LMFDB - Embedded newform 784.2.bb.a.111.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(111,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 11]))

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

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

chi := DirichletCharacter("784.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bb (of order $14$, degree $6$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.7
Character	$\chi$	$=$	784.111
Dual form			784.2.bb.a.671.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.969349 + 1.21553i) q^{3} +(-1.39014 + 1.10860i) q^{5} +(-0.267553 + 2.63219i) q^{7} +(0.129699 - 0.568247i) q^{9} +O(q^{10})$	\(q+(0.969349 + 1.21553i) q^{3} +(-1.39014 + 1.10860i) q^{5} +(-0.267553 + 2.63219i) q^{7} +(0.129699 - 0.568247i) q^{9} +(-2.43732 + 0.556302i) q^{11} +(-5.14006 + 1.17319i) q^{13} +(-2.69507 - 0.615132i) q^{15} +(0.0272541 - 0.0565938i) q^{17} -1.00192 q^{19} +(-3.45884 + 2.22629i) q^{21} +(-0.107144 - 0.222488i) q^{23} +(-0.409105 + 1.79241i) q^{25} +(5.01869 - 2.41687i) q^{27} +(-4.86206 - 2.34145i) q^{29} +5.33623 q^{31} +(-3.03881 - 2.42337i) q^{33} +(-2.54611 - 3.95573i) q^{35} +(-2.06907 - 0.996411i) q^{37} +(-6.40855 - 5.11065i) q^{39} +(-2.80032 + 2.23318i) q^{41} +(1.83065 + 1.45989i) q^{43} +(0.449660 + 0.933729i) q^{45} +(2.40775 + 10.5491i) q^{47} +(-6.85683 - 1.40850i) q^{49} +(0.0952100 - 0.0217311i) q^{51} +(-3.85131 + 1.85469i) q^{53} +(2.77151 - 3.47536i) q^{55} +(-0.971208 - 1.21786i) q^{57} +(3.91279 - 4.90648i) q^{59} +(-5.94308 + 12.3409i) q^{61} +(1.46103 + 0.493428i) q^{63} +(5.84483 - 7.32918i) q^{65} -5.43170i q^{67} +(0.166579 - 0.345905i) q^{69} +(-1.70512 - 3.54073i) q^{71} +(5.36315 + 1.22410i) q^{73} +(-2.57528 + 1.24019i) q^{75} +(-0.812180 - 6.56433i) q^{77} +14.8054i q^{79} +(6.22722 + 2.99887i) q^{81} +(-0.714859 + 3.13200i) q^{83} +(0.0248529 + 0.108887i) q^{85} +(-1.86695 - 8.17964i) q^{87} +(7.71016 + 1.75979i) q^{89} +(-1.71281 - 13.8435i) q^{91} +(5.17267 + 6.48632i) q^{93} +(1.39281 - 1.11073i) q^{95} +4.97992i q^{97} +1.45715i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^9	$ 48 q - 4 q^{9} + 14 q^{17} + 12 q^{25} + 28 q^{29} + 42 q^{37} + 28 q^{41} + 56 q^{49} - 38 q^{53} + 42 q^{57} + 84 q^{61} + 8 q^{65} + 56 q^{69} - 42 q^{73} - 42 q^{77} - 44 q^{81} - 12 q^{85} - 28 q^{89} + 98 q^{93}+O(q^{100}) $ 48 * q - 4 * q^9 + 14 * q^17 + 12 * q^25 + 28 * q^29 + 42 * q^37 + 28 * q^41 + 56 * q^49 - 38 * q^53 + 42 * q^57 + 84 * q^61 + 8 * q^65 + 56 * q^69 - 42 * q^73 - 42 * q^77 - 44 * q^81 - 12 * q^85 - 28 * q^89 + 98 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{14}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.969349	+	1.21553i	0.559654	+	0.701784i	0.978494	−	0.206276i	$-0.0661346\pi$
$3$	0.969349	+	1.21553i	0.559654	+	0.701784i	−0.418840	+	0.908060i	$0.637563\pi$
$4$		0			0
$5$	−1.39014	+	1.10860i	−0.621691	+	0.495782i	−0.882938	−	0.469490i	$-0.844438\pi$
$5$	−1.39014	+	1.10860i	−0.621691	+	0.495782i	0.261247	+	0.965272i	$0.415866\pi$
$6$		0			0
$7$	−0.267553	+	2.63219i	−0.101126	+	0.994874i
$7$	−0.267553	+	2.63219i	−0.101126	+	0.994874i
$8$		0			0
$9$	0.129699	−	0.568247i	0.0432329	−	0.189416i
$10$		0			0
$11$	−2.43732	+	0.556302i	−0.734880	+	0.167731i	−0.573552	−	0.819169i	$-0.694435\pi$
$11$	−2.43732	+	0.556302i	−0.734880	+	0.167731i	−0.161328	+	0.986901i	$0.551578\pi$
$12$		0			0
$13$	−5.14006	+	1.17319i	−1.42560	+	0.325383i	−0.864611	−	0.502442i	$-0.832435\pi$
$13$	−5.14006	+	1.17319i	−1.42560	+	0.325383i	−0.560986	+	0.827825i	$0.689578\pi$
$14$		0			0
$15$	−2.69507	−	0.615132i	−0.695864	−	0.158826i
$16$		0			0
$17$	0.0272541	−	0.0565938i	0.00661010	−	0.0137260i	−0.897638	−	0.440734i	$-0.854718\pi$
$17$	0.0272541	−	0.0565938i	0.00661010	−	0.0137260i	0.904248	+	0.427008i	$0.140432\pi$
$18$		0			0
$19$	−1.00192			−0.229856			−0.114928	−	0.993374i	$-0.536664\pi$
$19$	−1.00192			−0.229856			−0.114928	+	0.993374i	$0.536664\pi$
$20$		0			0
$21$	−3.45884	+	2.22629i	−0.754782	+	0.485817i
$22$		0			0
$23$	−0.107144	−	0.222488i	−0.0223411	−	0.0463919i	0.889500	−	0.456936i	$-0.151053\pi$
$23$	−0.107144	−	0.222488i	−0.0223411	−	0.0463919i	−0.911841	+	0.410544i	$0.865339\pi$
$24$		0			0
$25$	−0.409105	+	1.79241i	−0.0818211	+	0.358482i
$26$		0			0
$27$	5.01869	−	2.41687i	0.965848	−	0.465128i
$28$		0			0
$29$	−4.86206	−	2.34145i	−0.902863	−	0.434796i	−0.0759407	−	0.997112i	$-0.524196\pi$
$29$	−4.86206	−	2.34145i	−0.902863	−	0.434796i	−0.826922	+	0.562317i	$0.809910\pi$
$30$		0			0
$31$	5.33623			0.958415			0.479207	−	0.877702i	$-0.340924\pi$
$31$	5.33623			0.958415			0.479207	+	0.877702i	$0.340924\pi$
$32$		0			0
$33$	−3.03881	−	2.42337i	−0.528989	−	0.421855i
$34$		0			0
$35$	−2.54611	−	3.95573i	−0.430372	−	0.668640i
$36$		0			0
$37$	−2.06907	−	0.996411i	−0.340153	−	0.163809i	0.256007	−	0.966675i	$-0.417593\pi$
$37$	−2.06907	−	0.996411i	−0.340153	−	0.163809i	−0.596159	+	0.802866i	$0.703307\pi$
$38$		0			0
$39$	−6.40855	−	5.11065i	−1.02619	−	0.818359i
$40$		0			0
$41$	−2.80032	+	2.23318i	−0.437336	+	0.348764i	−0.817275	−	0.576248i	$-0.804516\pi$
$41$	−2.80032	+	2.23318i	−0.437336	+	0.348764i	0.379939	+	0.925011i	$0.375945\pi$
$42$		0			0
$43$	1.83065	+	1.45989i	0.279171	+	0.222632i	0.753058	−	0.657954i	$-0.228578\pi$
$43$	1.83065	+	1.45989i	0.279171	+	0.222632i	−0.473887	+	0.880586i	$0.657149\pi$
$44$		0			0
$45$	0.449660	+	0.933729i	0.0670314	+	0.139192i
$46$		0			0
$47$	2.40775	+	10.5491i	0.351207	+	1.53874i	0.774398	+	0.632699i	$0.218053\pi$
$47$	2.40775	+	10.5491i	0.351207	+	1.53874i	−0.423191	+	0.906040i	$0.639090\pi$
$48$		0			0
$49$	−6.85683	−	1.40850i	−0.979547	−	0.201214i
$50$		0			0
$51$	0.0952100	−	0.0217311i	0.0133321	−	0.00304296i
$52$		0			0
$53$	−3.85131	+	1.85469i	−0.529018	+	0.254762i	−0.679273	−	0.733886i	$-0.737705\pi$
$53$	−3.85131	+	1.85469i	−0.529018	+	0.254762i	0.150255	+	0.988647i	$0.451991\pi$
$54$		0			0
$55$	2.77151	−	3.47536i	0.373710	−	0.468617i
$56$		0			0
$57$	−0.971208	−	1.21786i	−0.128640	−	0.161309i
$58$		0			0
$59$	3.91279	−	4.90648i	0.509401	−	0.638769i	−0.458920	−	0.888478i	$-0.651763\pi$
$59$	3.91279	−	4.90648i	0.509401	−	0.638769i	0.968321	+	0.249709i	$0.0803349\pi$
$60$		0			0
$61$	−5.94308	+	12.3409i	−0.760934	+	1.58010i	0.0526263	+	0.998614i	$0.483241\pi$
$61$	−5.94308	+	12.3409i	−0.760934	+	1.58010i	−0.813560	+	0.581481i	$0.802474\pi$
$62$		0			0
$63$	1.46103	+	0.493428i	0.184073	+	0.0621660i
$64$		0			0
$65$	5.84483	−	7.32918i	0.724961	−	0.909073i
$66$		0			0
$67$		−	5.43170i		−	0.663588i	−0.943352	−	0.331794i	$-0.892346\pi$
$67$		−	5.43170i		−	0.663588i	0.943352	−	0.331794i	$-0.107654\pi$
$68$		0			0
$69$	0.166579	−	0.345905i	0.0200537	−	0.0416420i
$70$		0			0
$71$	−1.70512	−	3.54073i	−0.202361	−	0.420207i	0.774948	−	0.632025i	$-0.217776\pi$
$71$	−1.70512	−	3.54073i	−0.202361	−	0.420207i	−0.977309	+	0.211818i	$0.932062\pi$
$72$		0			0
$73$	5.36315	+	1.22410i	0.627710	+	0.143271i	0.524530	−	0.851392i	$-0.324241\pi$
$73$	5.36315	+	1.22410i	0.627710	+	0.143271i	0.103180	+	0.994663i	$0.467098\pi$
$74$		0			0
$75$	−2.57528	+	1.24019i	−0.297368	+	0.143205i
$76$		0			0
$77$	−0.812180	−	6.56433i	−0.0925565	−	0.748074i
$78$		0			0
$79$			14.8054i			1.66574i	0.553466	+	0.832872i	$0.313305\pi$
$79$			14.8054i			1.66574i	−0.553466	+	0.832872i	$0.686695\pi$
$80$		0			0
$81$	6.22722	+	2.99887i	0.691913	+	0.333208i
$82$		0			0
$83$	−0.714859	+	3.13200i	−0.0784660	+	0.343782i	−0.998888	−	0.0471440i	$-0.984988\pi$
$83$	−0.714859	+	3.13200i	−0.0784660	+	0.343782i	0.920422	+	0.390926i	$0.127845\pi$
$84$		0			0
$85$	0.0248529	+	0.108887i	0.00269567	+	0.0118105i
$86$		0			0
$87$	−1.86695	−	8.17964i	−0.200158	−	0.876950i
$88$		0			0
$89$	7.71016	+	1.75979i	0.817275	+	0.186538i	0.610669	−	0.791886i	$-0.290901\pi$
$89$	7.71016	+	1.75979i	0.817275	+	0.186538i	0.206607	+	0.978424i	$0.433758\pi$
$90$		0			0
$91$	−1.71281	−	13.8435i	−0.179551	−	1.45119i
$92$		0			0
$93$	5.17267	+	6.48632i	0.536381	+	0.672600i
$94$		0			0
$95$	1.39281	−	1.11073i	0.142899	−	0.113958i
$96$		0			0
$97$			4.97992i			0.505635i	0.967514	+	0.252817i	$0.0813572\pi$
$97$			4.97992i			0.505635i	−0.967514	+	0.252817i	$0.918643\pi$
$98$		0			0
$99$			1.45715i			0.146449i
$100$		0			0
$101$	4.52308	−	3.60704i	0.450063	−	0.358914i	−0.372074	−	0.928203i	$-0.621353\pi$
$101$	4.52308	−	3.60704i	0.450063	−	0.358914i	0.822137	+	0.569290i	$0.192782\pi$
$102$		0			0
$103$	5.43488	+	6.81513i	0.535515	+	0.671515i	0.973822	−	0.227311i	$-0.0729932\pi$
$103$	5.43488	+	6.81513i	0.535515	+	0.671515i	−0.438307	+	0.898825i	$0.644422\pi$
$104$		0			0
$105$	2.34022	−	6.92935i	0.228382	−	0.676235i
$106$		0			0
$107$	0.00768058	+	0.00175304i	0.000742510	+	0.000169473i	0.222892	−	0.974843i	$-0.428450\pi$
$107$	0.00768058	+	0.00175304i	0.000742510	+	0.000169473i	−0.222150	+	0.975013i	$0.571307\pi$
$108$		0			0
$109$	2.94476	+	12.9018i	0.282057	+	1.23577i	0.895152	+	0.445762i	$0.147067\pi$
$109$	2.94476	+	12.9018i	0.282057	+	1.23577i	−0.613095	+	0.790009i	$0.710076\pi$
$110$		0			0
$111$	−0.794487	−	3.48087i	−0.0754094	−	0.330390i
$112$		0			0
$113$	4.45811	−	19.5322i	0.419383	−	1.83744i	−0.116558	−	0.993184i	$-0.537186\pi$
$113$	4.45811	−	19.5322i	0.419383	−	1.83744i	0.535941	−	0.844255i	$-0.319957\pi$
$114$		0			0
$115$	0.395596	+	0.190509i	0.0368895	+	0.0177651i
$116$		0			0
$117$			3.07299i			0.284098i
$118$		0			0
$119$	0.141674	+	0.0868799i	0.0129872	+	0.00796427i
$120$		0			0
$121$	−4.27960	+	2.06095i	−0.389055	+	0.187359i
$122$		0			0
$123$	−5.42897	−	1.23913i	−0.489513	−	0.111728i
$124$		0			0
$125$	−5.27571	−	10.9551i	−0.471874	−	0.979856i
$126$		0			0
$127$	−4.61575	+	9.58470i	−0.409581	+	0.850505i	0.589505	+	0.807765i	$0.299323\pi$
$127$	−4.61575	+	9.58470i	−0.409581	+	0.850505i	−0.999086	+	0.0427398i	$0.986391\pi$
$128$		0			0
$129$			3.64034i			0.320514i
$130$		0			0
$131$	−11.0627	+	13.8722i	−0.966553	+	1.21202i	0.0106999	+	0.999943i	$0.496594\pi$
$131$	−11.0627	+	13.8722i	−0.966553	+	1.21202i	−0.977253	+	0.212077i	$0.931977\pi$
$132$		0			0
$133$	0.268066	−	2.63724i	0.0232443	−	0.228677i
$134$		0			0
$135$	−4.29735	+	8.92353i	−0.369857	+	0.768016i
$136$		0			0
$137$	6.92836	−	8.68788i	0.591929	−	0.742256i	−0.392166	−	0.919894i	$-0.628274\pi$
$137$	6.92836	−	8.68788i	0.591929	−	0.742256i	0.984096	+	0.177638i	$0.0568457\pi$
$138$		0			0
$139$	5.46215	+	6.84932i	0.463293	+	0.580951i	0.957515	−	0.288385i	$-0.0931182\pi$
$139$	5.46215	+	6.84932i	0.463293	+	0.580951i	−0.494221	+	0.869336i	$0.664547\pi$
$140$		0			0
$141$	−10.4887	+	13.1524i	−0.883308	+	1.10763i
$142$		0			0
$143$	11.8753	−	5.71886i	0.993065	−	0.478235i
$144$		0			0
$145$	9.35470	−	2.13515i	0.776865	−	0.177314i
$146$		0			0
$147$	−4.93460	−	9.69998i	−0.406999	−	0.800041i
$148$		0			0
$149$	−2.73684	−	11.9909i	−0.224211	−	0.982331i	−0.954270	−	0.298947i	$-0.903365\pi$
$149$	−2.73684	−	11.9909i	−0.224211	−	0.982331i	0.730059	−	0.683384i	$-0.239493\pi$
$150$		0			0
$151$	−6.11726	−	12.7026i	−0.497816	−	1.03373i	−0.986877	−	0.161476i	$-0.948375\pi$
$151$	−6.11726	−	12.7026i	−0.497816	−	1.03373i	0.489061	−	0.872250i	$-0.337340\pi$
$152$		0			0
$153$	−0.0286244	−	0.0228272i	−0.00231415	−	0.00184547i
$154$		0			0
$155$	−7.41812	+	5.91575i	−0.595838	+	0.475165i
$156$		0			0
$157$	4.63906	+	3.69952i	0.370237	+	0.295254i	0.790879	−	0.611973i	$-0.209624\pi$
$157$	4.63906	+	3.69952i	0.370237	+	0.295254i	−0.420642	+	0.907227i	$0.638195\pi$
$158$		0			0
$159$	−5.98769	−	2.88352i	−0.474855	−	0.228678i
$160$		0			0
$161$	0.614296	−	0.222497i	0.0484133	−	0.0175352i
$162$		0			0
$163$	16.8583	+	13.4441i	1.32045	+	1.05302i	0.994179	+	0.107744i	$0.0343628\pi$
$163$	16.8583	+	13.4441i	1.32045	+	1.05302i	0.326269	+	0.945277i	$0.394209\pi$
$164$		0			0
$165$	6.91094			0.538016
$166$		0			0
$167$	19.6427	+	9.45943i	1.52000	+	0.731992i	0.993027	−	0.117891i	$-0.0376133\pi$
$167$	19.6427	+	9.45943i	1.52000	+	0.731992i	0.526971	+	0.849883i	$0.323328\pi$
$168$		0			0
$169$	13.3313	−	6.42000i	1.02548	−	0.493846i
$170$		0			0
$171$	−0.129947	+	0.569337i	−0.00993733	+	0.0435383i
$172$		0			0
$173$	−1.91694	−	3.98056i	−0.145742	−	0.302636i	0.815300	−	0.579039i	$-0.196572\pi$
$173$	−1.91694	−	3.98056i	−0.145742	−	0.302636i	−0.961042	+	0.276403i	$0.910858\pi$
$174$		0			0
$175$	−4.60850	−	1.55641i	−0.348370	−	0.117653i
$176$		0			0
$177$	9.75680			0.733366
$178$		0			0
$179$	−10.5798	+	21.9691i	−0.790770	+	1.64205i	−0.0243553	+	0.999703i	$0.507753\pi$
$179$	−10.5798	+	21.9691i	−0.790770	+	1.64205i	−0.766414	+	0.642347i	$0.777961\pi$
$180$		0			0
$181$	20.1087	+	4.58969i	1.49467	+	0.341149i	0.890234	−	0.455504i	$-0.150541\pi$
$181$	20.1087	+	4.58969i	1.49467	+	0.341149i	0.604437	+	0.796653i	$0.293398\pi$
$182$		0			0
$183$	−20.7616	+	4.73871i	−1.53474	+	0.350295i
$184$		0			0
$185$	3.98092	−	0.908620i	0.292683	−	0.0668031i
$186$		0			0
$187$	−0.0349438	+	0.153099i	−0.00255534	+	0.0111957i
$188$		0			0
$189$	5.01890	+	13.8568i	0.365071	+	1.00793i
$190$		0			0
$191$	18.8875	−	15.0623i	1.36665	−	1.08987i	0.380363	−	0.924837i	$-0.375799\pi$
$191$	18.8875	−	15.0623i	1.36665	−	1.08987i	0.986288	−	0.165030i	$-0.0527722\pi$
$192$		0			0
$193$	−4.96626	−	6.22749i	−0.357479	−	0.448265i	0.570277	−	0.821453i	$-0.306836\pi$
$193$	−4.96626	−	6.22749i	−0.357479	−	0.448265i	−0.927756	+	0.373188i	$0.878265\pi$
$194$		0			0
$195$	14.5745			1.04370
$196$		0			0
$197$	9.10270			0.648541			0.324270	−	0.945964i	$-0.394881\pi$
$197$	9.10270			0.648541			0.324270	+	0.945964i	$0.394881\pi$
$198$		0			0
$199$	−11.5771	−	14.5172i	−0.820676	−	1.02910i	−0.998982	−	0.0451205i	$-0.985633\pi$
$199$	−11.5771	−	14.5172i	−0.820676	−	1.02910i	0.178305	−	0.983975i	$-0.442939\pi$
$200$		0			0
$201$	6.60237	−	5.26522i	0.465695	−	0.371380i
$202$		0			0
$203$	7.46399	−	12.1714i	0.523869	−	0.854265i
$204$		0			0
$205$	1.41713	−	6.20887i	0.0989770	−	0.433646i
$206$		0			0
$207$	−0.140324	+	0.0320281i	−0.00975322	+	0.00222611i
$208$		0			0
$209$	2.44199	−	0.557369i	0.168916	−	0.0385540i
$210$		0			0
$211$	−13.1801	−	3.00827i	−0.907356	−	0.207098i	−0.256718	−	0.966486i	$-0.582641\pi$
$211$	−13.1801	−	3.00827i	−0.907356	−	0.207098i	−0.650638	+	0.759388i	$0.725498\pi$
$212$		0			0
$213$	2.65098	−	5.50482i	0.181642	−	0.377184i
$214$		0			0
$215$	−4.16330			−0.283935
$216$		0			0
$217$	−1.42772	+	14.0460i	−0.0969202	+	0.953501i
$218$		0			0
$219$	3.71084	+	7.70563i	0.250755	+	0.520698i
$220$		0			0
$221$	−0.0736929	+	0.322870i	−0.00495712	+	0.0217186i
$222$		0			0
$223$	9.34470	−	4.50017i	0.625767	−	0.301354i	−0.0939966	−	0.995573i	$-0.529964\pi$
$223$	9.34470	−	4.50017i	0.625767	−	0.301354i	0.719764	+	0.694219i	$0.244250\pi$
$224$		0			0
$225$	0.965470	+	0.464946i	0.0643647	+	0.0309964i
$226$		0			0
$227$	27.9091			1.85239			0.926194	−	0.377046i	$-0.123060\pi$
$227$	27.9091			1.85239			0.926194	+	0.377046i	$0.123060\pi$
$228$		0			0
$229$	−9.73419	−	7.76275i	−0.643253	−	0.512977i	0.246663	−	0.969101i	$-0.420666\pi$
$229$	−9.73419	−	7.76275i	−0.643253	−	0.512977i	−0.889916	+	0.456124i	$0.849237\pi$
$230$		0			0
$231$	7.19182	−	7.35035i	0.473187	−	0.483617i
$232$		0			0
$233$	7.61580	+	3.66758i	0.498928	+	0.240271i	0.666384	−	0.745609i	$-0.267841\pi$
$233$	7.61580	+	3.66758i	0.498928	+	0.240271i	−0.167457	+	0.985879i	$0.553555\pi$
$234$		0			0
$235$	−15.0418	−	11.9955i	−0.981221	−	0.782498i
$236$		0			0
$237$	−17.9964	+	14.3516i	−1.16899	+	0.932240i
$238$		0			0
$239$	−18.3355	−	14.6221i	−1.18603	−	0.945825i	−0.186696	−	0.982418i	$-0.559778\pi$
$239$	−18.3355	−	14.6221i	−1.18603	−	0.945825i	−0.999330	+	0.0365929i	$0.988350\pi$
$240$		0			0
$241$	−1.49118	−	3.09647i	−0.0960554	−	0.199461i	0.847404	−	0.530948i	$-0.178164\pi$
$241$	−1.49118	−	3.09647i	−0.0960554	−	0.199461i	−0.943460	+	0.331487i	$0.892450\pi$
$242$		0			0
$243$	−1.32740	−	5.81571i	−0.0851526	−	0.373078i
$244$		0			0
$245$	11.0934	−	5.64348i	0.708734	−	0.360549i
$246$		0			0
$247$	5.14992	−	1.17544i	0.327682	−	0.0747912i
$248$		0			0
$249$	−4.49998	+	2.16707i	−0.285174	+	0.137333i
$250$		0			0
$251$	−0.560763	+	0.703175i	−0.0353951	+	0.0443840i	−0.799214	−	0.601047i	$-0.794751\pi$
$251$	−0.560763	+	0.703175i	−0.0353951	+	0.0443840i	0.763819	+	0.645431i	$0.223322\pi$
$252$		0			0
$253$	0.384915	+	0.482669i	0.0241994	+	0.0303451i
$254$		0			0
$255$	−0.108264	+	0.135759i	−0.00677978	+	0.00850158i
$256$		0			0
$257$	−1.35689	+	2.81761i	−0.0846403	+	0.175757i	−0.938993	−	0.343936i	$-0.888240\pi$
$257$	−1.35689	+	2.81761i	−0.0846403	+	0.175757i	0.854353	+	0.519694i	$0.173954\pi$
$258$		0			0
$259$	3.17633	−	5.17958i	0.197367	−	0.321844i
$260$		0			0
$261$	−1.96112	+	2.45917i	−0.121391	+	0.152219i
$262$		0			0
$263$		−	11.4866i		−	0.708294i	−0.935190	−	0.354147i	$-0.884771\pi$
$263$		−	11.4866i		−	0.708294i	0.935190	−	0.354147i	$-0.115229\pi$
$264$		0			0
$265$	3.29776	−	6.84786i	0.202580	−	0.420661i
$266$		0			0
$267$	5.33476	+	11.0777i	0.326482	+	0.677947i
$268$		0			0
$269$	−5.18971	−	1.18452i	−0.316422	−	0.0722213i	0.0613602	−	0.998116i	$-0.480456\pi$
$269$	−5.18971	−	1.18452i	−0.316422	−	0.0722213i	−0.377783	+	0.925894i	$0.623313\pi$
$270$		0			0
$271$	−0.588251	+	0.283287i	−0.0357337	+	0.0172084i	−0.451665	−	0.892187i	$-0.649170\pi$
$271$	−0.588251	+	0.283287i	−0.0357337	+	0.0172084i	0.415932	+	0.909396i	$0.363456\pi$
$272$		0			0
$273$	15.1668	−	15.5011i	0.917937	−	0.938172i
$274$		0			0
$275$		−	4.59626i		−	0.277165i
$276$		0			0
$277$	3.46526	+	1.66878i	0.208207	+	0.100267i	0.535081	−	0.844801i	$-0.320281\pi$
$277$	3.46526	+	1.66878i	0.208207	+	0.100267i	−0.326874	+	0.945068i	$0.605995\pi$
$278$		0			0
$279$	0.692102	−	3.03230i	0.0414350	−	0.181539i
$280$		0			0
$281$	3.45547	+	15.1394i	0.206136	+	0.903141i	0.967110	+	0.254358i	$0.0818643\pi$
$281$	3.45547	+	15.1394i	0.206136	+	0.903141i	−0.760974	+	0.648782i	$0.775279\pi$
$282$		0			0
$283$	−1.22224	−	5.35500i	−0.0726548	−	0.318321i	0.925521	−	0.378696i	$-0.123628\pi$
$283$	−1.22224	−	5.35500i	−0.0726548	−	0.318321i	−0.998176	+	0.0603749i	$0.980770\pi$
$284$		0			0
$285$	2.70024	+	0.616312i	0.159948	+	0.0365071i
$286$		0			0
$287$	−5.12891	−	7.96845i	−0.302750	−	0.470363i
$288$		0			0
$289$	10.5969	+	13.2881i	0.623345	+	0.781650i
$290$		0			0
$291$	−6.05322	+	4.82728i	−0.354846	+	0.282980i
$292$		0			0
$293$		−	17.2183i		−	1.00590i	−0.864314	−	0.502952i	$-0.832247\pi$
$293$		−	17.2183i		−	1.00590i	0.864314	−	0.502952i	$-0.167753\pi$
$294$		0			0
$295$			11.1584i			0.649669i
$296$		0			0
$297$	−10.8876	+	8.68261i	−0.631765	+	0.503816i
$298$		0			0
$299$	0.811748	+	1.01790i	0.0469446	+	0.0588666i
$300$		0			0
$301$	−4.33251	+	4.42801i	−0.249722	+	0.255226i
$302$		0			0
$303$	8.76889	+	2.00144i	0.503759	+	0.114980i
$304$		0			0
$305$	−5.41946	−	23.7442i	−0.310317	−	1.35959i
$306$		0			0
$307$	3.56600	+	15.6237i	0.203523	+	0.891691i	0.968771	+	0.247956i	$0.0797588\pi$
$307$	3.56600	+	15.6237i	0.203523	+	0.891691i	−0.765249	+	0.643735i	$0.777384\pi$
$308$		0			0
$309$	−3.01566	+	13.2125i	−0.171555	+	0.751632i
$310$		0			0
$311$	−17.2442	−	8.30439i	−0.977831	−	0.470899i	−0.124472	−	0.992223i	$-0.539724\pi$
$311$	−17.2442	−	8.30439i	−0.977831	−	0.470899i	−0.853359	+	0.521324i	$0.825438\pi$
$312$		0			0
$313$		−	8.69391i		−	0.491409i	−0.969345	−	0.245704i	$-0.920981\pi$
$313$		−	8.69391i		−	0.491409i	0.969345	−	0.245704i	$-0.0790193\pi$
$314$		0			0
$315$	−2.57806	+	0.933769i	−0.145257	+	0.0526119i
$316$		0			0
$317$	−30.7809	+	14.8233i	−1.72883	+	0.832561i	−0.742080	+	0.670311i	$0.766161\pi$
$317$	−30.7809	+	14.8233i	−1.72883	+	0.832561i	−0.986750	+	0.162249i	$0.948125\pi$
$318$		0			0
$319$	13.1530	+	3.00208i	0.736424	+	0.168084i
$320$		0			0
$321$	0.00531430	+	0.0110353i	0.000296615	+	0.000615928i
$322$		0			0
$323$	−0.0273064	+	0.0567024i	−0.00151937	+	0.00315500i
$324$		0			0
$325$		−	9.69304i		−	0.537673i
$326$		0			0
$327$	−12.8280	+	16.0858i	−0.709390	+	0.889547i
$328$		0			0
$329$	−28.4113	+	3.51523i	−1.56637	+	0.193801i
$330$		0			0
$331$	−12.7416	+	26.4583i	−0.700343	+	1.45428i	0.181820	+	0.983332i	$0.441801\pi$
$331$	−12.7416	+	26.4583i	−0.700343	+	1.45428i	−0.882163	+	0.470945i	$0.843913\pi$
$332$		0			0
$333$	−0.834563	+	1.04651i	−0.0457338	+	0.0573483i
$334$		0			0
$335$	6.02160	+	7.55085i	0.328995	+	0.412547i
$336$		0			0
$337$	−5.55556	+	6.96646i	−0.302631	+	0.379487i	−0.909773	−	0.415106i	$-0.863744\pi$
$337$	−5.55556	+	6.96646i	−0.302631	+	0.379487i	0.607142	+	0.794593i	$0.292316\pi$
$338$		0			0
$339$	28.0634	−	13.5146i	1.52419	−	0.734013i
$340$		0			0
$341$	−13.0061	+	2.96856i	−0.704319	+	0.160756i
$342$		0			0
$343$	5.54200	−	17.6716i	0.299240	−	0.954178i
$344$		0			0
$345$	0.151902	+	0.665527i	0.00817814	+	0.0358308i
$346$		0			0
$347$	0.236381	+	0.490850i	0.0126896	+	0.0263502i	0.907217	−	0.420662i	$-0.138202\pi$
$347$	0.236381	+	0.490850i	0.0126896	+	0.0263502i	−0.894528	+	0.447012i	$0.852488\pi$
$348$		0			0
$349$	3.90071	+	3.11071i	0.208800	+	0.166513i	0.722306	−	0.691573i	$-0.243082\pi$
$349$	3.90071	+	3.11071i	0.208800	+	0.166513i	−0.513506	+	0.858086i	$0.671654\pi$
$350$		0			0
$351$	−22.9609	+	18.3107i	−1.22556	+	0.977355i
$352$		0			0
$353$	−15.1220	−	12.0594i	−0.804865	−	0.641859i	0.132118	−	0.991234i	$-0.457822\pi$
$353$	−15.1220	−	12.0594i	−0.804865	−	0.641859i	−0.936983	+	0.349375i	$0.886394\pi$
$354$		0			0
$355$	6.29563	+	3.03181i	0.334137	+	0.160912i
$356$		0			0
$357$	0.0317265	+	0.256425i	0.00167915	+	0.0135714i
$358$		0			0
$359$	21.5260	+	17.1664i	1.13610	+	0.906010i	0.996450	−	0.0841911i	$-0.0268306\pi$
$359$	21.5260	+	17.1664i	1.13610	+	0.906010i	0.139651	+	0.990201i	$0.455402\pi$
$360$		0			0
$361$	−17.9962			−0.947166
$362$		0			0
$363$	−6.65356	−	3.20419i	−0.349221	−	0.168176i
$364$		0			0
$365$	−8.81260	+	4.24392i	−0.461272	+	0.222137i
$366$		0			0
$367$	−5.09226	+	22.3106i	−0.265814	+	1.16461i	0.649019	+	0.760772i	$0.275180\pi$
$367$	−5.09226	+	22.3106i	−0.265814	+	1.16461i	−0.914833	+	0.403833i	$0.867678\pi$
$368$		0			0
$369$	0.905799	+	1.88091i	0.0471540	+	0.0979163i
$370$		0			0
$371$	−3.85147	−	10.6336i	−0.199959	−	0.552069i
$372$		0			0
$373$	−31.0352			−1.60694			−0.803472	−	0.595343i	$-0.797016\pi$
$373$	−31.0352			−1.60694			−0.803472	+	0.595343i	$0.797016\pi$
$374$		0			0
$375$	8.20222	−	17.0321i	0.423561	−	0.879534i
$376$		0			0
$377$	27.7383	+	6.33108i	1.42859	+	0.326067i
$378$		0			0
$379$	6.84782	−	1.56297i	0.351749	−	0.0802843i	−0.0429959	−	0.999075i	$-0.513690\pi$
$379$	6.84782	−	1.56297i	0.351749	−	0.0802843i	0.394745	+	0.918791i	$0.370833\pi$
$380$		0			0
$381$	−16.1247	+	3.68036i	−0.826094	+	0.188551i
$382$		0			0
$383$	−6.61839	+	28.9971i	−0.338184	+	1.48168i	0.464658	+	0.885490i	$0.346177\pi$
$383$	−6.61839	+	28.9971i	−0.338184	+	1.48168i	−0.802842	+	0.596191i	$0.796680\pi$
$384$		0			0
$385$	8.40627	+	8.22497i	0.428423	+	0.419183i
$386$		0			0
$387$	1.06701	−	0.850914i	0.0542393	−	0.0432544i
$388$		0			0
$389$	−17.6464	−	22.1279i	−0.894707	−	1.12193i	−0.991945	−	0.126666i	$-0.959572\pi$
$389$	−17.6464	−	22.1279i	−0.894707	−	1.12193i	0.0972386	−	0.995261i	$-0.468999\pi$
$390$		0			0
$391$	−0.0155115			−0.000784452
$392$		0			0
$393$	−27.5856			−1.39151
$394$		0			0
$395$	−16.4134	−	20.5817i	−0.825845	−	1.03558i
$396$		0			0
$397$	2.25647	−	1.79948i	0.113249	−	0.0903132i	−0.565228	−	0.824935i	$-0.691212\pi$
$397$	2.25647	−	1.79948i	0.113249	−	0.0903132i	0.678477	+	0.734622i	$0.262640\pi$
$398$		0			0
$399$	3.46548	−	2.23056i	0.173491	−	0.111668i
$400$		0			0
$401$	3.48625	−	15.2742i	0.174095	−	0.762760i	−0.810189	−	0.586168i	$-0.800636\pi$
$401$	3.48625	−	15.2742i	0.174095	−	0.762760i	0.984284	−	0.176591i	$-0.0565071\pi$
$402$		0			0
$403$	−27.4285	+	6.26038i	−1.36631	+	0.311852i
$404$		0			0
$405$	−11.9813	+	2.73465i	−0.595355	+	0.135886i
$406$		0			0
$407$	5.59729	+	1.27754i	0.277447	+	0.0633255i
$408$		0			0
$409$	−6.27966	+	13.0399i	−0.310509	+	0.644779i	−0.996569	−	0.0827660i	$-0.973625\pi$
$409$	−6.27966	+	13.0399i	−0.310509	+	0.644779i	0.686060	+	0.727545i	$0.259339\pi$
$410$		0			0
$411$	17.2763			0.852179
$412$		0			0
$413$	11.8679	+	11.6119i	0.583981	+	0.571386i
$414$		0			0
$415$	−2.47839	−	5.14643i	−0.121659	−	0.252628i
$416$		0			0
$417$	−3.03079	+	13.2788i	−0.148418	+	0.650263i
$418$		0			0
$419$	−1.74439	+	0.840056i	−0.0852192	+	0.0410394i	−0.476008	−	0.879441i	$-0.657917\pi$
$419$	−1.74439	+	0.840056i	−0.0852192	+	0.0410394i	0.390789	+	0.920480i	$0.372202\pi$
$420$		0			0
$421$	17.8356	+	8.58918i	0.869254	+	0.418611i	0.814688	−	0.579899i	$-0.196908\pi$
$421$	17.8356	+	8.58918i	0.869254	+	0.418611i	0.0545663	+	0.998510i	$0.482622\pi$
$422$		0			0
$423$	6.30676			0.306645
$424$		0			0
$425$	0.0902894	+	0.0720034i	0.00437968	+	0.00349268i
$426$		0			0
$427$	−30.8936	−	18.9452i	−1.49505	−	0.916821i
$428$		0			0
$429$	18.4628	+	8.89119i	0.891390	+	0.429271i
$430$		0			0
$431$	−16.5836	−	13.2250i	−0.798806	−	0.637026i	0.136591	−	0.990628i	$-0.456386\pi$
$431$	−16.5836	−	13.2250i	−0.798806	−	0.637026i	−0.935396	+	0.353601i	$0.884957\pi$
$432$		0			0
$433$	0.447818	−	0.357123i	0.0215207	−	0.0171622i	−0.612670	−	0.790339i	$-0.709905\pi$
$433$	0.447818	−	0.357123i	0.0215207	−	0.0171622i	0.634191	+	0.773176i	$0.281333\pi$
$434$		0			0
$435$	11.6633	+	9.30117i	0.559212	+	0.445957i
$436$		0			0
$437$	0.107350	+	0.222914i	0.00513524	+	0.0106634i
$438$		0			0
$439$	5.06402	+	22.1869i	0.241692	+	1.05892i	0.939476	+	0.342615i	$0.111312\pi$
$439$	5.06402	+	22.1869i	0.241692	+	1.05892i	−0.697784	+	0.716308i	$0.745830\pi$
$440$		0			0
$441$	−1.68970	+	3.71369i	−0.0804618	+	0.176843i
$442$		0			0
$443$	−30.3903	+	6.93639i	−1.44389	+	0.329558i	−0.871488	−	0.490417i	$-0.836845\pi$
$443$	−30.3903	+	6.93639i	−1.44389	+	0.329558i	−0.572400	+	0.819975i	$0.693987\pi$
$444$		0			0
$445$	−12.6691	+	6.10113i	−0.600575	+	0.289222i
$446$		0			0
$447$	11.9223	−	14.9500i	0.563904	−	0.707113i
$448$		0			0
$449$	−9.57640	−	12.0084i	−0.451938	−	0.566713i	0.502707	−	0.864457i	$-0.332337\pi$
$449$	−9.57640	−	12.0084i	−0.451938	−	0.566713i	−0.954646	+	0.297744i	$0.903766\pi$
$450$		0			0
$451$	5.58294	−	7.00079i	0.262890	−	0.329654i
$452$		0			0
$453$	9.51060	−	19.7490i	0.446847	−	0.927887i
$454$		0			0
$455$	17.7280	+	17.3456i	0.831101	+	0.813175i
$456$		0			0
$457$	−20.1512	+	25.2688i	−0.942633	+	1.18202i	0.0405087	+	0.999179i	$0.487102\pi$
$457$	−20.1512	+	25.2688i	−0.942633	+	1.18202i	−0.983142	+	0.182845i	$0.941469\pi$
$458$		0			0
$459$		−	0.349897i		−	0.0163318i
$460$		0			0
$461$	12.7548	−	26.4856i	0.594050	−	1.23356i	−0.359732	−	0.933056i	$-0.617132\pi$
$461$	12.7548	−	26.4856i	0.594050	−	1.23356i	0.953781	−	0.300501i	$-0.0971540\pi$
$462$		0			0
$463$	−7.76099	−	16.1159i	−0.360684	−	0.748967i	0.639113	−	0.769113i	$-0.279301\pi$
$463$	−7.76099	−	16.1159i	−0.360684	−	0.748967i	−0.999797	+	0.0201451i	$0.993587\pi$
$464$		0			0
$465$	−14.3815	−	3.28248i	−0.666926	−	0.152221i
$466$		0			0
$467$	−21.6491	+	10.4257i	−1.00180	+	0.482442i	−0.861549	−	0.507674i	$-0.830505\pi$
$467$	−21.6491	+	10.4257i	−1.00180	+	0.482442i	−0.140251	+	0.990116i	$0.544791\pi$
$468$		0			0
$469$	14.2973	+	1.45327i	0.660186	+	0.0671057i
$470$		0			0
$471$			9.22502i			0.425067i
$472$		0			0
$473$	−5.27401	−	2.53983i	−0.242499	−	0.116782i
$474$		0			0
$475$	0.409890	−	1.79585i	0.0188071	−	0.0823991i
$476$		0			0
$477$	0.554414	+	2.42905i	0.0253849	+	0.111218i
$478$		0			0
$479$	−1.98352	−	8.69038i	−0.0906295	−	0.397074i	0.909184	−	0.416395i	$-0.136707\pi$
$479$	−1.98352	−	8.69038i	−0.0906295	−	0.397074i	−0.999813	+	0.0193212i	$0.993849\pi$
$480$		0			0
$481$	11.8041	+	2.69421i	0.538221	+	0.122845i
$482$		0			0
$483$	0.865918	+	0.531015i	0.0394006	+	0.0241620i
$484$		0			0
$485$	−5.52075	−	6.92281i	−0.250684	−	0.314348i
$486$		0			0
$487$	21.9052	−	17.4688i	0.992619	−	0.791587i	0.0145551	−	0.999894i	$-0.495367\pi$
$487$	21.9052	−	17.4688i	0.992619	−	0.791587i	0.978063	+	0.208307i	$0.0667954\pi$
$488$		0			0
$489$			33.5237i			1.51600i
$490$		0			0
$491$		−	3.89685i		−	0.175862i	−0.996127	−	0.0879311i	$-0.971974\pi$
$491$		−	3.89685i		−	0.175862i	0.996127	−	0.0879311i	$-0.0280255\pi$
$492$		0			0
$493$	−0.265023	+	0.211349i	−0.0119360	+	0.00951866i
$494$		0			0
$495$	−1.61540	−	2.02565i	−0.0726069	−	0.0910462i
$496$		0			0
$497$	9.77607	−	3.54088i	0.438517	−	0.158830i
$498$		0			0
$499$	2.80004	+	0.639092i	0.125347	+	0.0286097i	0.284734	−	0.958606i	$-0.408095\pi$
$499$	2.80004	+	0.639092i	0.125347	+	0.0286097i	−0.159387	+	0.987216i	$0.550952\pi$
$500$		0			0
$501$	7.54246	+	33.0457i	0.336972	+	1.47637i
$502$		0			0
$503$	−1.31471	−	5.76012i	−0.0586200	−	0.256831i	0.937124	−	0.348998i	$-0.113478\pi$
$503$	−1.31471	−	5.76012i	−0.0586200	−	0.256831i	−0.995744	+	0.0921666i	$0.970621\pi$
$504$		0			0
$505$	−2.28896	+	10.0286i	−0.101857	+	0.446267i
$506$		0			0
$507$	20.7263	+	9.98128i	0.920489	+	0.443284i
$508$		0			0
$509$		−	26.6534i		−	1.18139i	−0.806895	−	0.590695i	$-0.798854\pi$
$509$		−	26.6534i		−	1.18139i	0.806895	−	0.590695i	$-0.201146\pi$
$510$		0			0
$511$	−4.65700	+	13.7893i	−0.206014	+	0.610003i
$512$		0			0
$513$	−5.02832	+	2.42151i	−0.222006	+	0.106912i
$514$		0			0
$515$	−15.1105	−	3.44888i	−0.665850	−	0.151976i
$516$		0			0
$517$	−11.7369	−	24.3720i	−0.516190	−	1.07188i
$518$		0			0
$519$	2.98029	−	6.18863i	0.130820	−	0.271651i
$520$		0			0
$521$			28.2451i			1.23744i	0.785611	+	0.618720i	$0.212349\pi$
$521$			28.2451i			1.23744i	−0.785611	+	0.618720i	$0.787651\pi$
$522$		0			0
$523$	19.9058	−	24.9611i	0.870420	−	1.09147i	−0.124640	−	0.992202i	$-0.539778\pi$
$523$	19.9058	−	24.9611i	0.870420	−	1.09147i	0.995060	−	0.0992707i	$-0.0316510\pi$
$524$		0			0
$525$	−2.57539	−	7.11045i	−0.112399	−	0.310325i
$526$		0			0
$527$	0.145434	−	0.301997i	0.00633522	−	0.0131552i
$528$		0			0
$529$	14.3022	−	17.9344i	0.621837	−	0.779759i
$530$		0			0
$531$	−2.28061	−	2.85979i	−0.0989700	−	0.124104i
$532$		0			0
$533$	11.7739	−	14.7640i	0.509983	−	0.639498i
$534$		0			0
$535$	−0.0126205	+	0.00607773i	−0.000545633	+	0.000262763i
$536$		0			0
$537$	−36.9595	+	8.43577i	−1.59492	+	0.364030i
$538$		0			0
$539$	17.4958	−	0.381507i	0.753599	−	0.0164327i
$540$		0			0
$541$	1.75975	+	7.70995i	0.0756574	+	0.331477i	0.998566	−	0.0535435i	$-0.0170516\pi$
$541$	1.75975	+	7.70995i	0.0756574	+	0.331477i	−0.922908	+	0.385020i	$0.874194\pi$
$542$		0			0
$543$	13.9135	+	28.8917i	0.597086	+	1.23986i
$544$		0			0
$545$	−18.3966	−	14.6708i	−0.788025	−	0.628429i
$546$		0			0
$547$	22.8331	−	18.2088i	0.976271	−	0.778550i	0.00109905	−	0.999999i	$-0.499650\pi$
$547$	22.8331	−	18.2088i	0.976271	−	0.778550i	0.975172	+	0.221449i	$0.0710787\pi$
$548$		0			0
$549$	6.24189	+	4.97774i	0.266398	+	0.212445i
$550$		0			0
$551$	4.87139	+	2.34594i	0.207528	+	0.0999403i
$552$		0			0
$553$	−38.9707	−	3.96124i	−1.65720	−	0.168449i
$554$		0			0
$555$	4.96336	+	3.95814i	0.210683	+	0.168014i
$556$		0			0
$557$	25.6914			1.08858			0.544289	−	0.838898i	$-0.316799\pi$
$557$	25.6914			1.08858			0.544289	+	0.838898i	$0.316799\pi$
$558$		0			0
$559$	−11.1224	−	5.35625i	−0.470426	−	0.226545i
$560$		0			0
$561$	−0.219968	+	0.105931i	−0.00928706	+	0.00447241i
$562$		0			0
$563$	0.200460	−	0.878273i	0.00844839	−	0.0370148i	−0.970528	−	0.240988i	$-0.922528\pi$
$563$	0.200460	−	0.878273i	0.00844839	−	0.0370148i	0.978976	+	0.203973i	$0.0653856\pi$
$564$		0			0
$565$	15.4561	+	32.0949i	0.650242	+	1.35024i
$566$		0			0
$567$	−9.55970	+	15.5889i	−0.401470	+	0.654670i
$568$		0			0
$569$	−31.2257			−1.30905			−0.654525	−	0.756040i	$-0.727131\pi$
$569$	−31.2257			−1.30905			−0.654525	+	0.756040i	$0.727131\pi$
$570$		0			0
$571$	1.62998	−	3.38469i	0.0682125	−	0.141645i	−0.864075	−	0.503364i	$-0.832096\pi$
$571$	1.62998	−	3.38469i	0.0682125	−	0.141645i	0.932287	+	0.361719i	$0.117810\pi$
$572$		0			0
$573$	36.6171	+	8.35762i	1.52970	+	0.349145i
$574$		0			0
$575$	0.442622	−	0.101026i	0.0184586	−	0.00421306i
$576$		0			0
$577$	−7.95129	+	1.81483i	−0.331016	+	0.0755524i	−0.384799	−	0.923000i	$-0.625729\pi$
$577$	−7.95129	+	1.81483i	−0.331016	+	0.0755524i	0.0537827	+	0.998553i	$0.482872\pi$
$578$		0			0
$579$	2.75563	−	12.0732i	0.114520	−	0.501746i
$580$		0			0
$581$	−8.05276	−	2.71962i	−0.334085	−	0.112829i
$582$		0			0
$583$	8.35511	−	6.66298i	0.346033	−	0.275952i
$584$		0			0
$585$	−3.40672	−	4.27189i	−0.140851	−	0.176621i
$586$		0			0
$587$	25.0057			1.03210			0.516048	−	0.856560i	$-0.327403\pi$
$587$	25.0057			1.03210			0.516048	+	0.856560i	$0.327403\pi$
$588$		0			0
$589$	−5.34646			−0.220297
$590$		0			0
$591$	8.82370	+	11.0646i	0.362958	+	0.455135i
$592$		0			0
$593$	25.4025	−	20.2578i	1.04316	−	0.831888i	0.0571102	−	0.998368i	$-0.481811\pi$
$593$	25.4025	−	20.2578i	1.04316	−	0.831888i	0.986045	+	0.166479i	$0.0532399\pi$
$594$		0			0
$595$	−0.293262	+	0.0362842i	−0.0120226	+	0.00148751i
$596$		0			0
$597$	6.42378	−	28.1444i	0.262908	−	1.15187i
$598$		0			0
$599$	−32.7091	+	7.46565i	−1.33646	+	0.305038i	−0.830259	−	0.557378i	$-0.811807\pi$
$599$	−32.7091	+	7.46565i	−1.33646	+	0.305038i	−0.506200	+	0.862416i	$0.668950\pi$
$600$		0			0
$601$	−19.7207	+	4.50112i	−0.804424	+	0.183605i	−0.604914	−	0.796291i	$-0.706792\pi$
$601$	−19.7207	+	4.50112i	−0.804424	+	0.183605i	−0.199511	+	0.979896i	$0.563935\pi$
$602$		0			0
$603$	−3.08655	−	0.704485i	−0.125694	−	0.0286888i
$604$		0			0
$605$	3.66449	−	7.60939i	0.148983	−	0.309366i
$606$		0			0
$607$	−17.5578			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$607$	−17.5578			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$608$		0			0
$609$	22.0299	−	2.72568i	0.892695	−	0.110450i
$610$		0			0
$611$	−24.7520	−	51.3981i	−1.00136	−	2.07934i
$612$		0			0
$613$	6.73074	−	29.4893i	0.271852	−	1.19106i	−0.635973	−	0.771712i	$-0.719401\pi$
$613$	6.73074	−	29.4893i	0.271852	−	1.19106i	0.907825	−	0.419350i	$-0.137742\pi$
$614$		0			0
$615$	8.92074	−	4.29600i	0.359719	−	0.173231i
$616$		0			0
$617$	28.8391	+	13.8882i	1.16102	+	0.559117i	0.912325	−	0.409466i	$-0.134285\pi$
$617$	28.8391	+	13.8882i	1.16102	+	0.559117i	0.248692	+	0.968583i	$0.419999\pi$
$618$		0			0
$619$	33.1020			1.33048			0.665241	−	0.746628i	$-0.268329\pi$
$619$	33.1020			1.33048			0.665241	+	0.746628i	$0.268329\pi$
$620$		0			0
$621$	−1.07545	−	0.857642i	−0.0431563	−	0.0344160i
$622$		0			0
$623$	−6.69498	+	19.8238i	−0.268229	+	0.794222i
$624$		0			0
$625$	11.1967	+	5.39204i	0.447868	+	0.215682i
$626$		0			0
$627$	3.04464	+	2.42802i	0.121591	+	0.0969658i
$628$		0			0
$629$	−0.112781	+	0.0899401i	−0.00449689	+	0.00358615i
$630$		0			0
$631$	−9.01159	−	7.18650i	−0.358746	−	0.286090i	0.427486	−	0.904022i	$-0.359399\pi$
$631$	−9.01159	−	7.18650i	−0.358746	−	0.286090i	−0.786232	+	0.617932i	$0.787971\pi$
$632$		0			0
$633$	−9.11949	−	18.9368i	−0.362467	−	0.752671i
$634$		0			0
$635$	−4.20907	−	18.4411i	−0.167032	−	0.731814i
$636$		0			0
$637$	36.8970	−	0.804559i	1.46191	−	0.0318778i
$638$		0			0
$639$	−2.23316	+	0.509704i	−0.0883425	+	0.0201636i
$640$		0			0
$641$	−19.8837	+	9.57547i	−0.785358	+	0.378208i	−0.783185	−	0.621789i	$-0.786406\pi$
$641$	−19.8837	+	9.57547i	−0.785358	+	0.378208i	−0.00217321	+	0.999998i	$0.500692\pi$
$642$		0			0
$643$	−6.27461	+	7.86812i	−0.247447	+	0.310288i	−0.890007	−	0.455947i	$-0.849301\pi$
$643$	−6.27461	+	7.86812i	−0.247447	+	0.310288i	0.642560	+	0.766235i	$0.277872\pi$
$644$		0			0
$645$	−4.03569	−	5.06060i	−0.158905	−	0.199261i
$646$		0			0
$647$	−24.0109	+	30.1087i	−0.943964	+	1.18369i	0.0388774	+	0.999244i	$0.487622\pi$
$647$	−24.0109	+	30.1087i	−0.943964	+	1.18369i	−0.982842	+	0.184450i	$0.940950\pi$
$648$		0			0
$649$	−6.80722	+	14.1353i	−0.267207	+	0.554861i
$650$		0			0
$651$	−18.4572	+	11.8800i	−0.723394	+	0.465614i
$652$		0			0
$653$	23.1014	−	28.9683i	0.904030	−	1.13362i	−0.0864910	−	0.996253i	$-0.527565\pi$
$653$	23.1014	−	28.9683i	0.904030	−	1.13362i	0.990521	−	0.137365i	$-0.0438632\pi$
$654$		0			0
$655$		−	31.5485i		−	1.23270i
$656$		0			0
$657$	1.39119	−	2.88883i	0.0542754	−	0.112704i
$658$		0			0
$659$	4.10653	+	8.52729i	0.159968	+	0.332176i	0.965512	−	0.260360i	$-0.0838411\pi$
$659$	4.10653	+	8.52729i	0.159968	+	0.332176i	−0.805544	+	0.592536i	$0.798127\pi$
$660$		0			0
$661$	10.6537	+	2.43163i	0.414379	+	0.0945794i	0.424628	−	0.905368i	$-0.360405\pi$
$661$	10.6537	+	2.43163i	0.414379	+	0.0945794i	−0.0102482	+	0.999947i	$0.503262\pi$
$662$		0			0
$663$	−0.463891	+	0.223398i	−0.0180160	+	0.00867606i
$664$		0			0
$665$	2.55100	+	3.96332i	0.0989234	+	0.153691i
$666$		0			0
$667$			1.33262i			0.0515993i
$668$		0			0
$669$	14.5283	+	6.99648i	0.561698	+	0.270500i
$670$		0			0
$671$	7.61990	−	33.3850i	0.294163	−	1.28881i
$672$		0			0
$673$	0.273500	+	1.19828i	0.0105427	+	0.0461904i	0.979926	−	0.199363i	$-0.0638874\pi$
$673$	0.273500	+	1.19828i	0.0105427	+	0.0461904i	−0.969383	+	0.245554i	$0.921030\pi$
$674$		0			0
$675$	2.27885	+	9.98430i	0.0877130	+	0.384296i
$676$		0			0
$677$	−1.71647	−	0.391773i	−0.0659692	−	0.0150570i	0.189409	−	0.981898i	$-0.439343\pi$
$677$	−1.71647	−	0.391773i	−0.0659692	−	0.0150570i	−0.255378	+	0.966841i	$0.582200\pi$
$678$		0			0
$679$	−13.1081	−	1.33239i	−0.503043	−	0.0511326i
$680$		0			0
$681$	27.0536	+	33.9242i	1.03670	+	1.29998i
$682$		0			0
$683$	0.239842	−	0.191268i	0.00917731	−	0.00731866i	−0.618890	−	0.785477i	$-0.712418\pi$
$683$	0.239842	−	0.191268i	0.00917731	−	0.00731866i	0.628068	+	0.778159i	$0.283846\pi$
$684$		0			0
$685$			19.7582i			0.754922i
$686$		0			0
$687$		−	19.3570i		−	0.738514i
$688$		0			0
$689$	17.6201	−	14.0515i	0.671272	−	0.535321i
$690$		0			0
$691$	3.74270	+	4.69319i	0.142379	+	0.178538i	0.847908	−	0.530144i	$-0.177862\pi$
$691$	3.74270	+	4.69319i	0.142379	+	0.178538i	−0.705529	+	0.708681i	$0.749291\pi$
$692$		0			0
$693$	−3.83550	−	0.389865i	−0.145699	−	0.0148098i
$694$		0			0
$695$	−15.1863	−	3.46618i	−0.576050	−	0.131480i
$696$		0			0
$697$	0.0500638	+	0.219344i	0.00189630	+	0.00830824i
$698$		0			0
$699$	2.92434	+	12.8124i	0.110609	+	0.484608i
$700$		0			0
$701$	−1.98907	+	8.71468i	−0.0751261	+	0.329149i	−0.998500	−	0.0547531i	$-0.982563\pi$
$701$	−1.98907	+	8.71468i	−0.0751261	+	0.329149i	0.923374	+	0.383902i	$0.125420\pi$
$702$		0			0
$703$	2.07304	+	0.998322i	0.0781861	+	0.0376524i
$704$		0			0
$705$		−	29.9115i		−	1.12653i
$706$		0			0
$707$	8.28424	+	12.8707i	0.311561	+	0.484051i
$708$		0			0
$709$	8.32824	−	4.01067i	0.312774	−	0.150624i	−0.270911	−	0.962604i	$-0.587325\pi$
$709$	8.32824	−	4.01067i	0.312774	−	0.150624i	0.583684	+	0.811981i	$0.301611\pi$
$710$		0			0
$711$	8.41316	+	1.92025i	0.315518	+	0.0720149i
$712$		0			0
$713$	−0.571747	−	1.18724i	−0.0214121	−	0.0444626i
$714$		0			0
$715$	−10.1685	+	21.1150i	−0.380279	+	0.789658i
$716$		0			0
$717$		−	36.4612i		−	1.36167i
$718$		0			0
$719$	11.4342	−	14.3380i	0.426424	−	0.534718i	−0.521485	−	0.853260i	$-0.674622\pi$
$719$	11.4342	−	14.3380i	0.426424	−	0.534718i	0.947909	+	0.318542i	$0.103193\pi$
$720$		0			0
$721$	−19.3928	+	12.4822i	−0.722227	+	0.464863i
$722$		0			0
$723$	2.31836	−	4.81413i	0.0862208	−	0.179039i
$724$		0			0
$725$	6.18593	−	7.75691i	0.229740	−	0.288084i
$726$		0			0
$727$	−16.3660	−	20.5223i	−0.606980	−	0.761129i	0.379468	−	0.925205i	$-0.376107\pi$
$727$	−16.3660	−	20.5223i	−0.606980	−	0.761129i	−0.986448	+	0.164076i	$0.947536\pi$
$728$		0			0
$729$	18.7105	−	23.4623i	0.692983	−	0.868973i
$730$		0			0
$731$	0.132514	−	0.0638152i	0.00490119	−	0.00236029i
$732$		0			0
$733$	−16.6640	+	3.80344i	−0.615498	+	0.140483i	−0.518893	−	0.854839i	$-0.673656\pi$
$733$	−16.6640	+	3.80344i	−0.615498	+	0.140483i	−0.0966051	+	0.995323i	$0.530798\pi$
$734$		0			0
$735$	17.6132	+	8.01386i	0.649673	+	0.295596i
$736$		0			0
$737$	3.02167	+	13.2388i	0.111305	+	0.487657i
$738$		0			0
$739$	9.18604	+	19.0750i	0.337914	+	0.701685i	0.998809	−	0.0487930i	$-0.0155375\pi$
$739$	9.18604	+	19.0750i	0.337914	+	0.701685i	−0.660895	+	0.750478i	$0.729823\pi$
$740$		0			0
$741$	6.42084	+	5.12045i	0.235876	+	0.188104i
$742$		0			0
$743$	20.6912	−	16.5006i	0.759085	−	0.605350i	−0.165552	−	0.986201i	$-0.552940\pi$
$743$	20.6912	−	16.5006i	0.759085	−	0.605350i	0.924636	+	0.380851i	$0.124369\pi$
$744$		0			0
$745$	17.0977	+	13.6350i	0.626412	+	0.499547i
$746$		0			0
$747$	1.68704	+	0.812434i	0.0617254	+	0.0297254i
$748$		0			0
$749$	−0.00666930	+	0.0197477i	−0.000243691	+	0.000721565i
$750$		0			0
$751$	29.7528	+	23.7271i	1.08570	+	0.865813i	0.991547	−	0.129745i	$-0.0414159\pi$
$751$	29.7528	+	23.7271i	1.08570	+	0.865813i	0.0941480	+	0.995558i	$0.469987\pi$
$752$		0			0
$753$	−1.39830			−0.0509569
$754$		0			0
$755$	22.5860	+	10.8769i	0.821990	+	0.395849i
$756$		0			0
$757$	7.34071	−	3.53510i	0.266803	−	0.128485i	−0.295700	−	0.955281i	$-0.595553\pi$
$757$	7.34071	−	3.53510i	0.266803	−	0.128485i	0.562503	+	0.826795i	$0.309839\pi$
$758$		0			0
$759$	−0.213579	+	0.935749i	−0.00775241	+	0.0339655i
$760$		0			0
$761$	20.7793	+	43.1486i	0.753248	+	1.56414i	0.823966	+	0.566639i	$0.191756\pi$
$761$	20.7793	+	43.1486i	0.753248	+	1.56414i	−0.0707186	+	0.997496i	$0.522529\pi$
$762$		0			0
$763$	−34.7479	+	4.29924i	−1.25796	+	0.155643i
$764$		0			0
$765$	0.0650984			0.00235364
$766$		0			0
$767$	−14.3557	+	29.8100i	−0.518356	+	1.07638i
$768$		0			0
$769$	24.8582	+	5.67373i	0.896410	+	0.204600i	0.645817	−	0.763492i	$-0.276517\pi$
$769$	24.8582	+	5.67373i	0.896410	+	0.204600i	0.250594	+	0.968092i	$0.419374\pi$
$770$		0			0
$771$	−4.74017	+	1.08191i	−0.170713	+	0.0389641i
$772$		0			0
$773$	42.1743	−	9.62602i	1.51691	−	0.346224i	0.618639	−	0.785675i	$-0.287684\pi$
$773$	42.1743	−	9.62602i	1.51691	−	0.346224i	0.898266	+	0.439451i	$0.144827\pi$
$774$		0			0
$775$	−2.18308	+	9.56470i	−0.0784185	+	0.343574i
$776$		0			0
$777$	9.37489	−	1.15992i	0.336322	−	0.0416119i
$778$		0			0
$779$	2.80569	−	2.23746i	0.100524	−	0.0801653i
$780$		0			0
$781$	6.12565	+	7.68132i	0.219193	+	0.274859i
$782$		0			0
$783$	−30.0602			−1.07426
$784$		0			0
$785$	−10.5503			−0.376555
$786$		0			0
$787$	−19.0151	−	23.8442i	−0.677816	−	0.849954i	0.317335	−	0.948313i	$-0.397212\pi$
$787$	−19.0151	−	23.8442i	−0.677816	−	0.849954i	−0.995151	+	0.0983596i	$0.968640\pi$
$788$		0			0
$789$	13.9623	−	11.1345i	0.497070	−	0.396400i
$790$		0			0
$791$	50.2198	+	16.9605i	1.78561	+	0.603046i
$792$		0			0
$793$	16.0696	−	70.4055i	0.570648	−	2.50017i
$794$		0			0
$795$	11.5204	−	2.62946i	0.408587	−	0.0932574i
$796$		0			0
$797$	−38.1050	+	8.69722i	−1.34975	+	0.308071i	−0.835462	−	0.549548i	$-0.814800\pi$
$797$	−38.1050	+	8.69722i	−1.34975	+	0.308071i	−0.514286	+	0.857619i	$0.671943\pi$
$798$		0			0
$799$	0.662633	+	0.151242i	0.0234423	+	0.00535054i
$800$		0			0
$801$	2.00000	−	4.15303i	0.0706664	−	0.146740i
$802$		0			0
$803$	−13.7527			−0.485322
$804$		0			0
$805$	−0.607299	+	0.990312i	−0.0214045	+	0.0349039i
$806$		0			0
$807$	−3.59083	−	7.45644i	−0.126403	−	0.262479i
$808$		0			0
$809$	−5.01355	+	21.9658i	−0.176267	+	0.772276i	0.807066	+	0.590461i	$0.201054\pi$
$809$	−5.01355	+	21.9658i	−0.176267	+	0.772276i	−0.983333	+	0.181815i	$0.941803\pi$
$810$		0			0
$811$	−50.4039	+	24.2732i	−1.76992	+	0.852348i	−0.803530	+	0.595264i	$0.797048\pi$
$811$	−50.4039	+	24.2732i	−1.76992	+	0.852348i	−0.966389	+	0.257085i	$0.917238\pi$
$812$		0			0
$813$	−0.914562	−	0.440430i	−0.0320751	−	0.0154466i
$814$		0			0
$815$	−38.3396			−1.34298
$816$		0			0
$817$	−1.83416	−	1.46269i	−0.0641691	−	0.0511731i
$818$		0			0
$819$	−8.08868	−	0.822187i	−0.282641	−	0.0287295i
$820$		0			0
$821$	46.5505	+	22.4175i	1.62462	+	0.782377i	0.999999	+	0.00145198i	$0.000462179\pi$
$821$	46.5505	+	22.4175i	1.62462	+	0.782377i	0.624624	+	0.780925i	$0.285252\pi$
$822$		0			0
$823$	23.0477	+	18.3799i	0.803393	+	0.640685i	0.936599	−	0.350404i	$-0.113956\pi$
$823$	23.0477	+	18.3799i	0.803393	+	0.640685i	−0.133206	+	0.991088i	$0.542527\pi$
$824$		0			0
$825$	5.58687	−	4.45538i	0.194510	−	0.155116i
$826$		0			0
$827$	36.4354	+	29.0563i	1.26698	+	1.01039i	0.998895	+	0.0469921i	$0.0149636\pi$
$827$	36.4354	+	29.0563i	1.26698	+	1.01039i	0.268089	+	0.963394i	$0.413608\pi$
$828$		0			0
$829$	21.1356	+	43.8886i	0.734070	+	1.52431i	0.847517	+	0.530769i	$0.178097\pi$
$829$	21.1356	+	43.8886i	0.734070	+	1.52431i	−0.113446	+	0.993544i	$0.536189\pi$
$830$		0			0
$831$	1.33060	+	5.82975i	0.0461581	+	0.202232i
$832$		0			0
$833$	−0.266589	+	0.349667i	−0.00923678	+	0.0121152i
$834$		0			0
$835$	−37.7929	+	8.62598i	−1.30788	+	0.298514i
$836$		0			0
$837$	26.7809	−	12.8970i	0.925683	−	0.445785i
$838$		0			0
$839$	−20.8085	+	26.0930i	−0.718390	+	0.900832i	−0.998246	−	0.0592100i	$-0.981142\pi$
$839$	−20.8085	+	26.0930i	−0.718390	+	0.900832i	0.279856	+	0.960042i	$0.409713\pi$
$840$		0			0
$841$	0.0760944	+	0.0954193i	0.00262394	+	0.00329032i
$842$		0			0
$843$	−15.0528	+	18.8756i	−0.518445	+	0.650109i
$844$		0			0
$845$	−11.4151	+	23.7038i	−0.392693	+	0.815436i
$846$		0			0
$847$	−4.27978	−	11.8161i	−0.147055	−	0.406007i
$848$		0			0
$849$	5.32435	−	6.67653i	0.182731	−	0.229138i
$850$		0			0
$851$			0.567102i			0.0194400i
$852$		0			0
$853$	19.2146	−	39.8995i	0.657896	−	1.36613i	−0.258559	−	0.965995i	$-0.583248\pi$
$853$	19.2146	−	39.8995i	0.657896	−	1.36613i	0.916455	−	0.400139i	$-0.131038\pi$
$854$		0			0
$855$	−0.450523	−	0.935520i	−0.0154076	−	0.0319941i
$856$		0			0
$857$	30.5333	+	6.96902i	1.04300	+	0.238057i	0.709509	−	0.704697i	$-0.248917\pi$
$857$	30.5333	+	6.96902i	1.04300	+	0.238057i	0.333489	+	0.942754i	$0.391774\pi$
$858$		0			0
$859$	31.8786	−	15.3519i	1.08768	−	0.523801i	0.197918	−	0.980219i	$-0.436582\pi$
$859$	31.8786	−	15.3519i	1.08768	−	0.523801i	0.889765	+	0.456418i	$0.150868\pi$
$860$		0			0
$861$	4.71415	−	13.9585i	0.160658	−	0.475705i
$862$		0			0
$863$		−	9.44370i		−	0.321467i	−0.986998	−	0.160734i	$-0.948614\pi$
$863$		−	9.44370i		−	0.321467i	0.986998	−	0.160734i	$-0.0513860\pi$
$864$		0			0
$865$	7.07767	+	3.40843i	0.240648	+	0.115890i
$866$		0			0
$867$	−5.87990	+	25.7615i	−0.199692	+	0.874907i
$868$		0			0
$869$	−8.23631	−	36.0856i	−0.279398	−	1.22412i
$870$		0			0
$871$	6.37240	+	27.9193i	0.215920	+	0.946009i
$872$		0			0
$873$	2.82983	+	0.645890i	0.0957751	+	0.0218601i
$874$		0			0
$875$	30.2475	−	10.9556i	1.02255	−	0.370366i
$876$		0			0
$877$	9.34293	+	11.7157i	0.315488	+	0.395610i	0.914139	−	0.405400i	$-0.132868\pi$
$877$	9.34293	+	11.7157i	0.315488	+	0.395610i	−0.598651	+	0.801010i	$0.704296\pi$
$878$		0			0
$879$	20.9293	−	16.6905i	0.705927	−	0.562958i
$880$		0			0
$881$			37.7460i			1.27169i	0.771815	+	0.635847i	$0.219349\pi$
$881$			37.7460i			1.27169i	−0.771815	+	0.635847i	$0.780651\pi$
$882$		0			0
$883$			13.6898i			0.460698i	0.973108	+	0.230349i	$0.0739868\pi$
$883$			13.6898i			0.460698i	−0.973108	+	0.230349i	$0.926013\pi$
$884$		0			0
$885$	−13.5634	+	10.8164i	−0.455927	+	0.363590i
$886$		0			0
$887$	−1.16628	−	1.46247i	−0.0391599	−	0.0491049i	0.761866	−	0.647735i	$-0.224283\pi$
$887$	−1.16628	−	1.46247i	−0.0391599	−	0.0491049i	−0.801026	+	0.598630i	$0.795712\pi$
$888$		0			0
$889$	−23.9938	−	14.7139i	−0.804726	−	0.493490i
$890$		0			0
$891$	−16.8460	−	3.84499i	−0.564362	−	0.128812i
$892$		0			0
$893$	−2.41237	−	10.5693i	−0.0807270	−	0.353688i
$894$		0			0
$895$	−9.64762	−	42.2690i	−0.322484	−	1.41290i
$896$		0			0
$897$	−0.450416	+	1.97340i	−0.0150389	+	0.0658899i
$898$		0			0
$899$	−25.9451	−	12.4945i	−0.865317	−	0.416715i
$900$		0			0
$901$			0.268508i			0.00894531i
$902$		0			0
$903$	−9.58207	−	0.973985i	−0.318871	−	0.0324122i
$904$		0			0
$905$	−33.0422	+	15.9123i	−1.09836	+	0.528942i
$906$		0			0
$907$	43.9277	+	10.0262i	1.45859	+	0.332915i	0.876971	−	0.480543i	$-0.159561\pi$
$907$	43.9277	+	10.0262i	1.45859	+	0.332915i	0.581624	+	0.813458i	$0.302418\pi$
$908$		0			0
$909$	−1.46305	−	3.03806i	−0.0485263	−	0.100766i
$910$		0			0
$911$	15.6977	−	32.5965i	0.520087	−	1.07997i	−0.461178	−	0.887308i	$-0.652573\pi$
$911$	15.6977	−	32.5965i	0.520087	−	1.07997i	0.981265	−	0.192664i	$-0.0617126\pi$
$912$		0			0
$913$		−	8.03137i		−	0.265800i
$914$		0			0
$915$	23.6083	−	29.6039i	0.780467	−	0.978674i
$916$		0			0
$917$	−33.5544	−	32.8307i	−1.10806	−	1.08416i
$918$		0			0
$919$	6.07935	−	12.6239i	0.200539	−	0.416424i	−0.776310	−	0.630351i	$-0.782911\pi$
$919$	6.07935	−	12.6239i	0.200539	−	0.416424i	0.976850	+	0.213927i	$0.0686253\pi$
$920$		0			0
$921$	−15.5343	+	19.4794i	−0.511872	+	0.641867i
$922$		0			0
$923$	12.9184	+	16.1991i	0.425214	+	0.533201i
$924$		0			0
$925$	2.63244	−	3.30098i	0.0865542	−	0.108535i
$926$		0			0
$927$	4.57758	−	2.20444i	0.150347	−	0.0724035i
$928$		0			0
$929$	−26.2385	+	5.98876i	−0.860856	+	0.196485i	−0.630088	−	0.776524i	$-0.716981\pi$
$929$	−26.2385	+	5.98876i	−0.860856	+	0.196485i	−0.230768	+	0.973009i	$0.574124\pi$
$930$		0			0
$931$	6.86998	+	1.41120i	0.225155	+	0.0462503i
$932$		0			0
$933$	−6.62149	−	29.0107i	−0.216778	−	0.949766i
$934$		0			0
$935$	−0.121149	−	0.251568i	−0.00396199	−	0.00822715i
$936$		0			0
$937$	−42.0596	−	33.5414i	−1.37403	−	1.09575i	−0.984625	−	0.174684i	$-0.944110\pi$
$937$	−42.0596	−	33.5414i	−1.37403	−	1.09575i	−0.389404	−	0.921067i	$-0.627319\pi$
$938$		0			0
$939$	10.5677	−	8.42744i	0.344863	−	0.275019i
$940$		0			0
$941$	−16.8567	−	13.4427i	−0.549511	−	0.438221i	0.308965	−	0.951073i	$-0.400017\pi$
$941$	−16.8567	−	13.4427i	−0.549511	−	0.438221i	−0.858477	+	0.512853i	$0.828589\pi$
$942$		0			0
$943$	0.796892	+	0.383763i	0.0259504	+	0.0124970i
$944$		0			0
$945$	−22.3387	−	13.6989i	−0.726677	−	0.445627i
$946$		0			0
$947$	−39.5802	−	31.5641i	−1.28618	−	1.02570i	−0.997670	−	0.0682202i	$-0.978268\pi$
$947$	−39.5802	−	31.5641i	−1.28618	−	1.02570i	−0.288512	−	0.957476i	$-0.593161\pi$
$948$		0			0
$949$	−29.0030			−0.941478
$950$		0			0
$951$	−47.8556	−	23.0460i	−1.55182	−	0.747319i
$952$		0			0
$953$	12.4230	−	5.98261i	0.402421	−	0.193796i	−0.221715	−	0.975112i	$-0.571165\pi$
$953$	12.4230	−	5.98261i	0.402421	−	0.193796i	0.624136	+	0.781316i	$0.285451\pi$
$954$		0			0
$955$	−9.55825	+	41.8774i	−0.309298	+	1.35512i
$956$		0			0
$957$	9.10071	+	18.8978i	0.294184	+	0.610880i
$958$		0			0
$959$	21.0144	+	20.5612i	0.678592	+	0.663956i
$960$		0			0
$961$	−2.52468			−0.0814414
$962$		0			0
$963$	0.00199232	−	0.00413710i	6.42017e−5	−	0.000133316i
$964$		0			0
$965$	13.8076	+	3.15150i	0.444483	+	0.101450i
$966$		0			0
$967$	30.0317	−	6.85454i	0.965754	−	0.220427i	0.289568	−	0.957158i	$-0.406488\pi$
$967$	30.0317	−	6.85454i	0.965754	−	0.220427i	0.676187	+	0.736730i	$0.263631\pi$
$968$		0			0
$969$	−0.0953926	+	0.0217727i	−0.00306445	+	0.000699441i
$970$		0			0
$971$	2.24095	−	9.81826i	0.0719156	−	0.315083i	−0.926157	−	0.377138i	$-0.876908\pi$
$971$	2.24095	−	9.81826i	0.0719156	−	0.315083i	0.998073	+	0.0620550i	$0.0197654\pi$
$972$		0			0
$973$	−19.4901	+	12.5448i	−0.624824	+	0.402169i
$974$		0			0
$975$	11.7821	−	9.39594i	0.377330	−	0.300911i
$976$		0			0
$977$	36.4883	+	45.7549i	1.16736	+	1.46383i	0.858568	+	0.512699i	$0.171354\pi$
$977$	36.4883	+	45.7549i	1.16736	+	1.46383i	0.308796	+	0.951128i	$0.400074\pi$
$978$		0			0
$979$	−19.7711			−0.631887
$980$		0			0
$981$	7.71336			0.246269
$982$		0			0
$983$	−28.2737	−	35.4541i	−0.901791	−	1.13081i	−0.990875	−	0.134786i	$-0.956965\pi$
$983$	−28.2737	−	35.4541i	−0.901791	−	1.13081i	0.0890840	−	0.996024i	$-0.471606\pi$
$984$		0			0
$985$	−12.6541	+	10.0913i	−0.403192	+	0.321535i
$986$		0			0
$987$	−31.8133	−	31.1272i	−1.01263	−	0.990790i
$988$		0			0
$989$	0.128664	−	0.563715i	0.00409129	−	0.0179251i
$990$		0			0
$991$	48.8876	−	11.1583i	1.55296	−	0.354454i	0.641923	−	0.766769i	$-0.278137\pi$
$991$	48.8876	−	11.1583i	1.55296	−	0.354454i	0.911041	+	0.412315i	$0.135280\pi$
$992$		0			0
$993$	−44.5118	+	10.1595i	−1.41254	+	0.322403i
$994$		0			0
$995$	32.1876	+	7.34660i	1.02041	+	0.232903i
$996$		0			0
$997$	4.33454	−	9.00077i	0.137276	−	0.285057i	−0.820986	−	0.570949i	$-0.806575\pi$
$997$	4.33454	−	9.00077i	0.137276	−	0.285057i	0.958262	+	0.285892i	$0.0922897\pi$
$998$		0			0
$999$	−12.7922			−0.404728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bb.a.111.7	yes	48
4.3	odd	2	inner	784.2.bb.a.111.2	✓	48
49.34	odd	14	inner	784.2.bb.a.671.2	yes	48
196.83	even	14	inner	784.2.bb.a.671.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bb.a.111.2	✓	48	4.3	odd	2	inner
784.2.bb.a.111.7	yes	48	1.1	even	1	trivial
784.2.bb.a.671.2	yes	48	49.34	odd	14	inner
784.2.bb.a.671.7	yes	48	196.83	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bb (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.969349 + 1.21553i) q^{3} +(-1.39014 + 1.10860i) q^{5} +(-0.267553 + 2.63219i) q^{7} +(0.129699 - 0.568247i) q^{9} +O(q^{10})\)	\(q+(0.969349 + 1.21553i) q^{3} +(-1.39014 + 1.10860i) q^{5} +(-0.267553 + 2.63219i) q^{7} +(0.129699 - 0.568247i) q^{9} +(-2.43732 + 0.556302i) q^{11} +(-5.14006 + 1.17319i) q^{13} +(-2.69507 - 0.615132i) q^{15} +(0.0272541 - 0.0565938i) q^{17} -1.00192 q^{19} +(-3.45884 + 2.22629i) q^{21} +(-0.107144 - 0.222488i) q^{23} +(-0.409105 + 1.79241i) q^{25} +(5.01869 - 2.41687i) q^{27} +(-4.86206 - 2.34145i) q^{29} +5.33623 q^{31} +(-3.03881 - 2.42337i) q^{33} +(-2.54611 - 3.95573i) q^{35} +(-2.06907 - 0.996411i) q^{37} +(-6.40855 - 5.11065i) q^{39} +(-2.80032 + 2.23318i) q^{41} +(1.83065 + 1.45989i) q^{43} +(0.449660 + 0.933729i) q^{45} +(2.40775 + 10.5491i) q^{47} +(-6.85683 - 1.40850i) q^{49} +(0.0952100 - 0.0217311i) q^{51} +(-3.85131 + 1.85469i) q^{53} +(2.77151 - 3.47536i) q^{55} +(-0.971208 - 1.21786i) q^{57} +(3.91279 - 4.90648i) q^{59} +(-5.94308 + 12.3409i) q^{61} +(1.46103 + 0.493428i) q^{63} +(5.84483 - 7.32918i) q^{65} -5.43170i q^{67} +(0.166579 - 0.345905i) q^{69} +(-1.70512 - 3.54073i) q^{71} +(5.36315 + 1.22410i) q^{73} +(-2.57528 + 1.24019i) q^{75} +(-0.812180 - 6.56433i) q^{77} +14.8054i q^{79} +(6.22722 + 2.99887i) q^{81} +(-0.714859 + 3.13200i) q^{83} +(0.0248529 + 0.108887i) q^{85} +(-1.86695 - 8.17964i) q^{87} +(7.71016 + 1.75979i) q^{89} +(-1.71281 - 13.8435i) q^{91} +(5.17267 + 6.48632i) q^{93} +(1.39281 - 1.11073i) q^{95} +4.97992i q^{97} +1.45715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^9	\( 48 q - 4 q^{9} + 14 q^{17} + 12 q^{25} + 28 q^{29} + 42 q^{37} + 28 q^{41} + 56 q^{49} - 38 q^{53} + 42 q^{57} + 84 q^{61} + 8 q^{65} + 56 q^{69} - 42 q^{73} - 42 q^{77} - 44 q^{81} - 12 q^{85} - 28 q^{89} + 98 q^{93}+O(q^{100}) \) 48 * q - 4 * q^9 + 14 * q^17 + 12 * q^25 + 28 * q^29 + 42 * q^37 + 28 * q^41 + 56 * q^49 - 38 * q^53 + 42 * q^57 + 84 * q^61 + 8 * q^65 + 56 * q^69 - 42 * q^73 - 42 * q^77 - 44 * q^81 - 12 * q^85 - 28 * q^89 + 98 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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