163573i
$503$		−	34.2767i		−	1.52832i	−0.645025	−	0.764162i	$-0.723153\pi$
$503$		−	34.2767i		−	1.52832i	0.645025	−	0.764162i	$-0.276847\pi$
$504$		0			0
$505$	−3.44350			−0.153234
$506$	−0.372701	−	1.10327i	−0.0165686	−	0.0490462i
$507$		0			0
$508$	−7.96172	+	6.07214i	−0.353244	+	0.269407i
$509$	−15.7347			−0.697429			−0.348715	−	0.937229i	$-0.613382\pi$
$509$	−15.7347			−0.697429			−0.348715	+	0.937229i	$0.613382\pi$
$510$		0			0
$511$			1.66776i			0.0737775i
$512$	22.1323	+	4.70759i	0.978119	+	0.208048i
$513$		0			0
$514$	2.00127	+	5.92415i	0.0882722	+	0.261303i
$515$			3.77698i			0.166434i
$516$		0			0
$517$			13.3053i			0.585169i
$518$	−2.59680	−	7.68702i	−0.114097	−	0.337748i
$519$		0			0
$520$	3.04882	+	2.05666i	0.133700	+	0.0901907i
$521$			31.7648i			1.39164i	0.718215	+	0.695822i	$0.244960\pi$
$521$			31.7648i			1.39164i	−0.718215	+	0.695822i	$0.755040\pi$
$522$		0			0
$523$			36.2049i			1.58313i	0.611086	+	0.791564i	$0.290733\pi$
$523$			36.2049i			1.58313i	−0.611086	+	0.791564i	$0.709267\pi$
$524$	26.4661	−	20.1848i	1.15618	−	0.881778i
$525$		0			0
$526$	0.361385	+	1.06977i	0.0157571	+	0.0466442i
$527$	0.0269072			0.00117210
$528$		0			0
$529$	22.5414			0.980062
$530$	−0.832915	−	2.46559i	−0.0361795	−	0.107098i
$531$		0			0
$532$	3.62444	−	11.2309i	0.157139	−	0.486921i
$533$		−	6.50490i		−	0.281758i
$534$		0			0
$535$	2.87921			0.124479
$536$	5.77516	+	3.89578i	0.249449	+	0.168272i
$537$		0			0
$538$	19.2698	−	6.50964i	0.830779	−	0.280650i
$539$	−6.28358			−0.270653
$540$		0			0
$541$		−	13.8419i		−	0.595108i	−0.954705	−	0.297554i	$-0.903829\pi$
$541$		−	13.8419i		−	0.595108i	0.954705	−	0.297554i	$-0.0961708\pi$
$542$	13.4667	+	39.8640i	0.578444	+	1.71231i
$543$		0			0
$544$	0.00182539	+	0.0313827i	7.82631e−5	+	0.00134552i
$545$		−	2.63593i		−	0.112911i
$546$		0			0
$547$		−	12.2681i		−	0.524545i	−0.964994	−	0.262272i	$-0.915528\pi$
$547$		−	12.2681i		−	0.524545i	0.964994	−	0.262272i	$-0.0844719\pi$
$548$	21.1552	−	16.1343i	0.903704	−	0.689225i
$549$		0			0
$550$	7.89405	−	2.66673i	0.336603	−	0.113710i
$551$	12.5367	+	18.0498i	0.534083	+	0.768946i
$552$		0			0
$553$		−	15.0277i		−	0.639043i
$554$	−12.0962	−	35.8072i	−0.513920	−	1.52130i
$555$		0			0
$556$	23.7352	−	18.1020i	1.00660	−	0.767697i
$557$			41.7859i			1.77053i	0.465090	+	0.885263i	$0.346022\pi$
$557$			41.7859i			1.77053i	−0.465090	+	0.885263i	$0.653978\pi$
$558$		0			0
$559$	−15.2041			−0.643067
$560$	0.563214	−	2.05357i	0.0238001	−	0.0867790i
$561$		0			0
$562$	−4.39589	−	13.0127i	−0.185429	−	0.548906i
$563$		−	5.24786i		−	0.221171i	−0.993867	−	0.110585i	$-0.964727\pi$
$563$		−	5.24786i		−	0.221171i	0.993867	−	0.110585i	$-0.0352726\pi$
$564$		0			0
$565$	−0.803124			−0.0337877
$566$	0.375054	−	0.126699i	0.0157647	−	0.00532556i
$567$		0			0
$568$	0.670662	−	0.994197i	0.0281403	−	0.0417156i
$569$			32.6133i			1.36722i	0.729846	+	0.683611i	$0.239592\pi$
$569$			32.6133i			1.36722i	−0.729846	+	0.683611i	$0.760408\pi$
$570$		0			0
$571$	27.2472			1.14026			0.570129	−	0.821555i	$-0.306893\pi$
$571$	27.2472			1.14026			0.570129	+	0.821555i	$0.306893\pi$
$572$	6.39366	−	4.87623i	0.267332	−	0.203885i
$573$		0			0
$574$	−3.56829	+	1.20542i	−0.148938	+	0.0503135i
$575$		−	3.28118i		−	0.136835i
$576$		0			0
$577$	−13.9778			−0.581902			−0.290951	−	0.956738i	$-0.593972\pi$
$577$	−13.9778			−0.581902			−0.290951	+	0.956738i	$0.593972\pi$
$578$	22.7770	−	7.69444i	0.947400	−	0.320047i
$579$		0			0
$580$	2.40472	+	3.15305i	0.0998507	+	0.130923i
$581$		−	10.0507i		−	0.416974i
$582$		0			0
$583$	−5.69011			−0.235660
$584$	1.94872	−	2.88881i	0.0806387	−	0.119540i
$585$		0			0
$586$	35.7385	−	12.0730i	1.47634	−	0.498732i
$587$	−7.74807			−0.319797			−0.159899	−	0.987133i	$-0.551117\pi$
$587$	−7.74807			−0.319797			−0.159899	+	0.987133i	$0.551117\pi$
$588$		0			0
$589$	12.0399	+	17.3345i	0.496096	+	0.714255i
$590$	−5.21070	+	1.76025i	−0.214521	+	0.0724685i
$591$		0			0
$592$	−4.48398	+	16.3493i	−0.184291	+	0.671953i
$593$	10.7668			0.442140			0.221070	−	0.975258i	$-0.429045\pi$
$593$	10.7668			0.442140			0.221070	+	0.975258i	$0.429045\pi$
$594$		0			0
$595$	0.00295833			0.000121280
$596$	23.3616	+	30.6314i	0.956927	+	1.25471i
$597$		0			0
$598$	−1.01341	−	2.99989i	−0.0414414	−	0.122675i
$599$	17.5934			0.718845			0.359422	−	0.933175i	$-0.382974\pi$
$599$	17.5934			0.718845			0.359422	+	0.933175i	$0.382974\pi$
$600$		0			0
$601$			12.6891i			0.517599i	0.965931	+	0.258799i	$0.0833269\pi$
$601$			12.6891i			0.517599i	−0.965931	+	0.258799i	$0.916673\pi$
$602$	2.81749	+	8.34030i	0.114832	+	0.339925i
$603$		0			0
$604$	30.7391	−	23.4437i	1.25076	−	0.953910i
$605$		−	3.74436i		−	0.152230i
$606$		0			0
$607$	28.0538			1.13867			0.569334	−	0.822106i	$-0.307201\pi$
$607$	28.0538			1.13867			0.569334	+	0.822106i	$0.307201\pi$
$608$	−19.4010	+	15.2185i	−0.786813	+	0.617192i
$609$		0			0
$610$	2.63127	−	0.888883i	0.106537	−	0.0359898i
$611$			36.1785i			1.46363i
$612$		0			0
$613$			0.510517i			0.0206196i	0.999947	+	0.0103098i	$0.00328177\pi$
$613$			0.510517i			0.0206196i	−0.999947	+	0.0103098i	$0.996718\pi$
$614$	8.14856	+	24.1213i	0.328849	+	0.973457i
$615$		0			0
$616$	−3.85969	−	2.60365i	−0.155511	−	0.104904i
$617$	−31.9714			−1.28712			−0.643560	−	0.765396i	$-0.722543\pi$
$617$	−31.9714			−1.28712			−0.643560	+	0.765396i	$0.722543\pi$
$618$		0			0
$619$	8.53505			0.343053			0.171526	−	0.985180i	$-0.445130\pi$
$619$	8.53505			0.343053			0.171526	+	0.985180i	$0.445130\pi$
$620$	2.30943	+	3.02810i	0.0927488	+	0.121611i
$621$		0			0
$622$	−8.70647	−	25.7728i	−0.349098	−	1.03340i
$623$	−16.2176			−0.649745
$624$		0			0
$625$	22.7042			0.908166
$626$	26.8350	−	9.06529i	1.07254	−	0.362322i
$627$		0			0
$628$	3.10953	+	4.07719i	0.124084	+	0.162697i
$629$	−0.0235525			−0.000939099
$630$		0			0
$631$			4.94467i			0.196844i	0.995145	+	0.0984221i	$0.0313795\pi$
$631$			4.94467i			0.196844i	−0.995145	+	0.0984221i	$0.968620\pi$
$632$	−17.5593	+	26.0302i	−0.698473	+	1.03543i
$633$		0			0
$634$	14.8684	−	5.02278i	0.590499	−	0.199480i
$635$		−	1.96884i		−	0.0781309i
$636$		0			0
$637$	−17.0857			−0.676958
$638$	8.21401	−	2.77482i	0.325196	−	0.109856i
$639$		0			0
$640$	−3.37509	+	2.89898i	−0.133412	+	0.114592i
$641$			9.73828i			0.384639i	0.981332	+	0.192320i	$0.0616010\pi$
$641$			9.73828i			0.384639i	−0.981332	+	0.192320i	$0.938399\pi$
$642$		0			0
$643$	−34.7059			−1.36867			−0.684334	−	0.729168i	$-0.739907\pi$
$643$	−34.7059			−1.36867			−0.684334	+	0.729168i	$0.739907\pi$
$644$	−1.45781	+	1.11182i	−0.0574456	+	0.0438119i
$645$		0			0
$646$	−0.0275188	−	0.0204013i	−0.00108271	−	0.000802678i
$647$			15.7832i			0.620502i	0.950655	+	0.310251i	$0.100413\pi$
$647$			15.7832i			0.620502i	−0.950655	+	0.310251i	$0.899587\pi$
$648$		0			0
$649$			12.0253i			0.472034i
$650$	21.4647	−	7.25111i	0.841914	−	0.284412i
$651$		0			0
$652$	−25.5975	+	19.5224i	−1.00248	+	0.764556i
$653$			18.6709i			0.730650i	0.930880	+	0.365325i	$0.119042\pi$
$653$			18.6709i			0.730650i	−0.930880	+	0.365325i	$0.880958\pi$
$654$		0			0
$655$			6.54475i			0.255725i
$656$	7.58930	+	2.08145i	0.296312	+	0.0812670i
$657$		0			0
$658$	19.8459	−	6.70426i	0.773674	−	0.261359i
$659$			5.70895i			0.222389i	0.993799	+	0.111195i	$0.0354677\pi$
$659$			5.70895i			0.222389i	−0.993799	+	0.111195i	$0.964532\pi$
$660$		0			0
$661$	37.3664			1.45338			0.726692	−	0.686963i	$-0.241057\pi$
$661$	37.3664			1.45338			0.726692	+	0.686963i	$0.241057\pi$
$662$	10.4123	+	30.8225i	0.404687	+	1.19795i
$663$		0			0
$664$	−11.7439	+	17.4093i	−0.455752	+	0.675612i
$665$	1.32374	+	1.90585i	0.0513323	+	0.0739057i
$666$		0			0
$667$		−	3.41418i		−	0.132198i
$668$	26.2566	−	20.0251i	1.01590	−	0.774793i
$669$		0			0
$670$	−1.29773	+	0.438393i	−0.0501356	+	0.0169366i
$671$		−	6.07247i		−	0.234425i
$672$		0			0
$673$		−	23.1675i		−	0.893040i	−0.894774	−	0.446520i	$-0.852663\pi$
$673$		−	23.1675i		−	0.893040i	0.894774	−	0.446520i	$-0.147337\pi$
$674$	6.68626	+	19.7926i	0.257545	+	0.762384i
$675$		0			0
$676$	−3.28865	+	2.50814i	−0.126487	+	0.0964671i
$677$	28.2705			1.08652			0.543262	−	0.839564i	$-0.317189\pi$
$677$	28.2705			1.08652			0.543262	+	0.839564i	$0.317189\pi$
$678$		0			0
$679$	−2.78098			−0.106724
$680$	−0.00512425	−	0.00345670i	−0.000196506	−	0.000132558i
$681$		0			0
$682$	7.88850	−	2.66486i	0.302066	−	0.102043i
$683$			26.5216i			1.01482i	0.861704	+	0.507411i	$0.169397\pi$
$683$			26.5216i			1.01482i	−0.861704	+	0.507411i	$0.830603\pi$
$684$		0			0
$685$			5.23142i			0.199882i
$686$	7.45507	+	22.0684i	0.284636	+	0.842577i
$687$		0			0
$688$	4.86505	−	17.7388i	0.185478	−	0.676284i
$689$	−15.4720			−0.589435
$690$		0			0
$691$	8.53640			0.324740			0.162370	−	0.986730i	$-0.448086\pi$
$691$	8.53640			0.324740			0.162370	+	0.986730i	$0.448086\pi$
$692$	21.9857	−	16.7678i	0.835771	−	0.637414i
$693$		0			0
$694$	43.3444	−	14.6424i	1.64533	−	0.555818i
$695$			5.86942i			0.222640i
$696$		0			0
$697$			0.0109330i			0.000414116i
$698$	−13.0737	−	38.7007i	−0.494847	−	1.46484i
$699$		0			0
$700$	−7.95526	−	10.4308i	−0.300680	−	0.394249i
$701$			14.2487i			0.538166i	0.963117	+	0.269083i	$0.0867207\pi$
$701$			14.2487i			0.538166i	−0.963117	+	0.269083i	$0.913279\pi$
$702$		0			0
$703$	−10.5388	−	15.1733i	−0.397479	−	0.572271i
$704$	3.64327	+	9.01982i	0.137311	+	0.339947i
$705$		0			0
$706$	−29.6945	+	10.0313i	−1.11757	+	0.377531i
$707$	11.8535			0.445795
$708$		0			0
$709$		−	51.2166i		−	1.92348i	−0.273963	−	0.961740i	$-0.588335\pi$
$709$		−	51.2166i		−	1.92348i	0.273963	−	0.961740i	$-0.411665\pi$
$710$	0.0754697	+	0.223405i	0.00283233	+	0.00838423i
$711$		0			0
$712$	28.0913	+	18.9497i	1.05276	+	0.710170i
$713$		−	3.27888i		−	0.122795i
$714$		0			0
$715$			1.58107i			0.0591288i
$716$	11.0111	+	14.4376i	0.411503	+	0.539558i
$717$		0			0
$718$	9.50872	+	28.1477i	0.354862	+	1.05046i
$719$		−	39.4189i		−	1.47008i	−0.678026	−	0.735038i	$-0.737164\pi$
$719$		−	39.4189i		−	1.47008i	0.678026	−	0.735038i	$-0.262836\pi$
$720$		0			0
$721$		−	13.0014i		−	0.484197i
$722$	0.829608	−	26.8572i	0.0308748	−	0.999523i
$723$		0			0
$724$	−7.05810	+	5.38298i	−0.262312	+	0.200057i
$725$	24.4290			0.907270
$726$		0			0
$727$		−	32.9620i		−	1.22249i	−0.791440	−	0.611246i	$-0.790668\pi$
$727$		−	32.9620i		−	1.22249i	0.791440	−	0.611246i	$-0.209332\pi$
$728$	−10.4949	−	7.07959i	−0.388966	−	0.262387i
$729$		0			0
$730$	0.219290	+	0.649140i	0.00811628	+	0.0240258i
$731$	0.0255541			0.000945152
$732$		0			0
$733$		−	39.5261i		−	1.45993i	−0.683485	−	0.729965i	$-0.739536\pi$
$733$		−	39.5261i		−	1.45993i	0.683485	−	0.729965i	$-0.260464\pi$
$734$	−2.22217	−	6.57804i	−0.0820216	−	0.242800i
$735$		0			0
$736$	3.82426	−	0.222440i	0.140964	−	0.00819925i
$737$			2.99491i			0.110319i
$738$		0			0
$739$	−2.89967			−0.106666			−0.0533330	−	0.998577i	$-0.516984\pi$
$739$	−2.89967			−0.106666			−0.0533330	+	0.998577i	$0.516984\pi$
$740$	−2.02149	−	2.65056i	−0.0743116	−	0.0974366i
$741$		0			0
$742$	2.86712	+	8.48722i	0.105255	+	0.311576i
$743$	−44.8357			−1.64486			−0.822431	−	0.568865i	$-0.807383\pi$
$743$	−44.8357			−1.64486			−0.822431	+	0.568865i	$0.807383\pi$
$744$		0			0
$745$	−7.57478			−0.277519
$746$	22.2222	−	7.50702i	0.813614	−	0.274851i
$747$		0			0
$748$	−0.0107460	+	0.00819563i	−0.000392914	+	0.000299662i
$749$	−9.91101			−0.362141
$750$		0			0
$751$	19.9481			0.727918			0.363959	−	0.931415i	$-0.381425\pi$
$751$	19.9481			0.727918			0.363959	+	0.931415i	$0.381425\pi$
$752$	−42.2097	−	11.5765i	−1.53923	−	0.422151i
$753$		0			0
$754$	22.3347	−	7.54501i	0.813382	−	0.274773i
$755$			7.60141i			0.276644i
$756$		0			0
$757$		−	24.8537i		−	0.903322i	−0.892190	−	0.451661i	$-0.850832\pi$
$757$		−	24.8537i		−	0.903322i	0.892190	−	0.451661i	$-0.149168\pi$
$758$	−11.5979	−	34.3319i	−0.421253	−	1.24699i
$759$		0			0
$760$	−0.0659856	−	4.84795i	−0.00239355	−	0.175854i
$761$	29.7493			1.07841			0.539206	−	0.842174i	$-0.318725\pi$
$761$	29.7493			1.07841			0.539206	+	0.842174i	$0.318725\pi$
$762$		0			0
$763$			9.07356i			0.328485i
$764$	13.0236	+	17.0765i	0.471179	+	0.617804i
$765$		0			0
$766$	32.3159	−	10.9168i	1.16762	−	0.394441i
$767$			32.6980i			1.18065i
$768$		0			0
$769$	−17.7979			−0.641809			−0.320905	−	0.947112i	$-0.603987\pi$
$769$	−17.7979			−0.641809			−0.320905	+	0.947112i	$0.603987\pi$
$770$	0.867306	−	0.292989i	0.0312555	−	0.0105586i
$771$		0			0
$772$	−29.6578	−	38.8870i	−1.06741	−	1.39957i
$773$	−2.50404			−0.0900641			−0.0450320	−	0.998986i	$-0.514339\pi$
$773$	−2.50404			−0.0900641			−0.0450320	+	0.998986i	$0.514339\pi$
$774$		0			0
$775$	23.4609			0.842741
$776$	4.81707	+	3.24948i	0.172923	+	0.116650i
$777$		0			0
$778$	11.8527	+	35.0863i	0.424940	+	1.25790i
$779$	−7.04338	+	4.89208i	−0.252355	+	0.175277i
$780$		0			0
$781$	0.515576			0.0184488
$782$	0.00170327	+	0.00504201i	6.09088e−5	+	0.000180302i
$783$		0			0
$784$	5.46710	−	19.9339i	0.195254	−	0.711926i
$785$	−1.00824			−0.0359856
$786$		0			0
$787$		−	48.3385i		−	1.72308i	−0.507689	−	0.861540i	$-0.669500\pi$
$787$		−	48.3385i		−	1.72308i	0.507689	−	0.861540i	$-0.330500\pi$
$788$	0.730797	+	0.958213i	0.0260336	+	0.0341349i
$789$		0			0
$790$	−1.97595	−	5.84921i	−0.0703013	−	0.208105i
$791$	2.76457			0.0982967
$792$		0			0
$793$		−	16.5116i		−	0.586345i
$794$	2.64264	+	7.82274i	0.0937839	+	0.277619i
$795$		0			0
$796$	2.20972	+	2.89736i	0.0783214	+	0.102694i
$797$	−4.38865			−0.155454			−0.0777271	−	0.996975i	$-0.524766\pi$
$797$	−4.38865			−0.155454			−0.0777271	+	0.996975i	$0.524766\pi$
$798$		0			0
$799$		−	0.0608064i		−	0.00215118i
$800$	1.59160	+	27.3632i	0.0562714	+	0.967435i
$801$		0			0
$802$	4.90811	+	14.5290i	0.173312	+	0.513036i
$803$	1.49809			0.0528666
$804$		0			0
$805$		−	0.360498i		−	0.0127059i
$806$	21.4496	−	7.24602i	0.755530	−	0.255230i
$807$		0			0
$808$	−20.5319	−	13.8503i	−0.722310	−	0.487253i
$809$	1.71674			0.0603574			0.0301787	−	0.999545i	$-0.490392\pi$
$809$	1.71674			0.0603574			0.0301787	+	0.999545i	$0.490392\pi$
$810$		0			0
$811$			39.8836i			1.40050i	0.713897	+	0.700251i	$0.246928\pi$
$811$			39.8836i			1.40050i	−0.713897	+	0.700251i	$0.753072\pi$
$812$	−8.27770	−	10.8536i	−0.290490	−	0.380888i
$813$		0			0
$814$	−6.90499	+	2.33261i	−0.242020	+	0.0817580i
$815$		−	6.32997i		−	0.221729i
$816$		0			0
$817$	11.4345	+	16.4628i	0.400041	+	0.575959i
$818$	−10.8022	−	31.9767i	−0.377691	−	1.11804i
$819$		0			0
$820$	−1.23038	+	0.938371i	−0.0429668	+	0.0327693i
$821$		−	21.5429i		−	0.751853i	−0.926650	−	0.375926i	$-0.877325\pi$
$821$		−	21.5429i		−	0.751853i	0.926650	−	0.375926i	$-0.122675\pi$
$822$		0			0
$823$			51.4146i			1.79220i	0.443852	+	0.896100i	$0.353612\pi$
$823$			51.4146i			1.79220i	−0.443852	+	0.896100i	$0.646388\pi$
$824$	−15.1917	+	22.5203i	−0.529227	+	0.784532i
$825$		0			0
$826$	17.9366	−	6.05927i	0.624094	−	0.210829i
$827$		−	28.1995i		−	0.980592i	−0.871556	−	0.490296i	$-0.836889\pi$
$827$		−	28.1995i		−	0.980592i	0.871556	−	0.490296i	$-0.163111\pi$
$828$		0			0
$829$	−56.6258			−1.96670			−0.983348	−	0.181734i	$-0.941829\pi$
$829$	−56.6258			−1.96670			−0.983348	+	0.181734i	$0.941829\pi$
$830$	−1.32154	−	3.91202i	−0.0458714	−	0.135788i
$831$		0			0
$832$	9.90640	+	24.5258i	0.343443	+	0.850278i
$833$	0.0287164			0.000994964
$834$		0			0
$835$			6.49295i			0.224698i
$836$	−10.0883	−	3.25571i	−0.348912	−	0.112601i
$837$		0			0
$838$	13.5226	−	4.56814i	0.467130	−	0.157804i
$839$	−12.4990			−0.431513			−0.215756	−	0.976447i	$-0.569222\pi$
$839$	−12.4990			−0.431513			−0.215756	+	0.976447i	$0.569222\pi$
$840$		0			0
$841$	−3.58083			−0.123477
$842$	−28.4061	+	9.59604i	−0.978940	+	0.330701i
$843$		0			0
$844$	−6.07610	−	7.96691i	−0.209148	−	0.274232i
$845$		−	0.813244i		−	0.0279764i
$846$		0			0
$847$			12.8891i			0.442874i
$848$	4.95075	−	18.0512i	0.170009	−	0.619882i
$849$		0			0
$850$	−0.0360764	+	0.0121872i	−0.00123741	+	0.000418016i
$851$			2.87008i			0.0983850i
$852$		0			0
$853$		−	32.9738i		−	1.12900i	−0.825433	−	0.564500i	$-0.809069\pi$
$853$		−	32.9738i		−	1.12900i	0.825433	−	0.564500i	$-0.190931\pi$
$854$	−9.05753	+	3.05977i	−0.309942	+	0.104703i
$855$		0			0
$856$	17.1673	+	11.5807i	0.586767	+	0.395819i
$857$			32.4358i			1.10799i	0.832521	+	0.553993i	$0.186897\pi$
$857$			32.4358i			1.10799i	−0.832521	+	0.553993i	$0.813103\pi$
$858$		0			0
$859$	18.7433			0.639514			0.319757	−	0.947500i	$-0.396399\pi$
$859$	18.7433			0.639514			0.319757	+	0.947500i	$0.396399\pi$
$860$	2.19329	+	2.87582i	0.0747906	+	0.0980646i
$861$		0			0
$862$	−39.6927	+	13.4088i	−1.35194	+	0.456706i
$863$	−29.2455			−0.995529			−0.497765	−	0.867312i	$-0.665846\pi$
$863$	−29.2455			−0.995529			−0.497765	+	0.867312i	$0.665846\pi$
$864$		0			0
$865$			5.43680i			0.184857i
$866$	−17.0351	−	50.4271i	−0.578876	−	1.71358i
$867$		0			0
$868$	−7.94967	−	10.4235i	−0.269829	−	0.353797i
$869$	−13.4989			−0.457918
$870$		0			0
$871$			8.14345i			0.275930i
$872$	10.6021	−	15.7167i	0.359034	−	0.532236i
$873$		0			0
$874$	−2.48608	+	3.35340i	−0.0840928	+	0.113431i
$875$	5.24117			0.177184
$876$		0			0
$877$	29.1471			0.984229			0.492114	−	0.870531i	$-0.336224\pi$
$877$	29.1471			0.984229			0.492114	+	0.870531i	$0.336224\pi$
$878$	6.14685	−	2.07650i	0.207446	−	0.0700786i
$879$		0			0
$880$	−1.84465	−	0.505915i	−0.0621831	−	0.0170544i
$881$	9.86763			0.332449			0.166224	−	0.986088i	$-0.446842\pi$
$881$	9.86763			0.332449			0.166224	+	0.986088i	$0.446842\pi$
$882$		0			0
$883$	−45.5997			−1.53455			−0.767276	−	0.641317i	$-0.778388\pi$
$883$	−45.5997			−1.53455			−0.767276	+	0.641317i	$0.778388\pi$
$884$	−0.0292195	+	0.0222847i	−0.000982758	+	0.000749516i
$885$		0			0
$886$	−3.73333	+	1.26118i	−0.125424	+	0.0423701i
$887$	5.88747			0.197682			0.0988410	−	0.995103i	$-0.468486\pi$
$887$	5.88747			0.197682			0.0988410	+	0.995103i	$0.468486\pi$
$888$		0			0
$889$			6.77726i			0.227302i
$890$	−6.31235	+	2.13241i	−0.211591	+	0.0714786i
$891$		0			0
$892$	−10.1588	+	7.74781i	−0.340143	+	0.259416i
$893$	39.1734	−	27.2085i	1.31089	−	0.910497i
$894$		0			0
$895$	−3.57024			−0.119340
$896$	11.6180	−	9.97908i	0.388129	−	0.333378i
$897$		0			0
$898$	11.7344	+	34.7362i	0.391583	+	1.15916i
$899$	24.4118			0.814181
$900$		0			0
$901$	0.0260042			0.000866326
$902$	1.08279	+	3.20527i	0.0360530	+	0.106724i
$903$		0			0
$904$	−4.78864	−	3.23030i	−0.159268	−	0.107438i
$905$		−	1.74538i		−	0.0580185i
$906$		0			0
$907$		−	32.4697i		−	1.07814i	−0.842261	−	0.539069i	$-0.818776\pi$
$907$		−	32.4697i		−	1.07814i	0.842261	−	0.539069i	$-0.181224\pi$
$908$	14.8243	+	19.4375i	0.491962	+	0.645055i
$909$		0			0
$910$	2.35829	−	0.796667i	0.0781765	−	0.0264092i
$911$	−22.2375			−0.736760			−0.368380	−	0.929675i	$-0.620087\pi$
$911$	−22.2375			−0.736760			−0.368380	+	0.929675i	$0.620087\pi$
$912$		0			0
$913$	−9.02821			−0.298790
$914$	−14.8882	+	5.02947i	−0.492458	+	0.166360i
$915$		0			0
$916$	27.0314	+	35.4433i	0.893142	+	1.17108i
$917$		−	22.5288i		−	0.743966i
$918$		0			0
$919$		−	1.82361i		−	0.0601553i	−0.999548	−	0.0300776i	$-0.990425\pi$
$919$		−	1.82361i		−	0.0601553i	0.999548	−	0.0300776i	$-0.00957546\pi$
$920$	−0.421229	+	0.624435i	−0.0138875	+	0.0205870i
$921$		0			0
$922$	18.2628	+	54.0614i	0.601453	+	1.78042i
$923$	1.40190			0.0461441
$924$		0			0
$925$	−20.5359			−0.675215
$926$	−1.55784	−	4.61152i	−0.0511939	−	0.151544i
$927$		0			0
$928$	1.65611	+	28.4723i	0.0543644	+	0.934648i
$929$	48.0824			1.57753			0.788767	−	0.614693i	$-0.210720\pi$
$929$	48.0824			1.57753			0.788767	+	0.614693i	$0.210720\pi$
$930$		0			0
$931$	12.8495	+	18.5000i	0.421124	+	0.606314i
$932$	−11.0787	+	8.44939i	−0.362896	+	0.276769i
$933$		0			0
$934$	−41.7943	+	14.1188i	−1.36755	+	0.461980i
$935$		−	0.00265736i		−	8.69050e-5i
$936$		0			0
$937$	12.8423			0.419540			0.209770	−	0.977751i	$-0.432728\pi$
$937$	12.8423			0.419540			0.209770	+	0.977751i	$0.432728\pi$
$938$	4.46713	−	1.50907i	0.145857	−	0.0492727i
$939$		0			0
$940$	6.84306	−	5.21897i	0.223196	−	0.170224i
$941$	4.78698			0.156051			0.0780256	−	0.996951i	$-0.475138\pi$
$941$	4.78698			0.156051			0.0780256	+	0.996951i	$0.475138\pi$
$942$		0			0
$943$	1.33228			0.0433850
$944$	−38.1489	−	10.4628i	−1.24164	−	0.340534i
$945$		0			0
$946$	7.49181	−	2.53085i	0.243580	−	0.0822850i
$947$	26.3364			0.855817			0.427908	−	0.903822i	$-0.359251\pi$
$947$	26.3364			0.855817			0.427908	+	0.903822i	$0.359251\pi$
$948$		0			0
$949$	4.07346			0.132230
$950$	−23.9941	−	17.7883i	−0.778472	−	0.577128i
$951$		0			0
$952$	0.0176391	+	0.0118989i	0.000571685	+	0.000385645i
$953$			50.7687i			1.64456i	0.569084	+	0.822279i	$0.307298\pi$
$953$			50.7687i			1.64456i	−0.569084	+	0.822279i	$0.692702\pi$
$954$		0			0
$955$	−4.22280			−0.136647
$956$	−11.2248	−	14.7178i	−0.363036	−	0.476009i
$957$		0			0
$958$	−0.382053	−	1.13095i	−0.0123436	−	0.0365394i
$959$		−	18.0079i		−	0.581507i
$960$		0			0
$961$	−7.55556			−0.243728
$962$	−18.7753	+	6.34260i	−0.605341	+	0.204494i
$963$		0			0
$964$	−9.50719	−	12.4657i	−0.306206	−	0.401494i
$965$	9.61628			0.309559
$966$		0			0
$967$			49.0390i			1.57699i	0.615042	+	0.788494i	$0.289139\pi$
$967$			49.0390i			1.57699i	−0.615042	+	0.788494i	$0.710861\pi$
$968$	15.0604	−	22.3258i	0.484060	−	0.717577i
$969$		0			0
$970$	−1.08244	+	0.365665i	−0.0347550	+	0.0117408i
$971$		−	22.1251i		−	0.710027i	−0.934861	−	0.355013i	$-0.884476\pi$
$971$		−	22.1251i		−	0.710027i	0.934861	−	0.355013i	$-0.115524\pi$
$972$		0			0
$973$		−	20.2041i		−	0.647715i
$974$	42.1150	−	14.2271i	1.34945	−	0.455866i
$975$		0			0
$976$	19.2642	+	5.28342i	0.616632	+	0.169118i
$977$		−	45.0576i		−	1.44152i	−0.693184	−	0.720761i	$-0.743793\pi$
$977$		−	45.0576i		−	1.44152i	0.693184	−	0.720761i	$-0.256207\pi$
$978$		0			0
$979$			14.5677i			0.465586i
$980$	2.46471	+	3.23170i	0.0787322	+	0.103233i
$981$		0			0
$982$	44.5251	−	15.0413i	1.42085	−	0.479986i
$983$	−58.9765			−1.88106			−0.940529	−	0.339713i	$-0.889670\pi$
$983$	−58.9765			−1.88106			−0.940529	+	0.339713i	$0.889670\pi$
$984$		0			0
$985$	−0.236955			−0.00755000
$986$	−0.0375386	+	0.0126811i	−0.00119547	+	0.000403850i
$987$		0			0
$988$	−27.4311	−	8.85259i	−0.872700	−	0.281638i
$989$		−	3.11399i		−	0.0990192i
$990$		0			0
$991$	−36.9320			−1.17318			−0.586592	−	0.809882i	$-0.699531\pi$
$991$	−36.9320			−1.17318			−0.586592	+	0.809882i	$0.699531\pi$
$992$	1.59048	+	27.3440i	0.0504977	+	0.868172i
$993$		0			0
$994$	−0.259787	−	0.769019i	−0.00823994	−	0.0243918i
$995$	−0.716481			−0.0227140
$996$		0			0
$997$		−	34.0903i		−	1.07965i	−0.841777	−	0.539825i	$-0.818490\pi$
$997$		−	34.0903i		−	1.07965i	0.841777	−	0.539825i	$-0.181510\pi$
$998$	1.44642	−	0.488623i	0.0457856	−	0.0154671i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.e.g.379.6		40
3.2	odd	2		456.2.e.a.379.35	yes	40
4.3	odd	2		5472.2.e.g.5167.32		40
8.3	odd	2	inner	1368.2.e.g.379.36		40
8.5	even	2		5472.2.e.g.5167.15		40
12.11	even	2		1824.2.e.a.1519.26		40
19.18	odd	2	inner	1368.2.e.g.379.35		40
24.5	odd	2		1824.2.e.a.1519.10		40
24.11	even	2		456.2.e.a.379.5	✓	40
57.56	even	2		456.2.e.a.379.6	yes	40
76.75	even	2		5472.2.e.g.5167.16		40
152.37	odd	2		5472.2.e.g.5167.31		40
152.75	even	2	inner	1368.2.e.g.379.5		40
228.227	odd	2		1824.2.e.a.1519.9		40
456.227	odd	2		456.2.e.a.379.36	yes	40
456.341	even	2		1824.2.e.a.1519.25		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.e.a.379.5	✓	40	24.11	even	2
456.2.e.a.379.6	yes	40	57.56	even	2
456.2.e.a.379.35	yes	40	3.2	odd	2
456.2.e.a.379.36	yes	40	456.227	odd	2
1368.2.e.g.379.5		40	152.75	even	2	inner
1368.2.e.g.379.6		40	1.1	even	1	trivial
1368.2.e.g.379.35		40	19.18	odd	2	inner
1368.2.e.g.379.36		40	8.3	odd	2	inner
1824.2.e.a.1519.9		40	228.227	odd	2
1824.2.e.a.1519.10		40	24.5	odd	2
1824.2.e.a.1519.25		40	456.341	even	2
1824.2.e.a.1519.26		40	12.11	even	2
5472.2.e.g.5167.15		40	8.5	even	2
5472.2.e.g.5167.16		40	76.75	even	2
5472.2.e.g.5167.31		40	152.37	odd	2
5472.2.e.g.5167.32		40	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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33983 + 0.452615i) q^{2} +(1.59028 - 1.21285i) q^{4} +0.393257i q^{5} -1.35370i q^{7} +(-1.58175 + 2.34480i) q^{8} +O(q^{10})\)	\(q+(-1.33983 + 0.452615i) q^{2} +(1.59028 - 1.21285i) q^{4} +0.393257i q^{5} -1.35370i q^{7} +(-1.58175 + 2.34480i) q^{8} +(-0.177994 - 0.526897i) q^{10} -1.21598 q^{11} -3.30636 q^{13} +(0.612703 + 1.81372i) q^{14} +(1.05798 - 3.85755i) q^{16} +0.00555711 q^{17} +(2.48659 + 3.58007i) q^{19} +(0.476963 + 0.625388i) q^{20} +(1.62920 - 0.550370i) q^{22} -0.677182i q^{23} +4.84535 q^{25} +(4.42996 - 1.49651i) q^{26} +(-1.64183 - 2.15275i) q^{28} +5.04174 q^{29} +4.84195 q^{31} +(0.328479 + 5.64731i) q^{32} +(-0.00744557 + 0.00251523i) q^{34} +0.532350 q^{35} -4.23826 q^{37} +(-4.95199 - 3.67121i) q^{38} +(-0.922108 - 0.622032i) q^{40} +1.96739i q^{41} +4.59845 q^{43} +(-1.93374 + 1.47480i) q^{44} +(0.306503 + 0.907308i) q^{46} -10.9421i q^{47} +5.16751 q^{49} +(-6.49194 + 2.19308i) q^{50} +(-5.25804 + 4.01013i) q^{52} +4.67945 q^{53} -0.478192i q^{55} +(3.17414 + 2.14120i) q^{56} +(-6.75507 + 2.28197i) q^{58} -9.88941i q^{59} +4.99390i q^{61} +(-6.48738 + 2.19154i) q^{62} +(-2.99616 - 7.41775i) q^{64} -1.30025i q^{65} -2.46296i q^{67} +(0.00883735 - 0.00673995i) q^{68} +(-0.713258 + 0.240950i) q^{70} -0.424001 q^{71} -1.23201 q^{73} +(5.67855 - 1.91830i) q^{74} +(8.29646 + 2.67744i) q^{76} +1.64606i q^{77} +11.1012 q^{79} +(1.51701 + 0.416056i) q^{80} +(-0.890470 - 2.63596i) q^{82} +7.42465 q^{83} +0.00218537i q^{85} +(-6.16114 + 2.08133i) q^{86} +(1.92337 - 2.85122i) q^{88} -11.9802i q^{89} +4.47581i q^{91} +(-0.821323 - 1.07691i) q^{92} +(4.95256 + 14.6605i) q^{94} +(-1.40789 + 0.977868i) q^{95} -2.05436i q^{97} +(-6.92357 + 2.33889i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4}+O(q^{10}) \) 40 * q - 4 * q^4	\( 40 q - 4 q^{4} + 4 q^{16} + 8 q^{19} - 32 q^{20} - 40 q^{25} - 40 q^{26} - 8 q^{28} + 48 q^{35} + 8 q^{44} - 56 q^{49} + 16 q^{58} - 40 q^{62} + 68 q^{64} + 88 q^{68} - 16 q^{73} + 40 q^{74} - 12 q^{76} + 32 q^{80} - 64 q^{82} - 80 q^{83} + 48 q^{92}+O(q^{100}) \) 40 * q - 4 * q^4 + 4 * q^16 + 8 * q^19 - 32 * q^20 - 40 * q^25 - 40 * q^26 - 8 * q^28 + 48 * q^35 + 8 * q^44 - 56 * q^49 + 16 * q^58 - 40 * q^62 + 68 * q^64 + 88 * q^68 - 16 * q^73 + 40 * q^74 - 12 * q^76 + 32 * q^80 - 64 * q^82 - 80 * q^83 + 48 * q^92

Introduction

L-functions

Modular forms

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Database

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