LMFDB - Embedded newform 1134.2.k.a.647.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(647,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("1134.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			647.8
Root			$1.73109 + 0.0577511i$ of defining polynomial
Character	$\chi$	$=$	1134.647
Dual form			1134.2.k.a.971.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.14095 + 1.97618i) q^{5} +(-2.64314 - 0.117551i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.14095 + 1.97618i) q^{5} +(-2.64314 - 0.117551i) q^{7} -1.00000i q^{8} +(1.97618 + 1.14095i) q^{10} +(0.946590 + 0.546514i) q^{11} +6.82946i q^{13} +(-2.34780 + 1.21977i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.35863 + 5.81732i) q^{17} +(-2.47987 + 1.43175i) q^{19} +2.28190 q^{20} +1.09303 q^{22} +(3.38264 - 1.95297i) q^{23} +(-0.103535 + 0.179327i) q^{25} +(3.41473 + 5.91448i) q^{26} +(-1.42337 + 2.23025i) q^{28} -1.84674i q^{29} +(1.75081 + 1.01083i) q^{31} +(-0.866025 - 0.500000i) q^{32} +6.71727i q^{34} +(-2.78339 - 5.35745i) q^{35} +(3.57920 + 6.19935i) q^{37} +(-1.43175 + 2.47987i) q^{38} +(1.97618 - 1.14095i) q^{40} -4.91031 q^{41} +7.48493 q^{43} +(0.946590 - 0.546514i) q^{44} +(1.95297 - 3.38264i) q^{46} +(-3.40174 - 5.89199i) q^{47} +(6.97236 + 0.621407i) q^{49} +0.207069i q^{50} +(5.91448 + 3.41473i) q^{52} +(0.222069 + 0.128212i) q^{53} +2.49418i q^{55} +(-0.117551 + 2.64314i) q^{56} +(-0.923371 - 1.59933i) q^{58} +(-0.971009 + 1.68184i) q^{59} +(-1.15315 + 0.665771i) q^{61} +2.02166 q^{62} -1.00000 q^{64} +(-13.4963 + 7.79207i) q^{65} +(-2.54959 + 4.41602i) q^{67} +(3.35863 + 5.81732i) q^{68} +(-5.08921 - 3.24799i) q^{70} +0.233507i q^{71} +(5.89272 + 3.40216i) q^{73} +(6.19935 + 3.57920i) q^{74} +2.86351i q^{76} +(-2.43773 - 1.55578i) q^{77} +(3.63624 + 6.29816i) q^{79} +(1.14095 - 1.97618i) q^{80} +(-4.25245 + 2.45515i) q^{82} +5.82706 q^{83} -15.3281 q^{85} +(6.48214 - 3.74246i) q^{86} +(0.546514 - 0.946590i) q^{88} +(-8.99707 - 15.5834i) q^{89} +(0.802809 - 18.0512i) q^{91} -3.90593i q^{92} +(-5.89199 - 3.40174i) q^{94} +(-5.65882 - 3.26712i) q^{95} +4.77934i q^{97} +(6.34895 - 2.94803i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 4 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 - 4 * q^7	$ 16 q + 8 q^{4} - 4 q^{7} - 12 q^{11} - 8 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{31} + 30 q^{35} - 2 q^{37} + 12 q^{41} + 4 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} - 2 q^{49} + 6 q^{52} - 36 q^{53} - 6 q^{56} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{70} - 18 q^{74} + 24 q^{77} - 16 q^{79} + 24 q^{85} - 24 q^{86} - 24 q^{89} - 12 q^{91} - 66 q^{95} - 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 4 * q^7 - 12 * q^11 - 8 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^31 + 30 * q^35 - 2 * q^37 + 12 * q^41 + 4 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 - 2 * q^49 + 6 * q^52 - 36 * q^53 - 6 * q^56 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^70 - 18 * q^74 + 24 * q^77 - 16 * q^79 + 24 * q^85 - 24 * q^86 - 24 * q^89 - 12 * q^91 - 66 * q^95 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.14095	+	1.97618i	0.510248	+	0.883776i	0.999929	+	0.0118746i	$0.00377989\pi$
$5$	1.14095	+	1.97618i	0.510248	+	0.883776i	−0.489681	+	0.871902i	$0.662887\pi$
$6$		0			0
$7$	−2.64314	−	0.117551i	−0.999012	−	0.0444301i
$7$	−2.64314	−	0.117551i	−0.999012	−	0.0444301i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.97618	+	1.14095i	0.624924	+	0.360800i
$11$	0.946590	+	0.546514i	0.285408	+	0.164780i	0.635869	−	0.771797i	$-0.280642\pi$
$11$	0.946590	+	0.546514i	0.285408	+	0.164780i	−0.350461	+	0.936577i	$0.613975\pi$
$12$		0			0
$13$			6.82946i			1.89415i	0.321012	+	0.947075i	$0.395977\pi$
$13$			6.82946i			1.89415i	−0.321012	+	0.947075i	$0.604023\pi$
$14$	−2.34780	+	1.21977i	−0.627476	+	0.325996i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.35863	+	5.81732i	−0.814588	+	1.41091i	0.0950352	+	0.995474i	$0.469704\pi$
$17$	−3.35863	+	5.81732i	−0.814588	+	1.41091i	−0.909623	+	0.415434i	$0.863630\pi$
$18$		0			0
$19$	−2.47987	+	1.43175i	−0.568922	+	0.328467i	−0.756718	−	0.653741i	$-0.773199\pi$
$19$	−2.47987	+	1.43175i	−0.568922	+	0.328467i	0.187797	+	0.982208i	$0.439865\pi$
$20$	2.28190			0.510248
$21$		0			0
$22$	1.09303			0.233034
$23$	3.38264	−	1.95297i	0.705328	−	0.407221i	−0.104001	−	0.994577i	$-0.533164\pi$
$23$	3.38264	−	1.95297i	0.705328	−	0.407221i	0.809329	+	0.587356i	$0.199831\pi$
$24$		0			0
$25$	−0.103535	+	0.179327i	−0.0207069	+	0.0358655i
$26$	3.41473	+	5.91448i	0.669683	+	1.15993i
$27$		0			0
$28$	−1.42337	+	2.23025i	−0.268992	+	0.421478i
$29$		−	1.84674i		−	0.342932i	−0.985190	−	0.171466i	$-0.945150\pi$
$29$		−	1.84674i		−	0.342932i	0.985190	−	0.171466i	$-0.0548503\pi$
$30$		0			0
$31$	1.75081	+	1.01083i	0.314455	+	0.181551i	0.648918	−	0.760858i	$-0.275222\pi$
$31$	1.75081	+	1.01083i	0.314455	+	0.181551i	−0.334463	+	0.942409i	$0.608555\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			6.71727i			1.15200i
$35$	−2.78339	−	5.35745i	−0.470478	−	0.905574i
$36$		0			0
$37$	3.57920	+	6.19935i	0.588416	+	1.01917i	0.994440	+	0.105305i	$0.0335818\pi$
$37$	3.57920	+	6.19935i	0.588416	+	1.01917i	−0.406024	+	0.913863i	$0.633085\pi$
$38$	−1.43175	+	2.47987i	−0.232261	+	0.402288i
$39$		0			0
$40$	1.97618	−	1.14095i	0.312462	−	0.180400i
$41$	−4.91031			−0.766861			−0.383431	−	0.923570i	$-0.625257\pi$
$41$	−4.91031			−0.766861			−0.383431	+	0.923570i	$0.625257\pi$
$42$		0			0
$43$	7.48493			1.14144			0.570721	−	0.821144i	$-0.306664\pi$
$43$	7.48493			1.14144			0.570721	+	0.821144i	$0.306664\pi$
$44$	0.946590	−	0.546514i	0.142704	−	0.0823901i
$45$		0			0
$46$	1.95297	−	3.38264i	0.287949	−	0.498742i
$47$	−3.40174	−	5.89199i	−0.496195	−	0.859435i	0.503795	−	0.863823i	$-0.331937\pi$
$47$	−3.40174	−	5.89199i	−0.496195	−	0.859435i	−0.999990	+	0.00438774i	$0.998603\pi$
$48$		0			0
$49$	6.97236	+	0.621407i	0.996052	+	0.0887724i
$50$			0.207069i			0.0292840i
$51$		0			0
$52$	5.91448	+	3.41473i	0.820191	+	0.473538i
$53$	0.222069	+	0.128212i	0.0305036	+	0.0176112i	0.515174	−	0.857085i	$-0.327727\pi$
$53$	0.222069	+	0.128212i	0.0305036	+	0.0176112i	−0.484671	+	0.874697i	$0.661061\pi$
$54$		0			0
$55$			2.49418i			0.336315i
$56$	−0.117551	+	2.64314i	−0.0157084	+	0.353204i
$57$		0			0
$58$	−0.923371	−	1.59933i	−0.121245	−	0.210002i
$59$	−0.971009	+	1.68184i	−0.126415	+	0.218957i	−0.922285	−	0.386510i	$-0.873680\pi$
$59$	−0.971009	+	1.68184i	−0.126415	+	0.218957i	0.795870	+	0.605467i	$0.207014\pi$
$60$		0			0
$61$	−1.15315	+	0.665771i	−0.147646	+	0.0852432i	−0.572003	−	0.820252i	$-0.693833\pi$
$61$	−1.15315	+	0.665771i	−0.147646	+	0.0852432i	0.424357	+	0.905495i	$0.360500\pi$
$62$	2.02166			0.256752
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−13.4963	+	7.79207i	−1.67400	+	0.966487i
$66$		0			0
$67$	−2.54959	+	4.41602i	−0.311482	+	0.539503i	−0.978683	−	0.205375i	$-0.934159\pi$
$67$	−2.54959	+	4.41602i	−0.311482	+	0.539503i	0.667201	+	0.744877i	$0.267492\pi$
$68$	3.35863	+	5.81732i	0.407294	+	0.705454i
$69$		0			0
$70$	−5.08921	−	3.24799i	−0.608277	−	0.388209i
$71$			0.233507i			0.0277121i	0.999904	+	0.0138561i	$0.00441066\pi$
$71$			0.233507i			0.0277121i	−0.999904	+	0.0138561i	$0.995589\pi$
$72$		0			0
$73$	5.89272	+	3.40216i	0.689690	+	0.398193i	0.803496	−	0.595310i	$-0.202971\pi$
$73$	5.89272	+	3.40216i	0.689690	+	0.398193i	−0.113806	+	0.993503i	$0.536304\pi$
$74$	6.19935	+	3.57920i	0.720660	+	0.416073i
$75$		0			0
$76$			2.86351i			0.328467i
$77$	−2.43773	−	1.55578i	−0.277805	−	0.177298i
$78$		0			0
$79$	3.63624	+	6.29816i	0.409109	+	0.708598i	0.994790	−	0.101944i	$-0.0325062\pi$
$79$	3.63624	+	6.29816i	0.409109	+	0.708598i	−0.585681	+	0.810542i	$0.699173\pi$
$80$	1.14095	−	1.97618i	0.127562	−	0.220944i
$81$		0			0
$82$	−4.25245	+	2.45515i	−0.469605	+	0.271126i
$83$	5.82706			0.639603			0.319801	−	0.947485i	$-0.396384\pi$
$83$	5.82706			0.639603			0.319801	+	0.947485i	$0.396384\pi$
$84$		0			0
$85$	−15.3281			−1.66257
$86$	6.48214	−	3.74246i	0.698987	−	0.403560i
$87$		0			0
$88$	0.546514	−	0.946590i	0.0582586	−	0.100907i
$89$	−8.99707	−	15.5834i	−0.953687	−	1.65184i	−0.737344	−	0.675518i	$-0.763920\pi$
$89$	−8.99707	−	15.5834i	−0.953687	−	1.65184i	−0.216344	−	0.976317i	$-0.569413\pi$
$90$		0			0
$91$	0.802809	−	18.0512i	0.0841573	−	1.89228i
$92$		−	3.90593i		−	0.407221i
$93$		0			0
$94$	−5.89199	−	3.40174i	−0.607713	−	0.350863i
$95$	−5.65882	−	3.26712i	−0.580583	−	0.335200i
$96$		0			0
$97$			4.77934i			0.485269i	0.970118	+	0.242634i	$0.0780115\pi$
$97$			4.77934i			0.485269i	−0.970118	+	0.242634i	$0.921989\pi$
$98$	6.34895	−	2.94803i	0.641341	−	0.297796i
$99$		0			0
$100$	0.103535	+	0.179327i	0.0103535	+	0.0179327i
$101$	−5.22981	+	9.05829i	−0.520385	+	0.901334i	0.479334	+	0.877633i	$0.340878\pi$
$101$	−5.22981	+	9.05829i	−0.520385	+	0.901334i	−0.999719	+	0.0237012i	$0.992455\pi$
$102$		0			0
$103$	11.0398	−	6.37383i	1.08778	−	0.628033i	0.154799	−	0.987946i	$-0.450527\pi$
$103$	11.0398	−	6.37383i	1.08778	−	0.628033i	0.932986	+	0.359914i	$0.117194\pi$
$104$	6.82946			0.669683
$105$		0			0
$106$	0.256424			0.0249061
$107$	8.25865	−	4.76813i	0.798394	−	0.460953i	−0.0445153	−	0.999009i	$-0.514174\pi$
$107$	8.25865	−	4.76813i	0.798394	−	0.460953i	0.842909	+	0.538056i	$0.180841\pi$
$108$		0			0
$109$	−2.88251	+	4.99266i	−0.276095	+	0.478210i	−0.970411	−	0.241460i	$-0.922374\pi$
$109$	−2.88251	+	4.99266i	−0.276095	+	0.478210i	0.694316	+	0.719670i	$0.255707\pi$
$110$	1.24709	+	2.16002i	0.118905	+	0.205950i
$111$		0			0
$112$	1.21977	+	2.34780i	0.115257	+	0.221846i
$113$		−	11.9318i		−	1.12245i	−0.827662	−	0.561227i	$-0.810330\pi$
$113$		−	11.9318i		−	1.12245i	0.827662	−	0.561227i	$-0.189670\pi$
$114$		0			0
$115$	7.71884	+	4.45647i	0.719785	+	0.415568i
$116$	−1.59933	−	0.923371i	−0.148494	−	0.0857329i
$117$		0			0
$118$			1.94202i			0.178777i
$119$	9.56116	−	14.9812i	0.876470	−	1.37332i
$120$		0			0
$121$	−4.90265	−	8.49163i	−0.445695	−	0.771966i
$122$	−0.665771	+	1.15315i	−0.0602760	+	0.104401i
$123$		0			0
$124$	1.75081	−	1.01083i	0.157228	−	0.0907754i
$125$	10.9370			0.978234
$126$		0			0
$127$	−10.9133			−0.968400			−0.484200	−	0.874957i	$-0.660889\pi$
$127$	−10.9133			−0.968400			−0.484200	+	0.874957i	$0.660889\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−7.79207	+	13.4963i	−0.683410	+	1.18370i
$131$	0.989677	+	1.71417i	0.0864684	+	0.149768i	0.906016	−	0.423243i	$-0.139108\pi$
$131$	0.989677	+	1.71417i	0.0864684	+	0.149768i	−0.819548	+	0.573011i	$0.805775\pi$
$132$		0			0
$133$	6.72295	−	3.49281i	0.582954	−	0.302865i
$134$			5.09918i			0.440502i
$135$		0			0
$136$	5.81732	+	3.35863i	0.498831	+	0.288000i
$137$	−2.86923	−	1.65655i	−0.245135	−	0.141528i	0.372400	−	0.928072i	$-0.378535\pi$
$137$	−2.86923	−	1.65655i	−0.245135	−	0.141528i	−0.617534	+	0.786544i	$0.711868\pi$
$138$		0			0
$139$		−	3.47216i		−	0.294504i	−0.989099	−	0.147252i	$-0.952957\pi$
$139$		−	3.47216i		−	0.294504i	0.989099	−	0.147252i	$-0.0470429\pi$
$140$	−6.03138	−	0.268240i	−0.509745	−	0.0226704i
$141$		0			0
$142$	0.116753	+	0.202223i	0.00979772	+	0.0169701i
$143$	−3.73239	+	6.46469i	−0.312118	+	0.540605i
$144$		0			0
$145$	3.64950	−	2.10704i	0.303075	−	0.174980i
$146$	6.80432			0.563130
$147$		0			0
$148$	7.15840			0.588416
$149$	11.5534	−	6.67036i	0.946492	−	0.546457i	0.0545027	−	0.998514i	$-0.482643\pi$
$149$	11.5534	−	6.67036i	0.946492	−	0.546457i	0.891989	+	0.452056i	$0.149309\pi$
$150$		0			0
$151$	2.66995	−	4.62450i	0.217278	−	0.376336i	−0.736697	−	0.676223i	$-0.763616\pi$
$151$	2.66995	−	4.62450i	0.217278	−	0.376336i	0.953975	+	0.299887i	$0.0969489\pi$
$152$	1.43175	+	2.47987i	0.116131	+	0.201144i
$153$		0			0
$154$	−2.88902	−	0.128486i	−0.232804	−	0.0103537i
$155$			4.61324i			0.370544i
$156$		0			0
$157$	15.3003	+	8.83364i	1.22110	+	0.705002i	0.965152	−	0.261689i	$-0.0842796\pi$
$157$	15.3003	+	8.83364i	1.22110	+	0.705002i	0.255946	+	0.966691i	$0.417613\pi$
$158$	6.29816	+	3.63624i	0.501054	+	0.289284i
$159$		0			0
$160$		−	2.28190i		−	0.180400i
$161$	−9.17035	+	4.76433i	−0.722725	+	0.375481i
$162$		0			0
$163$	7.94915	+	13.7683i	0.622625	+	1.07842i	0.988995	+	0.147949i	$0.0472672\pi$
$163$	7.94915	+	13.7683i	0.622625	+	1.07842i	−0.366370	+	0.930469i	$0.619400\pi$
$164$	−2.45515	+	4.25245i	−0.191715	+	0.332061i
$165$		0			0
$166$	5.04638	−	2.91353i	0.391675	−	0.226134i
$167$	−5.71756			−0.442438			−0.221219	−	0.975224i	$-0.571004\pi$
$167$	−5.71756			−0.442438			−0.221219	+	0.975224i	$0.571004\pi$
$168$		0			0
$169$	−33.6415			−2.58780
$170$	−13.2746	+	7.66407i	−1.01811	+	0.587807i
$171$		0			0
$172$	3.74246	−	6.48214i	0.285360	−	0.494258i
$173$	−7.60258	−	13.1681i	−0.578013	−	1.00115i	−0.995707	−	0.0925606i	$-0.970495\pi$
$173$	−7.60258	−	13.1681i	−0.578013	−	1.00115i	0.417694	−	0.908588i	$-0.362839\pi$
$174$		0			0
$175$	0.294737	−	0.461817i	0.0222800	−	0.0349101i
$176$		−	1.09303i		−	0.0823901i
$177$		0			0
$178$	−15.5834	−	8.99707i	−1.16802	−	0.674359i
$179$	3.51582	+	2.02986i	0.262785	+	0.151719i	0.625604	−	0.780141i	$-0.284852\pi$
$179$	3.51582	+	2.02986i	0.262785	+	0.151719i	−0.362819	+	0.931859i	$0.618186\pi$
$180$		0			0
$181$			3.68452i			0.273869i	0.990580	+	0.136934i	$0.0437249\pi$
$181$			3.68452i			0.273869i	−0.990580	+	0.136934i	$0.956275\pi$
$182$	−8.33035	−	16.0342i	−0.617486	−	1.18853i
$183$		0			0
$184$	−1.95297	−	3.38264i	−0.143975	−	0.249371i
$185$	−8.16737	+	14.1463i	−0.600477	+	1.04006i
$186$		0			0
$187$	−6.35850	+	3.67108i	−0.464979	+	0.268456i
$188$	−6.80349			−0.496195
$189$		0			0
$190$	−6.53424			−0.474044
$191$	22.3425	−	12.8994i	1.61664	−	0.933370i	0.628864	−	0.777516i	$-0.283520\pi$
$191$	22.3425	−	12.8994i	1.61664	−	0.933370i	0.987780	−	0.155854i	$-0.0498130\pi$
$192$		0			0
$193$	4.64331	−	8.04245i	0.334233	−	0.578908i	−0.649104	−	0.760699i	$-0.724856\pi$
$193$	4.64331	−	8.04245i	0.334233	−	0.578908i	0.983337	+	0.181791i	$0.0581894\pi$
$194$	2.38967	+	4.13903i	0.171568	+	0.297165i
$195$		0			0
$196$	4.02434	−	5.72754i	0.287453	−	0.409110i
$197$		−	5.86237i		−	0.417677i	−0.977950	−	0.208838i	$-0.933032\pi$
$197$		−	5.86237i		−	0.417677i	0.977950	−	0.208838i	$-0.0669683\pi$
$198$		0			0
$199$	−13.9117	−	8.03191i	−0.986173	−	0.569367i	−0.0820447	−	0.996629i	$-0.526145\pi$
$199$	−13.9117	−	8.03191i	−0.986173	−	0.569367i	−0.904128	+	0.427262i	$0.859478\pi$
$200$	0.179327	+	0.103535i	0.0126804	+	0.00732101i
$201$		0			0
$202$			10.4596i			0.735936i
$203$	−0.217086	+	4.88120i	−0.0152365	+	0.342593i
$204$		0			0
$205$	−5.60242	−	9.70367i	−0.391290	−	0.677734i
$206$	6.37383	−	11.0398i	0.444086	−	0.769180i
$207$		0			0
$208$	5.91448	−	3.41473i	0.410096	−	0.236769i
$209$	−3.12989			−0.216499
$210$		0			0
$211$	−24.7482			−1.70373			−0.851867	−	0.523759i	$-0.824529\pi$
$211$	−24.7482			−1.70373			−0.851867	+	0.523759i	$0.824529\pi$
$212$	0.222069	−	0.128212i	0.0152518	−	0.00880562i
$213$		0			0
$214$	4.76813	−	8.25865i	0.325943	−	0.564550i
$215$	8.53993	+	14.7916i	0.582419	+	1.00878i
$216$		0			0
$217$	−4.50882	−	2.87758i	−0.306078	−	0.195343i
$218$			5.76503i			0.390457i
$219$		0			0
$220$	2.16002	+	1.24709i	0.145629	+	0.0840788i
$221$	−39.7291	−	22.9376i	−2.67247	−	1.54295i
$222$		0			0
$223$		−	3.69551i		−	0.247470i	−0.992315	−	0.123735i	$-0.960513\pi$
$223$		−	3.69551i		−	0.247470i	0.992315	−	0.123735i	$-0.0394873\pi$
$224$	2.23025	+	1.42337i	0.149015	+	0.0951030i
$225$		0			0
$226$	−5.96592	−	10.3333i	−0.396847	−	0.687359i
$227$	2.30549	−	3.99322i	0.153020	−	0.265039i	−0.779316	−	0.626631i	$-0.784433\pi$
$227$	2.30549	−	3.99322i	0.153020	−	0.265039i	0.932336	+	0.361592i	$0.117767\pi$
$228$		0			0
$229$	13.8220	−	7.98016i	0.913386	−	0.527344i	0.0318672	−	0.999492i	$-0.489855\pi$
$229$	13.8220	−	7.98016i	0.913386	−	0.527344i	0.881519	+	0.472148i	$0.156521\pi$
$230$	8.91294			0.587702
$231$		0			0
$232$	−1.84674			−0.121245
$233$	−6.17609	+	3.56577i	−0.404609	+	0.233601i	−0.688471	−	0.725264i	$-0.741718\pi$
$233$	−6.17609	+	3.56577i	−0.404609	+	0.233601i	0.283862	+	0.958865i	$0.408384\pi$
$234$		0			0
$235$	7.76244	−	13.4449i	0.506366	−	0.877051i
$236$	0.971009	+	1.68184i	0.0632073	+	0.109478i
$237$		0			0
$238$	0.789621	−	17.7547i	0.0511835	−	1.15086i
$239$			15.7292i			1.01744i	0.860932	+	0.508720i	$0.169881\pi$
$239$			15.7292i			1.01744i	−0.860932	+	0.508720i	$0.830119\pi$
$240$		0			0
$241$	−1.39292	−	0.804201i	−0.0897257	−	0.0518031i	0.454466	−	0.890764i	$-0.349830\pi$
$241$	−1.39292	−	0.804201i	−0.0897257	−	0.0518031i	−0.544191	+	0.838961i	$0.683163\pi$
$242$	−8.49163	−	4.90265i	−0.545863	−	0.315154i
$243$		0			0
$244$			1.33154i			0.0852432i
$245$	6.72711	+	14.4877i	0.429779	+	0.925583i
$246$		0			0
$247$	−9.77810	−	16.9362i	−0.622166	−	1.07762i
$248$	1.01083	−	1.75081i	0.0641879	−	0.111177i
$249$		0			0
$250$	9.47171	−	5.46850i	0.599044	−	0.345858i
$251$	−18.3728			−1.15968			−0.579841	−	0.814729i	$-0.696885\pi$
$251$	−18.3728			−1.15968			−0.579841	+	0.814729i	$0.696885\pi$
$252$		0			0
$253$	4.26929			0.268408
$254$	−9.45121	+	5.45666i	−0.593021	+	0.342381i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.73678	+	15.1326i	0.544986	+	0.943943i	0.998608	+	0.0527487i	$0.0167982\pi$
$257$	8.73678	+	15.1326i	0.544986	+	0.943943i	−0.453622	+	0.891194i	$0.649868\pi$
$258$		0			0
$259$	−8.73158	−	16.8065i	−0.542554	−	1.04430i
$260$			15.5841i			0.966487i
$261$		0			0
$262$	1.71417	+	0.989677i	0.105902	+	0.0611424i
$263$	−23.9148	−	13.8072i	−1.47465	−	0.851389i	−0.475057	−	0.879955i	$-0.657572\pi$
$263$	−23.9148	−	13.8072i	−1.47465	−	0.851389i	−0.999592	+	0.0285666i	$0.990906\pi$
$264$		0			0
$265$			0.585133i			0.0359444i
$266$	4.07584	−	6.38634i	0.249906	−	0.391572i
$267$		0			0
$268$	2.54959	+	4.41602i	0.155741	+	0.269751i
$269$	−3.38607	+	5.86484i	−0.206452	+	0.357586i	−0.950594	−	0.310435i	$-0.899525\pi$
$269$	−3.38607	+	5.86484i	−0.206452	+	0.357586i	0.744142	+	0.668021i	$0.232858\pi$
$270$		0			0
$271$	7.23822	−	4.17899i	0.439691	−	0.253856i	−0.263776	−	0.964584i	$-0.584968\pi$
$271$	7.23822	−	4.17899i	0.439691	−	0.253856i	0.703466	+	0.710729i	$0.251635\pi$
$272$	6.71727			0.407294
$273$		0			0
$274$	−3.31310			−0.200152
$275$	−0.196010	+	0.113166i	−0.0118198	+	0.00682419i
$276$		0			0
$277$	8.10617	−	14.0403i	0.487053	−	0.843600i	−0.512837	−	0.858486i	$-0.671405\pi$
$277$	8.10617	−	14.0403i	0.487053	−	0.843600i	0.999889	+	0.0148865i	$0.00473868\pi$
$278$	−1.73608	−	3.00698i	−0.104123	−	0.180346i
$279$		0			0
$280$	−5.35745	+	2.78339i	−0.320169	+	0.166339i
$281$			29.2545i			1.74518i	0.488453	+	0.872590i	$0.337561\pi$
$281$			29.2545i			1.74518i	−0.488453	+	0.872590i	$0.662439\pi$
$282$		0			0
$283$	−1.24230	−	0.717242i	−0.0738470	−	0.0426356i	0.462622	−	0.886556i	$-0.346909\pi$
$283$	−1.24230	−	0.717242i	−0.0738470	−	0.0426356i	−0.536469	+	0.843920i	$0.680242\pi$
$284$	0.202223	+	0.116753i	0.0119997	+	0.00692803i
$285$		0			0
$286$			7.46479i			0.441402i
$287$	12.9786	+	0.577211i	0.766104	+	0.0340717i
$288$		0			0
$289$	−14.0608	−	24.3541i	−0.827108	−	1.43259i
$290$	2.10704	−	3.64950i	0.123730	−	0.214306i
$291$		0			0
$292$	5.89272	−	3.40216i	0.344845	−	0.199096i
$293$	21.6519			1.26492			0.632459	−	0.774594i	$-0.282046\pi$
$293$	21.6519			1.26492			0.632459	+	0.774594i	$0.282046\pi$
$294$		0			0
$295$	−4.43149			−0.258011
$296$	6.19935	−	3.57920i	0.360330	−	0.208037i
$297$		0			0
$298$	6.67036	−	11.5534i	0.386404	−	0.669271i
$299$	13.3377	+	23.1016i	0.771338	+	1.33600i
$300$		0			0
$301$	−19.7837	−	0.879861i	−1.14031	−	0.0507143i
$302$		−	5.33991i		−	0.307277i
$303$		0			0
$304$	2.47987	+	1.43175i	0.142230	+	0.0821167i
$305$	−2.63137	−	1.51922i	−0.150672	−	0.0869904i
$306$		0			0
$307$			13.4732i			0.768957i	0.923134	+	0.384479i	$0.125619\pi$
$307$			13.4732i			0.768957i	−0.923134	+	0.384479i	$0.874381\pi$
$308$	−2.56621	+	1.33324i	−0.146223	+	0.0759684i
$309$		0			0
$310$	2.30662	+	3.99518i	0.131007	+	0.226911i
$311$	14.3669	−	24.8842i	0.814672	−	1.41105i	−0.0948916	−	0.995488i	$-0.530250\pi$
$311$	14.3669	−	24.8842i	0.814672	−	1.41105i	0.909563	−	0.415565i	$-0.136416\pi$
$312$		0			0
$313$	20.4636	−	11.8147i	1.15667	−	0.667805i	0.206167	−	0.978517i	$-0.433901\pi$
$313$	20.4636	−	11.8147i	1.15667	−	0.667805i	0.950504	+	0.310712i	$0.100567\pi$
$314$	17.6673			0.997023
$315$		0			0
$316$	7.27248			0.409109
$317$	−0.760093	+	0.438840i	−0.0426911	+	0.0246477i	−0.521194	−	0.853438i	$-0.674513\pi$
$317$	−0.760093	+	0.438840i	−0.0426911	+	0.0246477i	0.478503	+	0.878086i	$0.341180\pi$
$318$		0			0
$319$	1.00927	−	1.74811i	0.0565083	−	0.0978753i
$320$	−1.14095	−	1.97618i	−0.0637811	−	0.110472i
$321$		0			0
$322$	−5.55959	+	8.71120i	−0.309824	+	0.485456i
$323$		−	19.2349i		−	1.07026i
$324$		0			0
$325$	−1.22471	−	0.707086i	−0.0679346	−	0.0392221i
$326$	13.7683	+	7.94915i	0.762557	+	0.440262i
$327$		0			0
$328$			4.91031i			0.271126i
$329$	8.29867	+	15.9732i	0.457521	+	0.880633i
$330$		0			0
$331$	10.0915	+	17.4790i	0.554680	+	0.960733i	0.997928	+	0.0643345i	$0.0204925\pi$
$331$	10.0915	+	17.4790i	0.554680	+	0.960733i	−0.443249	+	0.896399i	$0.646174\pi$
$332$	2.91353	−	5.04638i	0.159901	−	0.276956i
$333$		0			0
$334$	−4.95155	+	2.85878i	−0.270937	+	0.156425i
$335$	−11.6358			−0.635733
$336$		0			0
$337$	−1.51521			−0.0825388			−0.0412694	−	0.999148i	$-0.513140\pi$
$337$	−1.51521			−0.0825388			−0.0412694	+	0.999148i	$0.513140\pi$
$338$	−29.1344	+	16.8207i	−1.58470	+	0.914927i
$339$		0			0
$340$	−7.66407	+	13.2746i	−0.415642	+	0.719914i
$341$	1.10487	+	1.91369i	0.0598319	+	0.103632i
$342$		0			0
$343$	−18.3559	−	2.46207i	−0.991124	−	0.132939i
$344$		−	7.48493i		−	0.403560i
$345$		0			0
$346$	−13.1681	−	7.60258i	−0.707919	−	0.408717i
$347$	31.2622	+	18.0492i	1.67824	+	0.968934i	0.962781	+	0.270281i	$0.0871167\pi$
$347$	31.2622	+	18.0492i	1.67824	+	0.968934i	0.715461	+	0.698652i	$0.246217\pi$
$348$		0			0
$349$			19.3945i			1.03817i	0.854724	+	0.519083i	$0.173726\pi$
$349$			19.3945i			1.03817i	−0.854724	+	0.519083i	$0.826274\pi$
$350$	0.0243412	−	0.547313i	0.00130109	−	0.0292551i
$351$		0			0
$352$	−0.546514	−	0.946590i	−0.0291293	−	0.0504534i
$353$	2.01909	−	3.49717i	0.107465	−	0.186136i	−0.807277	−	0.590172i	$-0.799060\pi$
$353$	2.01909	−	3.49717i	0.107465	−	0.186136i	0.914743	+	0.404037i	$0.132393\pi$
$354$		0			0
$355$	−0.461452	+	0.266419i	−0.0244913	+	0.0141401i
$356$	−17.9941			−0.953687
$357$		0			0
$358$	4.05972			0.214563
$359$	21.2649	−	12.2773i	1.12232	−	0.647970i	0.180326	−	0.983607i	$-0.442285\pi$
$359$	21.2649	−	12.2773i	1.12232	−	0.647970i	0.941991	+	0.335637i	$0.108952\pi$
$360$		0			0
$361$	−5.40016	+	9.35335i	−0.284219	+	0.492282i
$362$	1.84226	+	3.19089i	0.0968272	+	0.167710i
$363$		0			0
$364$	−15.2314	−	9.72085i	−0.798342	−	0.509511i
$365$			15.5268i			0.812709i
$366$		0			0
$367$	6.28109	+	3.62639i	0.327870	+	0.189296i	0.654895	−	0.755720i	$-0.272713\pi$
$367$	6.28109	+	3.62639i	0.327870	+	0.189296i	−0.327025	+	0.945016i	$0.606046\pi$
$368$	−3.38264	−	1.95297i	−0.176332	−	0.101805i
$369$		0			0
$370$			16.3347i			0.849203i
$371$	−0.571889	−	0.364986i	−0.0296910	−	0.0189491i
$372$		0			0
$373$	14.8921	+	25.7939i	0.771083	+	1.33556i	0.936970	+	0.349410i	$0.113618\pi$
$373$	14.8921	+	25.7939i	0.771083	+	1.33556i	−0.165887	+	0.986145i	$0.553049\pi$
$374$	−3.67108	+	6.35850i	−0.189827	+	0.328790i
$375$		0			0
$376$	−5.89199	+	3.40174i	−0.303856	+	0.175432i
$377$	12.6122			0.649564
$378$		0			0
$379$	6.11280			0.313993			0.156997	−	0.987599i	$-0.449819\pi$
$379$	6.11280			0.313993			0.156997	+	0.987599i	$0.449819\pi$
$380$	−5.65882	+	3.26712i	−0.290291	+	0.167600i
$381$		0			0
$382$	12.8994	−	22.3425i	0.659992	−	1.14314i
$383$	−16.2451	−	28.1374i	−0.830088	−	1.43775i	−0.897968	−	0.440061i	$-0.854957\pi$
$383$	−16.2451	−	28.1374i	−0.830088	−	1.43775i	0.0678797	−	0.997694i	$-0.478377\pi$
$384$		0			0
$385$	0.293193	−	6.59247i	0.0149425	−	0.335983i
$386$		−	9.28662i		−	0.472677i
$387$		0			0
$388$	4.13903	+	2.38967i	0.210127	+	0.121317i
$389$	−1.80316	−	1.04105i	−0.0914236	−	0.0527834i	0.453591	−	0.891210i	$-0.350143\pi$
$389$	−1.80316	−	1.04105i	−0.0914236	−	0.0527834i	−0.545015	+	0.838426i	$0.683476\pi$
$390$		0			0
$391$			26.2372i			1.32687i
$392$	0.621407	−	6.97236i	0.0313858	−	0.352158i
$393$		0			0
$394$	−2.93119	−	5.07696i	−0.147671	−	0.255774i
$395$	−8.29754	+	14.3718i	−0.417495	+	0.723122i
$396$		0			0
$397$	16.3994	−	9.46822i	0.823064	−	0.475196i	−0.0284077	−	0.999596i	$-0.509044\pi$
$397$	16.3994	−	9.46822i	0.823064	−	0.475196i	0.851472	+	0.524400i	$0.175710\pi$
$398$	−16.0638			−0.805207
$399$		0			0
$400$	0.207069			0.0103535
$401$	−3.35718	+	1.93827i	−0.167650	+	0.0967926i	−0.581477	−	0.813563i	$-0.697525\pi$
$401$	−3.35718	+	1.93827i	−0.167650	+	0.0967926i	0.413827	+	0.910355i	$0.364192\pi$
$402$		0			0
$403$	−6.90343	+	11.9571i	−0.343884	+	0.595625i
$404$	5.22981	+	9.05829i	0.260193	+	0.450667i
$405$		0			0
$406$	2.25260	+	4.33578i	0.111794	+	0.215181i
$407$			7.82433i			0.387837i
$408$		0			0
$409$	−14.0286	−	8.09940i	−0.693669	−	0.400490i	0.111316	−	0.993785i	$-0.464493\pi$
$409$	−14.0286	−	8.09940i	−0.693669	−	0.400490i	−0.804985	+	0.593295i	$0.797827\pi$
$410$	−9.70367	−	5.60242i	−0.479230	−	0.276684i
$411$		0			0
$412$		−	12.7477i		−	0.628033i
$413$	2.76421	−	4.33119i	0.136018	−	0.213124i
$414$		0			0
$415$	6.64838	+	11.5153i	0.326356	+	0.565266i
$416$	3.41473	−	5.91448i	0.167421	−	0.289981i
$417$		0			0
$418$	−2.71057	+	1.56495i	−0.132578	+	0.0765441i
$419$	3.27579			0.160033			0.0800165	−	0.996794i	$-0.474503\pi$
$419$	3.27579			0.160033			0.0800165	+	0.996794i	$0.474503\pi$
$420$		0			0
$421$	1.68965			0.0823483			0.0411741	−	0.999152i	$-0.486890\pi$
$421$	1.68965			0.0823483			0.0411741	+	0.999152i	$0.486890\pi$
$422$	−21.4325	+	12.3741i	−1.04332	+	0.602361i
$423$		0			0
$424$	0.128212	−	0.222069i	0.00622651	−	0.0107846i
$425$	−0.695470	−	1.20459i	−0.0337353	−	0.0584312i
$426$		0			0
$427$	3.12619	−	1.62417i	0.151287	−	0.0785991i
$428$		−	9.53627i		−	0.460953i
$429$		0			0
$430$	14.7916	+	8.53993i	0.713314	+	0.411832i
$431$	0.0157083	+	0.00906921i	0.000756644	+	0.000436848i	0.500378	−	0.865807i	$-0.333194\pi$
$431$	0.0157083	+	0.00906921i	0.000756644	+	0.000436848i	−0.499622	+	0.866244i	$0.666528\pi$
$432$		0			0
$433$		−	5.36964i		−	0.258048i	−0.991641	−	0.129024i	$-0.958815\pi$
$433$		−	5.36964i		−	0.258048i	0.991641	−	0.129024i	$-0.0411845\pi$
$434$	−5.34354	−	0.237649i	−0.256498	−	0.0114075i
$435$		0			0
$436$	2.88251	+	4.99266i	0.138047	+	0.239105i
$437$	−5.59233	+	9.68621i	−0.267518	+	0.463354i
$438$		0			0
$439$	18.9141	−	10.9201i	0.902720	−	0.521186i	0.0246384	−	0.999696i	$-0.492157\pi$
$439$	18.9141	−	10.9201i	0.902720	−	0.521186i	0.878082	+	0.478511i	$0.158823\pi$
$440$	2.49418			0.118905
$441$		0			0
$442$	−45.8753			−2.18206
$443$	1.81806	−	1.04966i	0.0863785	−	0.0498707i	−0.456189	−	0.889883i	$-0.650786\pi$
$443$	1.81806	−	1.04966i	0.0863785	−	0.0498707i	0.542567	+	0.840012i	$0.317452\pi$
$444$		0			0
$445$	20.5304	−	35.5597i	0.973235	−	1.68569i
$446$	−1.84776	−	3.20041i	−0.0874938	−	0.151544i
$447$		0			0
$448$	2.64314	+	0.117551i	0.124877	+	0.00555376i
$449$			27.1356i			1.28061i	0.768122	+	0.640303i	$0.221191\pi$
$449$			27.1356i			1.28061i	−0.768122	+	0.640303i	$0.778809\pi$
$450$		0			0
$451$	−4.64805	−	2.68355i	−0.218868	−	0.126364i
$452$	−10.3333	−	5.96592i	−0.486036	−	0.280613i
$453$		0			0
$454$		−	4.61097i		−	0.216404i
$455$	36.5884	−	19.0090i	1.71529	−	0.891157i
$456$		0			0
$457$	−4.21598	−	7.30229i	−0.197215	−	0.341587i	0.750409	−	0.660974i	$-0.229856\pi$
$457$	−4.21598	−	7.30229i	−0.197215	−	0.341587i	−0.947624	+	0.319387i	$0.896523\pi$
$458$	7.98016	−	13.8220i	0.372888	−	0.645862i
$459$		0			0
$460$	7.71884	−	4.45647i	0.359893	−	0.207784i
$461$	−9.34306			−0.435150			−0.217575	−	0.976044i	$-0.569815\pi$
$461$	−9.34306			−0.435150			−0.217575	+	0.976044i	$0.569815\pi$
$462$		0			0
$463$	25.4563			1.18305			0.591526	−	0.806286i	$-0.298526\pi$
$463$	25.4563			1.18305			0.591526	+	0.806286i	$0.298526\pi$
$464$	−1.59933	+	0.923371i	−0.0742469	+	0.0428664i
$465$		0			0
$466$	−3.56577	+	6.17609i	−0.165181	+	0.286102i
$467$	−10.3199	−	17.8746i	−0.477547	−	0.827136i	0.522122	−	0.852871i	$-0.325141\pi$
$467$	−10.3199	−	17.8746i	−0.477547	−	0.827136i	−0.999669	+	0.0257351i	$0.991807\pi$
$468$		0			0
$469$	7.25803	−	11.3724i	0.335145	−	0.525131i
$470$		−	15.5249i		−	0.716109i
$471$		0			0
$472$	1.68184	+	0.971009i	0.0774128	+	0.0446943i
$473$	7.08516	+	4.09062i	0.325776	+	0.188087i
$474$		0			0
$475$		−	0.592945i		−	0.0272062i
$476$	−8.19350	−	15.7708i	−0.375548	−	0.722853i
$477$		0			0
$478$	7.86462	+	13.6219i	0.359720	+	0.623053i
$479$	3.07442	−	5.32505i	0.140474	−	0.243308i	−0.787201	−	0.616696i	$-0.788471\pi$
$479$	3.07442	−	5.32505i	0.140474	−	0.243308i	0.927675	+	0.373388i	$0.121804\pi$
$480$		0			0
$481$	−42.3382	+	24.4440i	−1.93046	+	1.11455i
$482$	−1.60840			−0.0732607
$483$		0			0
$484$	−9.80529			−0.445695
$485$	−9.44486	+	5.45299i	−0.428869	+	0.247608i
$486$		0			0
$487$	−9.86365	+	17.0843i	−0.446965	+	0.774166i	−0.998187	−	0.0601930i	$-0.980828\pi$
$487$	−9.86365	+	17.0843i	−0.446965	+	0.774166i	0.551222	+	0.834359i	$0.314162\pi$
$488$	0.665771	+	1.15315i	0.0301380	+	0.0522006i
$489$		0			0
$490$	13.0697	+	9.18313i	0.590428	+	0.414852i
$491$			3.95987i			0.178707i	0.996000	+	0.0893533i	$0.0284800\pi$
$491$			3.95987i			0.178707i	−0.996000	+	0.0893533i	$0.971520\pi$
$492$		0			0
$493$	10.7431	+	6.20253i	0.483845	+	0.279348i
$494$	−16.9362	−	9.77810i	−0.761994	−	0.439938i
$495$		0			0
$496$		−	2.02166i		−	0.0907754i
$497$	0.0274489	−	0.617190i	0.00123125	−	0.0276848i
$498$		0			0
$499$	18.4092	+	31.8856i	0.824108	+	1.42740i	0.902599	+	0.430482i	$0.141656\pi$
$499$	18.4092	+	31.8856i	0.824108	+	1.42740i	−0.0784916	+	0.996915i	$0.525010\pi$
$500$	5.46850	−	9.47171i	0.244559	−	0.423588i
$501$		0			0
$502$	−15.9113	+	9.18641i	−0.710158	+	0.410010i
$503$	12.3802			0.552004			0.276002	−	0.961157i	$-0.410990\pi$
$503$	12.3802			0.552004			0.276002	+	0.961157i	$0.410990\pi$
$504$		0			0
$505$	−23.8678			−1.06210
$506$	3.69731	−	2.13465i	0.164366	−	0.0948966i
$507$		0			0
$508$	−5.45666	+	9.45121i	−0.242100	+	0.419329i
$509$	−7.54528	−	13.0688i	−0.334438	−	0.579264i	0.648938	−	0.760841i	$-0.275213\pi$
$509$	−7.54528	−	13.0688i	−0.334438	−	0.579264i	−0.983377	+	0.181577i	$0.941880\pi$
$510$		0			0
$511$	−15.1753	−	9.68508i	−0.671317	−	0.428443i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	15.1326	+	8.73678i	0.667468	+	0.385363i
$515$	25.1917	+	14.5445i	1.11008	+	0.640905i
$516$		0			0
$517$		−	7.43640i		−	0.327053i
$518$	−15.9650	−	10.1891i	−0.701462	−	0.447681i
$519$		0			0
$520$	7.79207	+	13.4963i	0.341705	+	0.591850i
$521$	−12.4908	+	21.6347i	−0.547231	+	0.947832i	0.451232	+	0.892407i	$0.350985\pi$
$521$	−12.4908	+	21.6347i	−0.547231	+	0.947832i	−0.998463	+	0.0554255i	$0.982348\pi$
$522$		0			0
$523$	21.6818	−	12.5180i	0.948077	−	0.547372i	0.0555939	−	0.998453i	$-0.482295\pi$
$523$	21.6818	−	12.5180i	0.948077	−	0.547372i	0.892483	+	0.451081i	$0.148961\pi$
$524$	1.97935			0.0864684
$525$		0			0
$526$	−27.6144			−1.20405
$527$	−11.7607	+	6.79003i	−0.512303	+	0.295778i
$528$		0			0
$529$	−3.87185	+	6.70625i	−0.168341	+	0.291576i
$530$	0.292567	+	0.506740i	0.0127083	+	0.0220114i
$531$		0			0
$532$	0.336608	−	7.56865i	0.0145938	−	0.328143i
$533$		−	33.5347i		−	1.45255i
$534$		0			0
$535$	18.8454	+	10.8804i	0.814759	+	0.470401i
$536$	4.41602	+	2.54959i	0.190743	+	0.110126i
$537$		0			0
$538$			6.77214i			0.291968i
$539$	6.26036	+	4.39871i	0.269653	+	0.189466i
$540$		0			0
$541$	7.23042	+	12.5235i	0.310860	+	0.538426i	0.978549	−	0.206015i	$-0.0660496\pi$
$541$	7.23042	+	12.5235i	0.310860	+	0.538426i	−0.667689	+	0.744441i	$0.732716\pi$
$542$	4.17899	−	7.23822i	0.179503	−	0.310908i
$543$		0			0
$544$	5.81732	−	3.35863i	0.249416	−	0.144000i
$545$	−13.1552			−0.563508
$546$		0			0
$547$	−33.8321			−1.44655			−0.723277	−	0.690558i	$-0.757365\pi$
$547$	−33.8321			−1.44655			−0.723277	+	0.690558i	$0.757365\pi$
$548$	−2.86923	+	1.65655i	−0.122567	+	0.0707642i
$549$		0			0
$550$	−0.113166	+	0.196010i	−0.00482543	+	0.00835789i
$551$	2.64408	+	4.57968i	0.112642	+	0.195101i
$552$		0			0
$553$	−8.87074	−	17.0743i	−0.377222	−	0.726075i
$554$		−	16.2123i		−	0.688796i
$555$		0			0
$556$	−3.00698	−	1.73608i	−0.127524	−	0.0736261i
$557$	−5.09456	−	2.94134i	−0.215863	−	0.124629i	0.388170	−	0.921588i	$-0.373107\pi$
$557$	−5.09456	−	2.94134i	−0.215863	−	0.124629i	−0.604033	+	0.796959i	$0.706441\pi$
$558$		0			0
$559$			51.1180i			2.16206i
$560$	−3.24799	+	5.08921i	−0.137253	+	0.215058i
$561$		0			0
$562$	14.6273	+	25.3352i	0.617014	+	1.06870i
$563$	−7.78184	+	13.4785i	−0.327966	+	0.568053i	−0.982108	−	0.188318i	$-0.939696\pi$
$563$	−7.78184	+	13.4785i	−0.327966	+	0.568053i	0.654142	+	0.756371i	$0.273030\pi$
$564$		0			0
$565$	23.5795	−	13.6136i	0.991997	−	0.572730i
$566$	−1.43448			−0.0602958
$567$		0			0
$568$	0.233507			0.00979772
$569$	22.6993	−	13.1055i	0.951606	−	0.549410i	0.0580267	−	0.998315i	$-0.481519\pi$
$569$	22.6993	−	13.1055i	0.951606	−	0.549410i	0.893580	+	0.448905i	$0.148186\pi$
$570$		0			0
$571$	−12.8090	+	22.1859i	−0.536041	+	0.928451i	0.463071	+	0.886321i	$0.346748\pi$
$571$	−12.8090	+	22.1859i	−0.536041	+	0.928451i	−0.999112	+	0.0421295i	$0.986586\pi$
$572$	3.73239	+	6.46469i	0.156059	+	0.270302i
$573$		0			0
$574$	11.5284	−	5.98943i	0.481187	−	0.249994i
$575$			0.808799i			0.0337292i
$576$		0			0
$577$	28.0540	+	16.1970i	1.16790	+	0.674288i	0.953185	−	0.302388i	$-0.0977839\pi$
$577$	28.0540	+	16.1970i	1.16790	+	0.674288i	0.214717	+	0.976676i	$0.431117\pi$
$578$	−24.3541	−	14.0608i	−1.01300	−	0.584853i
$579$		0			0
$580$		−	4.21408i		−	0.174980i
$581$	−15.4017	−	0.684976i	−0.638971	−	0.0284176i
$582$		0			0
$583$	0.140139	+	0.242728i	0.00580397	+	0.0100528i
$584$	3.40216	−	5.89272i	0.140782	−	0.243842i
$585$		0			0
$586$	18.7511	−	10.8260i	0.774601	−	0.447216i
$587$	9.53702			0.393635			0.196818	−	0.980440i	$-0.436939\pi$
$587$	9.53702			0.393635			0.196818	+	0.980440i	$0.436939\pi$
$588$		0			0
$589$	−5.78905			−0.238534
$590$	−3.83779	+	2.21575i	−0.157999	+	0.0912208i
$591$		0			0
$592$	3.57920	−	6.19935i	0.147104	−	0.254792i
$593$	−1.89409	−	3.28065i	−0.0777808	−	0.134720i	0.824511	−	0.565845i	$-0.191450\pi$
$593$	−1.89409	−	3.28065i	−0.0777808	−	0.134720i	−0.902292	+	0.431125i	$0.858117\pi$
$594$		0			0
$595$	40.5144	+	1.80184i	1.66093	+	0.0738681i
$596$		−	13.3407i		−	0.546457i
$597$		0			0
$598$	23.1016	+	13.3377i	0.944693	+	0.545419i
$599$	31.2971	+	18.0694i	1.27876	+	0.738295i	0.976621	−	0.214968i	$-0.0689647\pi$
$599$	31.2971	+	18.0694i	1.27876	+	0.738295i	0.302143	+	0.953263i	$0.402298\pi$
$600$		0			0
$601$			15.9666i			0.651293i	0.945492	+	0.325646i	$0.105582\pi$
$601$			15.9666i			0.651293i	−0.945492	+	0.325646i	$0.894418\pi$
$602$	−17.5731	+	9.12987i	−0.716227	+	0.372106i
$603$		0			0
$604$	−2.66995	−	4.62450i	−0.108639	−	0.188168i
$605$	11.1873	−	19.3771i	0.454830	−	0.787789i
$606$		0			0
$607$	19.6190	−	11.3270i	0.796309	−	0.459749i	−0.0458701	−	0.998947i	$-0.514606\pi$
$607$	19.6190	−	11.3270i	0.796309	−	0.459749i	0.842179	+	0.539198i	$0.181273\pi$
$608$	2.86351			0.116131
$609$		0			0
$610$	−3.03844			−0.123023
$611$	40.2391	−	23.2321i	1.62790	−	0.939868i
$612$		0			0
$613$	−1.84758	+	3.20011i	−0.0746232	+	0.129251i	−0.900922	−	0.433980i	$-0.857109\pi$
$613$	−1.84758	+	3.20011i	−0.0746232	+	0.129251i	0.826299	+	0.563231i	$0.190442\pi$
$614$	6.73661	+	11.6682i	0.271868	+	0.470888i
$615$		0			0
$616$	−1.55578	+	2.43773i	−0.0626844	+	0.0982187i
$617$			26.0023i			1.04681i	0.852083	+	0.523407i	$0.175339\pi$
$617$			26.0023i			1.04681i	−0.852083	+	0.523407i	$0.824661\pi$
$618$		0			0
$619$	−20.5526	−	11.8660i	−0.826079	−	0.476937i	0.0264296	−	0.999651i	$-0.491586\pi$
$619$	−20.5526	−	11.8660i	−0.826079	−	0.476937i	−0.852508	+	0.522714i	$0.824920\pi$
$620$	3.99518	+	2.30662i	0.160450	+	0.0926360i
$621$		0			0
$622$		−	28.7338i		−	1.15212i
$623$	21.9487	+	42.2466i	0.879354	+	1.69258i
$624$		0			0
$625$	12.9962	+	22.5101i	0.519849	+	0.900406i
$626$	11.8147	−	20.4636i	0.472209	−	0.817890i
$627$		0			0
$628$	15.3003	−	8.83364i	0.610549	−	0.352501i
$629$	−48.0848			−1.91727
$630$		0			0
$631$	−0.664631			−0.0264586			−0.0132293	−	0.999912i	$-0.504211\pi$
$631$	−0.664631			−0.0264586			−0.0132293	+	0.999912i	$0.504211\pi$
$632$	6.29816	−	3.63624i	0.250527	−	0.144642i
$633$		0			0
$634$	−0.438840	+	0.760093i	−0.0174286	+	0.0301872i
$635$	−12.4515	−	21.5667i	−0.494125	−	0.855849i
$636$		0			0
$637$	−4.24387	+	47.6174i	−0.168148	+	1.88667i
$638$		−	2.01854i		−	0.0799148i
$639$		0			0
$640$	−1.97618	−	1.14095i	−0.0781155	−	0.0451000i
$641$	−7.27466	−	4.20003i	−0.287332	−	0.165891i	0.349406	−	0.936971i	$-0.386383\pi$
$641$	−7.27466	−	4.20003i	−0.287332	−	0.165891i	−0.636738	+	0.771080i	$0.719717\pi$
$642$		0			0
$643$		−	0.274789i		−	0.0108366i	−0.999985	−	0.00541831i	$-0.998275\pi$
$643$		−	0.274789i		−	0.0108366i	0.999985	−	0.00541831i	$-0.00172471\pi$
$644$	−0.459146	+	10.3239i	−0.0180929	+	0.406819i
$645$		0			0
$646$	−9.61747	−	16.6580i	−0.378394	−	0.655398i
$647$	17.0508	−	29.5328i	0.670335	−	1.16105i	−0.307474	−	0.951556i	$-0.599484\pi$
$647$	17.0508	−	29.5328i	0.670335	−	1.16105i	0.977809	−	0.209498i	$-0.0671829\pi$
$648$		0			0
$649$	−1.83830	+	1.06134i	−0.0721594	+	0.0416612i
$650$	−1.41417			−0.0554684
$651$		0			0
$652$	15.8983			0.622625
$653$	1.48356	−	0.856531i	0.0580560	−	0.0335187i	−0.470691	−	0.882298i	$-0.655995\pi$
$653$	1.48356	−	0.856531i	0.0580560	−	0.0335187i	0.528747	+	0.848779i	$0.322662\pi$
$654$		0			0
$655$	−2.25834	+	3.91157i	−0.0882408	+	0.152838i
$656$	2.45515	+	4.25245i	0.0958576	+	0.166030i
$657$		0			0
$658$	15.1735	+	9.68389i	0.591524	+	0.377517i
$659$		−	34.7052i		−	1.35192i	−0.736938	−	0.675961i	$-0.763729\pi$
$659$		−	34.7052i		−	1.35192i	0.736938	−	0.675961i	$-0.236271\pi$
$660$		0			0
$661$	33.2075	+	19.1724i	1.29162	+	0.745718i	0.978942	−	0.204140i	$-0.0654397\pi$
$661$	33.2075	+	19.1724i	1.29162	+	0.745718i	0.312681	+	0.949858i	$0.398773\pi$
$662$	17.4790	+	10.0915i	0.679341	+	0.392218i
$663$		0			0
$664$		−	5.82706i		−	0.226134i
$665$	14.5730	+	9.30065i	0.565116	+	0.360664i
$666$		0			0
$667$	−3.60662	−	6.24686i	−0.139649	−	0.241879i
$668$	−2.85878	+	4.95155i	−0.110610	+	0.191581i
$669$		0			0
$670$	−10.0769	+	5.81791i	−0.389305	+	0.224765i
$671$	−1.45541			−0.0561856
$672$		0			0
$673$	16.6708			0.642611			0.321305	−	0.946976i	$-0.395878\pi$
$673$	16.6708			0.642611			0.321305	+	0.946976i	$0.395878\pi$
$674$	−1.31221	+	0.757605i	−0.0505445	+	0.0291819i
$675$		0			0
$676$	−16.8207	+	29.1344i	−0.646951	+	1.12055i
$677$	−10.4682	−	18.1315i	−0.402327	−	0.696850i	0.591680	−	0.806173i	$-0.298465\pi$
$677$	−10.4682	−	18.1315i	−0.402327	−	0.696850i	−0.994006	+	0.109323i	$0.965132\pi$
$678$		0			0
$679$	0.561816	−	12.6325i	0.0215605	−	0.484789i
$680$			15.3281i			0.587807i
$681$		0			0
$682$	1.91369	+	1.10487i	0.0732789	+	0.0423076i
$683$	6.62003	+	3.82208i	0.253308	+	0.146248i	0.621278	−	0.783590i	$-0.286614\pi$
$683$	6.62003	+	3.82208i	0.253308	+	0.146248i	−0.367970	+	0.929838i	$0.619947\pi$
$684$		0			0
$685$		−	7.56016i		−	0.288859i
$686$	−17.1277	+	7.04572i	−0.653938	+	0.269007i
$687$		0			0
$688$	−3.74246	−	6.48214i	−0.142680	−	0.247129i
$689$	−0.875617	+	1.51661i	−0.0333583	+	0.0577783i
$690$		0			0
$691$	−9.10461	+	5.25655i	−0.346356	+	0.199969i	−0.663079	−	0.748549i	$-0.730751\pi$
$691$	−9.10461	+	5.25655i	−0.346356	+	0.199969i	0.316723	+	0.948518i	$0.397417\pi$
$692$	−15.2052			−0.578013
$693$		0			0
$694$	36.0985			1.37028
$695$	6.86162	−	3.96156i	0.260276	−	0.150270i
$696$		0			0
$697$	16.4919	−	28.5648i	0.624676	−	1.08197i
$698$	9.69727	+	16.7962i	0.367047	+	0.635744i
$699$		0			0
$700$	−0.252577	−	0.486158i	−0.00954650	−	0.0183750i
$701$			15.7336i			0.594250i	0.954839	+	0.297125i	$0.0960277\pi$
$701$			15.7336i			0.594250i	−0.954839	+	0.297125i	$0.903972\pi$
$702$		0			0
$703$	−17.7519	−	10.2491i	−0.669526	−	0.386551i
$704$	−0.946590	−	0.546514i	−0.0356759	−	0.0205975i
$705$		0			0
$706$		−	4.03818i		−	0.151979i
$707$	14.8879	−	23.3276i	0.559918	−	0.877323i
$708$		0			0
$709$	1.44973	+	2.51100i	0.0544456	+	0.0943025i	0.891964	−	0.452107i	$-0.149328\pi$
$709$	1.44973	+	2.51100i	0.0544456	+	0.0943025i	−0.837518	+	0.546410i	$0.815994\pi$
$710$	−0.266419	+	0.461452i	−0.00999854	+	0.0173180i
$711$		0			0
$712$	−15.5834	+	8.99707i	−0.584012	+	0.337179i
$713$	7.89648			0.295725
$714$		0			0
$715$	−17.0339			−0.637032
$716$	3.51582	−	2.02986i	0.131392	−	0.0758595i
$717$		0			0
$718$	12.2773	−	21.2649i	0.458184	−	0.793598i
$719$	20.5644	+	35.6186i	0.766924	+	1.32835i	0.939223	+	0.343307i	$0.111547\pi$
$719$	20.5644	+	35.6186i	0.766924	+	1.32835i	−0.172299	+	0.985045i	$0.555120\pi$
$720$		0			0
$721$	−29.9290	+	15.5492i	−1.11461	+	0.579082i
$722$			10.8003i			0.401946i
$723$		0			0
$724$	3.19089	+	1.84226i	0.118589	+	0.0684671i
$725$	0.331172	+	0.191202i	0.0122994	+	0.00710106i
$726$		0			0
$727$			38.8224i			1.43984i	0.694056	+	0.719921i	$0.255822\pi$
$727$			38.8224i			1.43984i	−0.694056	+	0.719921i	$0.744178\pi$
$728$	−18.0512	−	0.802809i	−0.669022	−	0.0297541i
$729$		0			0
$730$	7.76339	+	13.4466i	0.287336	+	0.497681i
$731$	−25.1391	+	43.5423i	−0.929804	+	1.61047i
$732$		0			0
$733$	−22.5362	+	13.0113i	−0.832394	+	0.480583i	−0.854672	−	0.519169i	$-0.826242\pi$
$733$	−22.5362	+	13.0113i	−0.832394	+	0.480583i	0.0222778	+	0.999752i	$0.492908\pi$
$734$	7.25277			0.267705
$735$		0			0
$736$	−3.90593			−0.143975
$737$	−4.82683	+	2.78677i	−0.177799	+	0.102652i
$738$		0			0
$739$	−3.70004	+	6.40866i	−0.136108	+	0.235746i	−0.926020	−	0.377474i	$-0.876793\pi$
$739$	−3.70004	+	6.40866i	−0.136108	+	0.235746i	0.789912	+	0.613220i	$0.210126\pi$
$740$	8.16737	+	14.1463i	0.300239	+	0.520028i
$741$		0			0
$742$	−0.677763	−	0.0301428i	−0.0248815	−	0.00110658i
$743$		−	28.0871i		−	1.03042i	−0.857065	−	0.515208i	$-0.827715\pi$
$743$		−	28.0871i		−	1.03042i	0.857065	−	0.515208i	$-0.172285\pi$
$744$		0			0
$745$	26.3637	+	15.2211i	0.965892	+	0.557658i
$746$	25.7939	+	14.8921i	0.944380	+	0.545238i
$747$		0			0
$748$			7.34216i			0.268456i
$749$	−22.3893	+	11.6320i	−0.818086	+	0.425025i
$750$		0			0
$751$	−21.1897	−	36.7016i	−0.773221	−	1.33926i	−0.935789	−	0.352561i	$-0.885311\pi$
$751$	−21.1897	−	36.7016i	−0.773221	−	1.33926i	0.162567	−	0.986697i	$-0.448023\pi$
$752$	−3.40174	+	5.89199i	−0.124049	+	0.214859i
$753$		0			0
$754$	10.9225	−	6.30612i	0.397775	−	0.229655i
$755$	12.1851			0.443463
$756$		0			0
$757$	−41.6462			−1.51366			−0.756828	−	0.653614i	$-0.773252\pi$
$757$	−41.6462			−1.51366			−0.756828	+	0.653614i	$0.773252\pi$
$758$	5.29384	−	3.05640i	0.192281	−	0.111013i
$759$		0			0
$760$	−3.26712	+	5.65882i	−0.118511	+	0.205267i
$761$	−17.4823	−	30.2802i	−0.633732	−	1.09766i	−0.986782	−	0.162051i	$-0.948189\pi$
$761$	−17.4823	−	30.2802i	−0.633732	−	1.09766i	0.353051	−	0.935604i	$-0.385144\pi$
$762$		0			0
$763$	8.20578	−	12.8575i	0.297069	−	0.465471i
$764$		−	25.7989i		−	0.933370i
$765$		0			0
$766$	−28.1374	−	16.2451i	−1.01665	−	0.586961i
$767$	−11.4860	−	6.63146i	−0.414737	−	0.239448i
$768$		0			0
$769$			21.8593i			0.788265i	0.919054	+	0.394133i	$0.128955\pi$
$769$			21.8593i			0.788265i	−0.919054	+	0.394133i	$0.871045\pi$
$770$	−3.04232	−	5.85584i	−0.109638	−	0.211030i
$771$		0			0
$772$	−4.64331	−	8.04245i	−0.167116	−	0.289454i
$773$	10.6368	−	18.4235i	0.382579	−	0.662646i	−0.608851	−	0.793285i	$-0.708369\pi$
$773$	10.6368	−	18.4235i	0.382579	−	0.662646i	0.991430	+	0.130638i	$0.0417026\pi$
$774$		0			0
$775$	−0.362540	+	0.209312i	−0.0130228	+	0.00751872i
$776$	4.77934			0.171568
$777$		0			0
$778$	−2.08210			−0.0746471
$779$	12.1769	−	7.03035i	0.436284	−	0.251889i
$780$		0			0
$781$	−0.127615	+	0.221035i	−0.00456641	+	0.00790925i
$782$	13.1186	+	22.7221i	0.469120	+	0.812539i
$783$		0			0
$784$	−2.94803	−	6.34895i	−0.105287	−	0.226748i
$785$			40.3150i			1.43890i
$786$		0			0
$787$	−40.7238	−	23.5119i	−1.45165	−	0.838108i	−0.453070	−	0.891475i	$-0.649671\pi$
$787$	−40.7238	−	23.5119i	−1.45165	−	0.838108i	−0.998575	+	0.0533671i	$0.983005\pi$
$788$	−5.07696	−	2.93119i	−0.180859	−	0.104419i
$789$		0			0
$790$			16.5951i			0.590427i
$791$	−1.40260	+	31.5375i	−0.0498707	+	1.12134i
$792$		0			0
$793$	−4.54685	−	7.87538i	−0.161463	−	0.279663i
$794$	9.46822	−	16.3994i	0.336015	−	0.581994i
$795$		0			0
$796$	−13.9117	+	8.03191i	−0.493086	+	0.284684i
$797$	−29.0406			−1.02867			−0.514336	−	0.857589i	$-0.671962\pi$
$797$	−29.0406			−1.02867			−0.514336	+	0.857589i	$0.671962\pi$
$798$		0			0
$799$	45.7008			1.61678
$800$	0.179327	−	0.103535i	0.00634018	−	0.00366051i
$801$		0			0
$802$	−1.93827	+	3.35718i	−0.0684427	+	0.118546i
$803$	3.71866	+	6.44090i	0.131229	+	0.227294i
$804$		0			0
$805$	−19.8781	−	12.6864i	−0.700611	−	0.447138i
$806$			13.8069i			0.486326i
$807$		0			0
$808$	9.05829	+	5.22981i	0.318670	+	0.183984i
$809$	47.5777	+	27.4690i	1.67274	+	0.965759i	0.966093	+	0.258195i	$0.0831279\pi$
$809$	47.5777	+	27.4690i	1.67274	+	0.965759i	0.706650	+	0.707563i	$0.250205\pi$
$810$		0			0
$811$		−	34.0190i		−	1.19457i	−0.802030	−	0.597284i	$-0.796246\pi$
$811$		−	34.0190i		−	1.19457i	0.802030	−	0.597284i	$-0.203754\pi$
$812$	4.11870	+	2.62860i	0.144538	+	0.0922458i
$813$		0			0
$814$	3.91216	+	6.77606i	0.137121	+	0.237501i
$815$	−18.1392	+	31.4179i	−0.635387	+	1.10052i
$816$		0			0
$817$	−18.5617	+	10.7166i	−0.649390	+	0.374926i
$818$	−16.1988			−0.566378
$819$		0			0
$820$	−11.2048			−0.391290
$821$	−6.92921	+	4.00058i	−0.241831	+	0.139621i	−0.616018	−	0.787732i	$-0.711255\pi$
$821$	−6.92921	+	4.00058i	−0.241831	+	0.139621i	0.374187	+	0.927353i	$0.377922\pi$
$822$		0			0
$823$	−3.51245	+	6.08375i	−0.122436	+	0.212066i	−0.920728	−	0.390205i	$-0.872404\pi$
$823$	−3.51245	+	6.08375i	−0.122436	+	0.212066i	0.798291	+	0.602271i	$0.205737\pi$
$824$	−6.37383	−	11.0398i	−0.222043	−	0.384590i
$825$		0			0
$826$	0.228286	−	5.13302i	0.00794309	−	0.178601i
$827$		−	37.4952i		−	1.30384i	−0.758290	−	0.651918i	$-0.773965\pi$
$827$		−	37.4952i		−	1.30384i	0.758290	−	0.651918i	$-0.226035\pi$
$828$		0			0
$829$	−2.96310	−	1.71074i	−0.102913	−	0.0594166i	0.447660	−	0.894204i	$-0.352257\pi$
$829$	−2.96310	−	1.71074i	−0.102913	−	0.0594166i	−0.550573	+	0.834787i	$0.685591\pi$
$830$	11.5153	+	6.64838i	0.399703	+	0.230769i
$831$		0			0
$832$		−	6.82946i		−	0.236769i
$833$	−27.0325	+	38.4734i	−0.936622	+	1.33302i
$834$		0			0
$835$	−6.52345	−	11.2989i	−0.225753	−	0.391016i
$836$	−1.56495	+	2.71057i	−0.0541248	+	0.0937470i
$837$		0			0
$838$	2.83692	−	1.63790i	0.0979998	−	0.0565802i
$839$	−9.75061			−0.336628			−0.168314	−	0.985733i	$-0.553832\pi$
$839$	−9.75061			−0.336628			−0.168314	+	0.985733i	$0.553832\pi$
$840$		0			0
$841$	25.5895			0.882398
$842$	1.46328	−	0.844823i	0.0504278	−	0.0291145i
$843$		0			0
$844$	−12.3741	+	21.4325i	−0.425933	+	0.737738i
$845$	−38.3832	−	66.4817i	−1.32042	−	2.28704i
$846$		0			0
$847$	11.9602	+	23.0209i	0.410956	+	0.791006i
$848$		−	0.256424i		−	0.00880562i
$849$		0			0
$850$	−1.20459	−	0.695470i	−0.0413171	−	0.0238544i
$851$	24.2142	+	13.9801i	0.830053	+	0.479232i
$852$		0			0
$853$			24.5773i			0.841512i	0.907174	+	0.420756i	$0.138235\pi$
$853$			24.5773i			0.841512i	−0.907174	+	0.420756i	$0.861765\pi$
$854$	1.89528	−	2.96967i	0.0648551	−	0.101620i
$855$		0			0
$856$	−4.76813	−	8.25865i	−0.162971	−	0.282275i
$857$	−14.9684	+	25.9260i	−0.511309	+	0.885614i	0.488605	+	0.872505i	$0.337506\pi$
$857$	−14.9684	+	25.9260i	−0.511309	+	0.885614i	−0.999914	+	0.0131086i	$0.995827\pi$
$858$		0			0
$859$	46.6403	−	26.9278i	1.59135	−	0.918765i	0.598271	−	0.801294i	$-0.295855\pi$
$859$	46.6403	−	26.9278i	1.59135	−	0.918765i	0.993076	−	0.117471i	$-0.0374787\pi$
$860$	17.0799			0.582419
$861$		0			0
$862$	0.0181384			0.000617797
$863$	−42.6599	+	24.6297i	−1.45216	+	0.838404i	−0.998604	−	0.0528239i	$-0.983178\pi$
$863$	−42.6599	+	24.6297i	−1.45216	+	0.838404i	−0.453555	+	0.891228i	$0.649844\pi$
$864$		0			0
$865$	17.3483	−	30.0482i	0.589861	−	1.02167i
$866$	−2.68482	−	4.65025i	−0.0912339	−	0.158022i
$867$		0			0
$868$	−4.74646	+	2.46596i	−0.161106	+	0.0837001i
$869$			7.94903i			0.269652i
$870$		0			0
$871$	−30.1590	−	17.4123i	−1.02190	−	0.589994i
$872$	4.99266	+	2.88251i	0.169073	+	0.0976142i
$873$		0			0
$874$			11.1847i			0.378327i
$875$	−28.9080	−	1.28565i	−0.977268	−	0.0434630i
$876$		0			0
$877$	−9.80382	−	16.9807i	−0.331051	−	0.573398i	0.651667	−	0.758505i	$-0.274070\pi$
$877$	−9.80382	−	16.9807i	−0.331051	−	0.573398i	−0.982718	+	0.185108i	$0.940737\pi$
$878$	10.9201	−	18.9141i	0.368534	−	0.638319i
$879$		0			0
$880$	2.16002	−	1.24709i	0.0728144	−	0.0420394i
$881$	−6.20452			−0.209036			−0.104518	−	0.994523i	$-0.533330\pi$
$881$	−6.20452			−0.209036			−0.104518	+	0.994523i	$0.533330\pi$
$882$		0			0
$883$	26.8733			0.904359			0.452180	−	0.891927i	$-0.350647\pi$
$883$	26.8733			0.904359			0.452180	+	0.891927i	$0.350647\pi$
$884$	−39.7291	+	22.9376i	−1.33624	+	0.771476i
$885$		0			0
$886$	1.04966	−	1.81806i	0.0352639	−	0.0610788i
$887$	2.93679	+	5.08668i	0.0986079	+	0.170794i	0.911109	−	0.412166i	$-0.135228\pi$
$887$	2.93679	+	5.08668i	0.0986079	+	0.170794i	−0.812501	+	0.582960i	$0.801894\pi$
$888$		0			0
$889$	28.8454	+	1.28287i	0.967444	+	0.0430261i
$890$		−	41.0608i		−	1.37636i
$891$		0			0
$892$	−3.20041	−	1.84776i	−0.107158	−	0.0618675i
$893$	16.8718	+	9.74092i	0.564592	+	0.325968i
$894$		0			0
$895$			9.26388i			0.309657i
$896$	2.34780	−	1.21977i	0.0784345	−	0.0407496i
$897$		0			0
$898$	13.5678	+	23.5001i	0.452763	+	0.784208i
$899$	1.86675	−	3.23330i	0.0622595	−	0.107837i
$900$		0			0
$901$	−1.49170	+	0.861233i	−0.0496957	+	0.0286918i
$902$	−5.36710			−0.178705
$903$		0			0
$904$	−11.9318			−0.396847
$905$	−7.28130	+	4.20386i	−0.242039	+	0.139741i
$906$		0			0
$907$	24.6305	−	42.6613i	0.817842	−	1.41654i	−0.0894269	−	0.995993i	$-0.528504\pi$
$907$	24.6305	−	42.6613i	0.817842	−	1.41654i	0.907269	−	0.420551i	$-0.138163\pi$
$908$	−2.30549	−	3.99322i	−0.0765102	−	0.132520i
$909$		0			0
$910$	22.1820	−	34.7565i	0.735327	−	1.15217i
$911$		−	16.1695i		−	0.535718i	−0.963458	−	0.267859i	$-0.913684\pi$
$911$		−	16.1695i		−	0.535718i	0.963458	−	0.267859i	$-0.0863162\pi$
$912$		0			0
$913$	5.51584	+	3.18457i	0.182548	+	0.105394i
$914$	−7.30229	−	4.21598i	−0.241538	−	0.139452i
$915$		0			0
$916$		−	15.9603i		−	0.527344i
$917$	−2.41435	−	4.64713i	−0.0797289	−	0.153462i
$918$		0			0
$919$	−26.5159	−	45.9269i	−0.874680	−	1.51499i	−0.857104	−	0.515144i	$-0.827738\pi$
$919$	−26.5159	−	45.9269i	−0.874680	−	1.51499i	−0.0175762	−	0.999846i	$-0.505595\pi$
$920$	4.45647	−	7.71884i	0.146926	−	0.254482i
$921$		0			0
$922$	−8.09133	+	4.67153i	−0.266474	+	0.153849i
$923$	−1.59472			−0.0524909
$924$		0			0
$925$	−1.48228			−0.0487372
$926$	22.0458	−	12.7281i	0.724469	−	0.418272i
$927$		0			0
$928$	−0.923371	+	1.59933i	−0.0303112	+	0.0525005i
$929$	−1.47585	−	2.55624i	−0.0484209	−	0.0838675i	0.840799	−	0.541347i	$-0.182086\pi$
$929$	−1.47585	−	2.55624i	−0.0484209	−	0.0838675i	−0.889220	+	0.457480i	$0.848752\pi$
$930$		0			0
$931$	−18.1803	+	8.44170i	−0.595834	+	0.276666i
$932$			7.13153i			0.233601i
$933$		0			0
$934$	−17.8746	−	10.3199i	−0.584873	−	0.337677i
$935$	−14.5095	−	8.37704i	−0.474510	−	0.273958i
$936$		0			0
$937$			27.1986i			0.888540i	0.895893	+	0.444270i	$0.146537\pi$
$937$			27.1986i			0.888540i	−0.895893	+	0.444270i	$0.853463\pi$
$938$	0.599413	−	13.4778i	0.0195715	−	0.440067i
$939$		0			0
$940$	−7.76244	−	13.4449i	−0.253183	−	0.438526i
$941$	7.56366	−	13.1007i	0.246568	−	0.427069i	−0.716003	−	0.698097i	$-0.754030\pi$
$941$	7.56366	−	13.1007i	0.246568	−	0.427069i	0.962571	+	0.271028i	$0.0873637\pi$
$942$		0			0
$943$	−16.6098	+	9.58966i	−0.540889	+	0.312282i
$944$	1.94202			0.0632073
$945$		0			0
$946$	8.18124			0.265995
$947$	15.6804	−	9.05308i	0.509545	−	0.294186i	−0.223102	−	0.974795i	$-0.571618\pi$
$947$	15.6804	−	9.05308i	0.509545	−	0.294186i	0.732646	+	0.680609i	$0.238285\pi$
$948$		0			0
$949$	−23.2349	+	40.2440i	−0.754237	+	1.30638i
$950$	−0.296473	−	0.513506i	−0.00961884	−	0.0166603i
$951$		0			0
$952$	−14.9812	−	9.56116i	−0.485543	−	0.309879i
$953$			31.8552i			1.03189i	0.856621	+	0.515946i	$0.172559\pi$
$953$			31.8552i			1.03189i	−0.856621	+	0.515946i	$0.827441\pi$
$954$		0			0
$955$	50.9833	+	29.4352i	1.64978	+	0.952501i
$956$	13.6219	+	7.86462i	0.440565	+	0.254360i
$957$		0			0
$958$		−	6.14884i		−	0.198660i
$959$	7.38903	+	4.71577i	0.238604	+	0.152280i
$960$		0			0
$961$	−13.4564	−	23.3072i	−0.434079	−	0.751846i
$962$	−24.4440	+	42.3382i	−0.788105	+	1.36504i
$963$		0			0
$964$	−1.39292	+	0.804201i	−0.0448628	+	0.0259016i
$965$	21.1912			0.682167
$966$		0			0
$967$	−2.64610			−0.0850928			−0.0425464	−	0.999094i	$-0.513547\pi$
$967$	−2.64610			−0.0850928			−0.0425464	+	0.999094i	$0.513547\pi$
$968$	−8.49163	+	4.90265i	−0.272931	+	0.157577i
$969$		0			0
$970$	−5.45299	+	9.44486i	−0.175085	+	0.303256i
$971$	−17.9023	−	31.0077i	−0.574513	−	0.995086i	−0.996094	−	0.0882950i	$-0.971858\pi$
$971$	−17.9023	−	31.0077i	−0.574513	−	0.995086i	0.421581	−	0.906791i	$-0.361475\pi$
$972$		0			0
$973$	−0.408155	+	9.17739i	−0.0130849	+	0.294214i
$974$			19.7273i			0.632104i
$975$		0			0
$976$	1.15315	+	0.665771i	0.0369114	+	0.0213108i
$977$	3.83398	+	2.21355i	0.122660	+	0.0708178i	0.560075	−	0.828442i	$-0.310772\pi$
$977$	3.83398	+	2.21355i	0.122660	+	0.0708178i	−0.437415	+	0.899260i	$0.644106\pi$
$978$		0			0
$979$		−	19.6681i		−	0.628595i
$980$	15.9102	+	1.41799i	0.508234	+	0.0452960i
$981$		0			0
$982$	1.97994	+	3.42935i	0.0631823	+	0.109435i
$983$	−8.90634	+	15.4262i	−0.284068	+	0.492021i	−0.972383	−	0.233392i	$-0.925018\pi$
$983$	−8.90634	+	15.4262i	−0.284068	+	0.492021i	0.688315	+	0.725412i	$0.258351\pi$
$984$		0			0
$985$	11.5851	−	6.68868i	0.369133	−	0.213119i
$986$	12.4051			0.395058
$987$		0			0
$988$	−19.5562			−0.622166
$989$	25.3188	−	14.6178i	0.805091	−	0.464819i
$990$		0			0
$991$	7.62877	−	13.2134i	0.242336	−	0.419738i	−0.719043	−	0.694965i	$-0.755420\pi$
$991$	7.62877	−	13.2134i	0.242336	−	0.419738i	0.961379	+	0.275227i	$0.0887531\pi$
$992$	−1.01083	−	1.75081i	−0.0320940	−	0.0555884i
$993$		0			0
$994$	−0.284824	−	0.548227i	−0.00903406	−	0.0173887i
$995$		−	36.6560i		−	1.16207i
$996$		0			0
$997$	−35.7668	−	20.6500i	−1.13275	−	0.653991i	−0.188122	−	0.982146i	$-0.560240\pi$
$997$	−35.7668	−	20.6500i	−1.13275	−	0.653991i	−0.944624	+	0.328155i	$0.893573\pi$
$998$	31.8856	+	18.4092i	1.00932	+	0.582732i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.a.647.8		16
3.2	odd	2		1134.2.k.b.647.1		16
7.5	odd	6		1134.2.k.b.971.1		16
9.2	odd	6		126.2.t.a.59.5	yes	16
9.4	even	3		126.2.l.a.101.5	yes	16
9.5	odd	6		378.2.l.a.143.1		16
9.7	even	3		378.2.t.a.17.1		16
21.5	even	6	inner	1134.2.k.a.971.8		16
36.7	odd	6		3024.2.df.c.17.2		16
36.11	even	6		1008.2.df.c.689.8		16
36.23	even	6		3024.2.ca.c.2033.2		16
36.31	odd	6		1008.2.ca.c.353.6		16
63.2	odd	6		882.2.l.b.509.4		16
63.4	even	3		882.2.m.b.587.2		16
63.5	even	6		378.2.t.a.89.1		16
63.11	odd	6		882.2.m.a.293.3		16
63.13	odd	6		882.2.l.b.227.8		16
63.16	even	3		2646.2.l.a.1097.8		16
63.20	even	6		882.2.t.a.815.8		16
63.23	odd	6		2646.2.t.b.1979.4		16
63.25	even	3		2646.2.m.a.881.8		16
63.31	odd	6		882.2.m.a.587.3		16
63.32	odd	6		2646.2.m.b.1763.5		16
63.34	odd	6		2646.2.t.b.2285.4		16
63.38	even	6		882.2.m.b.293.2		16
63.40	odd	6		126.2.t.a.47.5	yes	16
63.41	even	6		2646.2.l.a.521.4		16
63.47	even	6		126.2.l.a.5.1	✓	16
63.52	odd	6		2646.2.m.b.881.5		16
63.58	even	3		882.2.t.a.803.8		16
63.59	even	6		2646.2.m.a.1763.8		16
63.61	odd	6		378.2.l.a.341.5		16
252.47	odd	6		1008.2.ca.c.257.6		16
252.103	even	6		1008.2.df.c.929.8		16
252.131	odd	6		3024.2.df.c.1601.2		16
252.187	even	6		3024.2.ca.c.2609.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.1	✓	16	63.47	even	6
126.2.l.a.101.5	yes	16	9.4	even	3
126.2.t.a.47.5	yes	16	63.40	odd	6
126.2.t.a.59.5	yes	16	9.2	odd	6
378.2.l.a.143.1		16	9.5	odd	6
378.2.l.a.341.5		16	63.61	odd	6
378.2.t.a.17.1		16	9.7	even	3
378.2.t.a.89.1		16	63.5	even	6
882.2.l.b.227.8		16	63.13	odd	6
882.2.l.b.509.4		16	63.2	odd	6
882.2.m.a.293.3		16	63.11	odd	6
882.2.m.a.587.3		16	63.31	odd	6
882.2.m.b.293.2		16	63.38	even	6
882.2.m.b.587.2		16	63.4	even	3
882.2.t.a.803.8		16	63.58	even	3
882.2.t.a.815.8		16	63.20	even	6
1008.2.ca.c.257.6		16	252.47	odd	6
1008.2.ca.c.353.6		16	36.31	odd	6
1008.2.df.c.689.8		16	36.11	even	6
1008.2.df.c.929.8		16	252.103	even	6
1134.2.k.a.647.8		16	1.1	even	1	trivial
1134.2.k.a.971.8		16	21.5	even	6	inner
1134.2.k.b.647.1		16	3.2	odd	2
1134.2.k.b.971.1		16	7.5	odd	6
2646.2.l.a.521.4		16	63.41	even	6
2646.2.l.a.1097.8		16	63.16	even	3
2646.2.m.a.881.8		16	63.25	even	3
2646.2.m.a.1763.8		16	63.59	even	6
2646.2.m.b.881.5		16	63.52	odd	6
2646.2.m.b.1763.5		16	63.32	odd	6
2646.2.t.b.1979.4		16	63.23	odd	6
2646.2.t.b.2285.4		16	63.34	odd	6
3024.2.ca.c.2033.2		16	36.23	even	6
3024.2.ca.c.2609.2		16	252.187	even	6
3024.2.df.c.17.2		16	36.7	odd	6
3024.2.df.c.1601.2		16	252.131	odd	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.14095 + 1.97618i) q^{5} +(-2.64314 - 0.117551i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.14095 + 1.97618i) q^{5} +(-2.64314 - 0.117551i) q^{7} -1.00000i q^{8} +(1.97618 + 1.14095i) q^{10} +(0.946590 + 0.546514i) q^{11} +6.82946i q^{13} +(-2.34780 + 1.21977i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.35863 + 5.81732i) q^{17} +(-2.47987 + 1.43175i) q^{19} +2.28190 q^{20} +1.09303 q^{22} +(3.38264 - 1.95297i) q^{23} +(-0.103535 + 0.179327i) q^{25} +(3.41473 + 5.91448i) q^{26} +(-1.42337 + 2.23025i) q^{28} -1.84674i q^{29} +(1.75081 + 1.01083i) q^{31} +(-0.866025 - 0.500000i) q^{32} +6.71727i q^{34} +(-2.78339 - 5.35745i) q^{35} +(3.57920 + 6.19935i) q^{37} +(-1.43175 + 2.47987i) q^{38} +(1.97618 - 1.14095i) q^{40} -4.91031 q^{41} +7.48493 q^{43} +(0.946590 - 0.546514i) q^{44} +(1.95297 - 3.38264i) q^{46} +(-3.40174 - 5.89199i) q^{47} +(6.97236 + 0.621407i) q^{49} +0.207069i q^{50} +(5.91448 + 3.41473i) q^{52} +(0.222069 + 0.128212i) q^{53} +2.49418i q^{55} +(-0.117551 + 2.64314i) q^{56} +(-0.923371 - 1.59933i) q^{58} +(-0.971009 + 1.68184i) q^{59} +(-1.15315 + 0.665771i) q^{61} +2.02166 q^{62} -1.00000 q^{64} +(-13.4963 + 7.79207i) q^{65} +(-2.54959 + 4.41602i) q^{67} +(3.35863 + 5.81732i) q^{68} +(-5.08921 - 3.24799i) q^{70} +0.233507i q^{71} +(5.89272 + 3.40216i) q^{73} +(6.19935 + 3.57920i) q^{74} +2.86351i q^{76} +(-2.43773 - 1.55578i) q^{77} +(3.63624 + 6.29816i) q^{79} +(1.14095 - 1.97618i) q^{80} +(-4.25245 + 2.45515i) q^{82} +5.82706 q^{83} -15.3281 q^{85} +(6.48214 - 3.74246i) q^{86} +(0.546514 - 0.946590i) q^{88} +(-8.99707 - 15.5834i) q^{89} +(0.802809 - 18.0512i) q^{91} -3.90593i q^{92} +(-5.89199 - 3.40174i) q^{94} +(-5.65882 - 3.26712i) q^{95} +4.77934i q^{97} +(6.34895 - 2.94803i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 4 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 4 * q^7	\( 16 q + 8 q^{4} - 4 q^{7} - 12 q^{11} - 8 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{31} + 30 q^{35} - 2 q^{37} + 12 q^{41} + 4 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} - 2 q^{49} + 6 q^{52} - 36 q^{53} - 6 q^{56} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{70} - 18 q^{74} + 24 q^{77} - 16 q^{79} + 24 q^{85} - 24 q^{86} - 24 q^{89} - 12 q^{91} - 66 q^{95} - 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 4 * q^7 - 12 * q^11 - 8 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^31 + 30 * q^35 - 2 * q^37 + 12 * q^41 + 4 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 - 2 * q^49 + 6 * q^52 - 36 * q^53 - 6 * q^56 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^70 - 18 * q^74 + 24 * q^77 - 16 * q^79 + 24 * q^85 - 24 * q^86 - 24 * q^89 - 12 * q^91 - 66 * q^95 - 24 * q^98

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