LMFDB - Embedded newform 378.2.t.a.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(17,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("378.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.t (of order $6$, degree $2$, not 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:	$3.01834519640$
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			89.1
Root			$1.73109 - 0.0577511i$ of defining polynomial
Character	$\chi$	$=$	378.89
Dual form			378.2.t.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -2.28190 q^{5} +(1.21977 - 2.34780i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -2.28190 q^{5} +(1.21977 - 2.34780i) q^{7} +1.00000i q^{8} +(1.97618 - 1.14095i) q^{10} +1.09303i q^{11} +(-5.91448 + 3.41473i) q^{13} +(0.117551 + 2.64314i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.35863 - 5.81732i) q^{17} +(-2.47987 - 1.43175i) q^{19} +(-1.14095 + 1.97618i) q^{20} +(-0.546514 - 0.946590i) q^{22} -3.90593i q^{23} +0.207069 q^{25} +(3.41473 - 5.91448i) q^{26} +(-1.42337 - 2.23025i) q^{28} +(-1.59933 - 0.923371i) q^{29} +(-1.75081 - 1.01083i) q^{31} +(0.866025 + 0.500000i) q^{32} +(5.81732 + 3.35863i) q^{34} +(-2.78339 + 5.35745i) q^{35} +(3.57920 - 6.19935i) q^{37} +2.86351 q^{38} -2.28190i q^{40} +(2.45515 + 4.25245i) q^{41} +(-3.74246 + 6.48214i) q^{43} +(0.946590 + 0.546514i) q^{44} +(1.95297 + 3.38264i) q^{46} +(-3.40174 - 5.89199i) q^{47} +(-4.02434 - 5.72754i) q^{49} +(-0.179327 + 0.103535i) q^{50} +6.82946i q^{52} +(0.222069 - 0.128212i) q^{53} -2.49418i q^{55} +(2.34780 + 1.21977i) q^{56} +1.84674 q^{58} +(-0.971009 + 1.68184i) q^{59} +(1.15315 - 0.665771i) q^{61} +2.02166 q^{62} -1.00000 q^{64} +(13.4963 - 7.79207i) q^{65} +(-2.54959 + 4.41602i) q^{67} -6.71727 q^{68} +(-0.268240 - 6.03138i) q^{70} -0.233507i q^{71} +(5.89272 - 3.40216i) q^{73} +7.15840i q^{74} +(-2.47987 + 1.43175i) q^{76} +(2.56621 + 1.33324i) q^{77} +(3.63624 + 6.29816i) q^{79} +(1.14095 + 1.97618i) q^{80} +(-4.25245 - 2.45515i) q^{82} +(-2.91353 + 5.04638i) q^{83} +(7.66407 + 13.2746i) q^{85} -7.48493i q^{86} -1.09303 q^{88} +(-8.99707 + 15.5834i) q^{89} +(0.802809 + 18.0512i) q^{91} +(-3.38264 - 1.95297i) q^{92} +(5.89199 + 3.40174i) q^{94} +(5.65882 + 3.26712i) q^{95} +(4.13903 + 2.38967i) q^{97} +(6.34895 + 2.94803i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 36 q^{53} - 12 q^{58} - 30 q^{59} - 60 q^{61} + 36 q^{62} - 16 q^{64} - 42 q^{65} + 14 q^{67} - 36 q^{68} + 18 q^{77} - 16 q^{79} - 12 q^{85} - 24 q^{89} - 12 q^{91} - 6 q^{92} + 66 q^{95} - 6 q^{97} - 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	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
$5$	−2.28190			−1.02050			−0.510248	−	0.860027i	$-0.670447\pi$
$5$	−2.28190			−1.02050			−0.510248	+	0.860027i	$0.670447\pi$
$6$		0			0
$7$	1.21977	−	2.34780i	0.461029	−	0.887385i
$7$	1.21977	−	2.34780i	0.461029	−	0.887385i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.97618	−	1.14095i	0.624924	−	0.360800i
$11$			1.09303i			0.329560i	0.986330	+	0.164780i	$0.0526915\pi$
$11$			1.09303i			0.329560i	−0.986330	+	0.164780i	$0.947309\pi$
$12$		0			0
$13$	−5.91448	+	3.41473i	−1.64038	+	0.947075i	−0.659685	+	0.751542i	$0.729310\pi$
$13$	−5.91448	+	3.41473i	−1.64038	+	0.947075i	−0.980697	+	0.195533i	$0.937356\pi$
$14$	0.117551	+	2.64314i	0.0314168	+	0.706409i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.35863	−	5.81732i	−0.814588	−	1.41091i	−0.909623	−	0.415434i	$-0.863630\pi$
$17$	−3.35863	−	5.81732i	−0.814588	−	1.41091i	0.0950352	−	0.995474i	$-0.469704\pi$
$18$		0			0
$19$	−2.47987	−	1.43175i	−0.568922	−	0.328467i	0.187797	−	0.982208i	$-0.439865\pi$
$19$	−2.47987	−	1.43175i	−0.568922	−	0.328467i	−0.756718	+	0.653741i	$0.773199\pi$
$20$	−1.14095	+	1.97618i	−0.255124	+	0.441888i
$21$		0			0
$22$	−0.546514	−	0.946590i	−0.116517	−	0.201814i
$23$		−	3.90593i		−	0.814443i	−0.913329	−	0.407221i	$-0.866498\pi$
$23$		−	3.90593i		−	0.814443i	0.913329	−	0.407221i	$-0.133502\pi$
$24$		0			0
$25$	0.207069			0.0414139
$26$	3.41473	−	5.91448i	0.669683	−	1.15993i
$27$		0			0
$28$	−1.42337	−	2.23025i	−0.268992	−	0.421478i
$29$	−1.59933	−	0.923371i	−0.296987	−	0.171466i	0.344101	−	0.938933i	$-0.388184\pi$
$29$	−1.59933	−	0.923371i	−0.296987	−	0.171466i	−0.641089	+	0.767467i	$0.721517\pi$
$30$		0			0
$31$	−1.75081	−	1.01083i	−0.314455	−	0.181551i	0.334463	−	0.942409i	$-0.391445\pi$
$31$	−1.75081	−	1.01083i	−0.314455	−	0.181551i	−0.648918	+	0.760858i	$0.724778\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	5.81732	+	3.35863i	0.997663	+	0.576001i
$35$	−2.78339	+	5.35745i	−0.470478	+	0.905574i
$36$		0			0
$37$	3.57920	−	6.19935i	0.588416	−	1.01917i	−0.406024	−	0.913863i	$-0.633085\pi$
$37$	3.57920	−	6.19935i	0.588416	−	1.01917i	0.994440	−	0.105305i	$-0.0335818\pi$
$38$	2.86351			0.464522
$39$		0			0
$40$		−	2.28190i		−	0.360800i
$41$	2.45515	+	4.25245i	0.383431	+	0.664121i	0.991550	−	0.129724i	$-0.0414092\pi$
$41$	2.45515	+	4.25245i	0.383431	+	0.664121i	−0.608120	+	0.793845i	$0.708076\pi$
$42$		0			0
$43$	−3.74246	+	6.48214i	−0.570721	+	0.988517i	0.425772	+	0.904831i	$0.360003\pi$
$43$	−3.74246	+	6.48214i	−0.570721	+	0.988517i	−0.996492	+	0.0836863i	$0.973331\pi$
$44$	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
$49$	−4.02434	−	5.72754i	−0.574905	−	0.818220i
$50$	−0.179327	+	0.103535i	−0.0253607	+	0.0146420i
$51$		0			0
$52$			6.82946i			0.947075i
$53$	0.222069	−	0.128212i	0.0305036	−	0.0176112i	−0.484671	−	0.874697i	$-0.661061\pi$
$53$	0.222069	−	0.128212i	0.0305036	−	0.0176112i	0.515174	+	0.857085i	$0.327727\pi$
$54$		0			0
$55$		−	2.49418i		−	0.336315i
$56$	2.34780	+	1.21977i	0.313738	+	0.162998i
$57$		0			0
$58$	1.84674			0.242489
$59$	−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	−0.424357	−	0.905495i	$-0.639500\pi$
$61$	1.15315	−	0.665771i	0.147646	−	0.0852432i	0.572003	+	0.820252i	$0.306167\pi$
$62$	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	$0.267492\pi$
$68$	−6.71727			−0.814588
$69$		0			0
$70$	−0.268240	−	6.03138i	−0.0320608	−	0.720888i
$71$		−	0.233507i		−	0.0277121i	−0.999904	−	0.0138561i	$-0.995589\pi$
$71$		−	0.233507i		−	0.0277121i	0.999904	−	0.0138561i	$-0.00441066\pi$
$72$		0			0
$73$	5.89272	−	3.40216i	0.689690	−	0.398193i	−0.113806	−	0.993503i	$-0.536304\pi$
$73$	5.89272	−	3.40216i	0.689690	−	0.398193i	0.803496	+	0.595310i	$0.202971\pi$
$74$			7.15840i			0.832147i
$75$		0			0
$76$	−2.47987	+	1.43175i	−0.284461	+	0.164233i
$77$	2.56621	+	1.33324i	0.292447	+	0.151937i
$78$		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
$83$	−2.91353	+	5.04638i	−0.319801	+	0.553912i	−0.980446	−	0.196786i	$-0.936950\pi$
$83$	−2.91353	+	5.04638i	−0.319801	+	0.553912i	0.660645	+	0.750698i	$0.270283\pi$
$84$		0			0
$85$	7.66407	+	13.2746i	0.831285	+	1.43983i
$86$		−	7.48493i		−	0.807121i
$87$		0			0
$88$	−1.09303			−0.116517
$89$	−8.99707	+	15.5834i	−0.953687	+	1.65184i	−0.216344	+	0.976317i	$0.569413\pi$
$89$	−8.99707	+	15.5834i	−0.953687	+	1.65184i	−0.737344	+	0.675518i	$0.763920\pi$
$90$		0			0
$91$	0.802809	+	18.0512i	0.0841573	+	1.89228i
$92$	−3.38264	−	1.95297i	−0.352664	−	0.203611i
$93$		0			0
$94$	5.89199	+	3.40174i	0.607713	+	0.350863i
$95$	5.65882	+	3.26712i	0.580583	+	0.335200i
$96$		0			0
$97$	4.13903	+	2.38967i	0.420255	+	0.242634i	0.695186	−	0.718830i	$-0.255322\pi$
$97$	4.13903	+	2.38967i	0.420255	+	0.242634i	−0.274931	+	0.961464i	$0.588655\pi$
$98$	6.34895	+	2.94803i	0.641341	+	0.297796i
$99$		0			0
$100$	0.103535	−	0.179327i	0.0103535	−	0.0179327i
$101$	10.4596			1.04077			0.520385	−	0.853932i	$-0.325788\pi$
$101$	10.4596			1.04077			0.520385	+	0.853932i	$0.325788\pi$
$102$		0			0
$103$		−	12.7477i		−	1.25607i	−0.778187	−	0.628033i	$-0.783860\pi$
$103$		−	12.7477i		−	1.25607i	0.778187	−	0.628033i	$-0.216140\pi$
$104$	−3.41473	−	5.91448i	−0.334842	−	0.579963i
$105$		0			0
$106$	−0.128212	+	0.222069i	−0.0124530	+	0.0215693i
$107$	8.25865	+	4.76813i	0.798394	+	0.460953i	0.842909	−	0.538056i	$-0.180841\pi$
$107$	8.25865	+	4.76813i	0.798394	+	0.460953i	−0.0445153	+	0.999009i	$0.514174\pi$
$108$		0			0
$109$	−2.88251	−	4.99266i	−0.276095	−	0.478210i	0.694316	−	0.719670i	$-0.255707\pi$
$109$	−2.88251	−	4.99266i	−0.276095	−	0.478210i	−0.970411	+	0.241460i	$0.922374\pi$
$110$	1.24709	+	2.16002i	0.118905	+	0.205950i
$111$		0			0
$112$	−2.64314	+	0.117551i	−0.249753	+	0.0111075i
$113$	10.3333	−	5.96592i	0.972073	−	0.561227i	0.0722053	−	0.997390i	$-0.476996\pi$
$113$	10.3333	−	5.96592i	0.972073	−	0.561227i	0.899868	+	0.436163i	$0.143663\pi$
$114$		0			0
$115$			8.91294i			0.831136i
$116$	−1.59933	+	0.923371i	−0.148494	+	0.0857329i
$117$		0			0
$118$		−	1.94202i		−	0.178777i
$119$	−17.7547	+	0.789621i	−1.62757	+	0.0723844i
$120$		0			0
$121$	9.80529			0.891390
$122$	−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
$131$	−1.97935			−0.172937			−0.0864684	−	0.996255i	$-0.527558\pi$
$131$	−1.97935			−0.172937			−0.0864684	+	0.996255i	$0.527558\pi$
$132$		0			0
$133$	−6.38634	+	4.07584i	−0.553766	+	0.353420i
$134$		−	5.09918i		−	0.440502i
$135$		0			0
$136$	5.81732	−	3.35863i	0.498831	−	0.288000i
$137$		−	3.31310i		−	0.283057i	−0.989934	−	0.141528i	$-0.954798\pi$
$137$		−	3.31310i		−	0.283057i	0.989934	−	0.141528i	$-0.0452017\pi$
$138$		0			0
$139$	3.00698	−	1.73608i	0.255048	−	0.147252i	−0.367025	−	0.930211i	$-0.619624\pi$
$139$	3.00698	−	1.73608i	0.255048	−	0.147252i	0.622074	+	0.782959i	$0.286290\pi$
$140$	3.24799	+	5.08921i	0.274505	+	0.430117i
$141$		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
$146$	−3.40216	+	5.89272i	−0.281565	+	0.487685i
$147$		0			0
$148$	−3.57920	−	6.19935i	−0.294208	−	0.509584i
$149$		−	13.3407i		−	1.09291i	−0.837487	−	0.546457i	$-0.815976\pi$
$149$		−	13.3407i		−	1.09291i	0.837487	−	0.546457i	$-0.184024\pi$
$150$		0			0
$151$	−5.33991			−0.434556			−0.217278	−	0.976110i	$-0.569718\pi$
$151$	−5.33991			−0.434556			−0.217278	+	0.976110i	$0.569718\pi$
$152$	1.43175	−	2.47987i	0.116131	−	0.201144i
$153$		0			0
$154$	−2.88902	+	0.128486i	−0.232804	+	0.0103537i
$155$	3.99518	+	2.30662i	0.320901	+	0.185272i
$156$		0			0
$157$	−15.3003	−	8.83364i	−1.22110	−	0.705002i	−0.255946	−	0.966691i	$-0.582387\pi$
$157$	−15.3003	−	8.83364i	−1.22110	−	0.705002i	−0.965152	+	0.261689i	$0.915720\pi$
$158$	−6.29816	−	3.63624i	−0.501054	−	0.289284i
$159$		0			0
$160$	−1.97618	−	1.14095i	−0.156231	−	0.0902000i
$161$	−9.17035	−	4.76433i	−0.722725	−	0.375481i
$162$		0			0
$163$	7.94915	−	13.7683i	0.622625	−	1.07842i	−0.366370	−	0.930469i	$-0.619400\pi$
$163$	7.94915	−	13.7683i	0.622625	−	1.07842i	0.988995	−	0.147949i	$-0.0472672\pi$
$164$	4.91031			0.383431
$165$		0			0
$166$		−	5.82706i		−	0.452268i
$167$	2.85878	+	4.95155i	0.221219	+	0.383163i	0.955178	−	0.296031i	$-0.0956631\pi$
$167$	2.85878	+	4.95155i	0.221219	+	0.383163i	−0.733959	+	0.679193i	$0.762330\pi$
$168$		0			0
$169$	16.8207	−	29.1344i	1.29390	−	2.24110i
$170$	−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
$175$	0.252577	−	0.486158i	0.0190930	−	0.0367501i
$176$	0.946590	−	0.546514i	0.0713519	−	0.0411950i
$177$		0			0
$178$		−	17.9941i		−	1.34872i
$179$	3.51582	−	2.02986i	0.262785	−	0.151719i	−0.362819	−	0.931859i	$-0.618186\pi$
$179$	3.51582	−	2.02986i	0.262785	−	0.151719i	0.625604	+	0.780141i	$0.284852\pi$
$180$		0			0
$181$		−	3.68452i		−	0.273869i	−0.990580	−	0.136934i	$-0.956275\pi$
$181$		−	3.68452i		−	0.273869i	0.990580	−	0.136934i	$-0.0437249\pi$
$182$	−9.72085	−	15.2314i	−0.720557	−	1.12903i
$183$		0			0
$184$	3.90593			0.287949
$185$	−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	$0.716480\pi$
$191$	−22.3425	+	12.8994i	−1.61664	+	0.933370i	−0.987780	+	0.155854i	$0.950187\pi$
$192$		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	$0.0581894\pi$
$194$	−4.77934			−0.343137
$195$		0			0
$196$	−6.97236	+	0.621407i	−0.498026	+	0.0443862i
$197$			5.86237i			0.417677i	0.977950	+	0.208838i	$0.0669683\pi$
$197$			5.86237i			0.417677i	−0.977950	+	0.208838i	$0.933032\pi$
$198$		0			0
$199$	−13.9117	+	8.03191i	−0.986173	+	0.569367i	−0.904128	−	0.427262i	$-0.859478\pi$
$199$	−13.9117	+	8.03191i	−0.986173	+	0.569367i	−0.0820447	+	0.996629i	$0.526145\pi$
$200$			0.207069i			0.0146420i
$201$		0			0
$202$	−9.05829	+	5.22981i	−0.637339	+	0.367968i
$203$	−4.11870	+	2.62860i	−0.289076	+	0.184492i
$204$		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
$209$	1.56495	−	2.71057i	0.108250	−	0.187494i
$210$		0			0
$211$	12.3741	+	21.4325i	0.851867	+	1.47548i	0.879522	+	0.475859i	$0.157863\pi$
$211$	12.3741	+	21.4325i	0.851867	+	1.47548i	−0.0276550	+	0.999618i	$0.508804\pi$
$212$		−	0.256424i		−	0.0176112i
$213$		0			0
$214$	−9.53627			−0.651886
$215$	8.53993	−	14.7916i	0.582419	−	1.00878i
$216$		0			0
$217$	−4.50882	+	2.87758i	−0.306078	+	0.195343i
$218$	4.99266	+	2.88251i	0.338146	+	0.195228i
$219$		0			0
$220$	−2.16002	−	1.24709i	−0.145629	−	0.0840788i
$221$	39.7291	+	22.9376i	2.67247	+	1.54295i
$222$		0			0
$223$	−3.20041	−	1.84776i	−0.214315	−	0.123735i	0.389000	−	0.921238i	$-0.372821\pi$
$223$	−3.20041	−	1.84776i	−0.214315	−	0.123735i	−0.603315	+	0.797503i	$0.706154\pi$
$224$	2.23025	−	1.42337i	0.149015	−	0.0951030i
$225$		0			0
$226$	−5.96592	+	10.3333i	−0.396847	+	0.687359i
$227$	−4.61097			−0.306041			−0.153020	−	0.988223i	$-0.548900\pi$
$227$	−4.61097			−0.306041			−0.153020	+	0.988223i	$0.548900\pi$
$228$		0			0
$229$		−	15.9603i		−	1.05469i	−0.849652	−	0.527344i	$-0.823188\pi$
$229$		−	15.9603i		−	1.05469i	0.849652	−	0.527344i	$-0.176812\pi$
$230$	−4.45647	−	7.71884i	−0.293851	−	0.508965i
$231$		0			0
$232$	0.923371	−	1.59933i	0.0606223	−	0.105001i
$233$	−6.17609	−	3.56577i	−0.404609	−	0.233601i	0.283862	−	0.958865i	$-0.408384\pi$
$233$	−6.17609	−	3.56577i	−0.404609	−	0.233601i	−0.688471	+	0.725264i	$0.741718\pi$
$234$		0			0
$235$	7.76244	+	13.4449i	0.506366	+	0.877051i
$236$	0.971009	+	1.68184i	0.0632073	+	0.109478i
$237$		0			0
$238$	14.9812	−	9.56116i	0.971086	−	0.619758i
$239$	−13.6219	+	7.86462i	−0.881129	+	0.508720i	−0.871031	−	0.491229i	$-0.836548\pi$
$239$	−13.6219	+	7.86462i	−0.881129	+	0.508720i	−0.0100987	+	0.999949i	$0.503215\pi$
$240$		0			0
$241$		−	1.60840i		−	0.103606i	−0.998657	−	0.0518031i	$-0.983503\pi$
$241$		−	1.60840i		−	0.103606i	0.998657	−	0.0518031i	$-0.0164968\pi$
$242$	−8.49163	+	4.90265i	−0.545863	+	0.315154i
$243$		0			0
$244$		−	1.33154i		−	0.0852432i
$245$	9.18313	+	13.0697i	0.586689	+	0.834991i
$246$		0			0
$247$	19.5562			1.24433
$248$	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
$257$	−17.4736			−1.08997			−0.544986	−	0.838445i	$-0.683465\pi$
$257$	−17.4736			−1.08997			−0.544986	+	0.838445i	$0.683465\pi$
$258$		0			0
$259$	−10.1891	−	15.9650i	−0.633117	−	0.992017i
$260$		−	15.5841i		−	0.966487i
$261$		0			0
$262$	1.71417	−	0.989677i	0.105902	−	0.0611424i
$263$		−	27.6144i		−	1.70278i	−0.524535	−	0.851389i	$-0.675761\pi$
$263$		−	27.6144i		−	1.70278i	0.524535	−	0.851389i	$-0.324239\pi$
$264$		0			0
$265$	−0.506740	+	0.292567i	−0.0311288	+	0.0179722i
$266$	3.49281	−	6.72295i	0.214158	−	0.412210i
$267$		0			0
$268$	2.54959	+	4.41602i	0.155741	+	0.269751i
$269$	−3.38607	−	5.86484i	−0.206452	−	0.357586i	0.744142	−	0.668021i	$-0.232858\pi$
$269$	−3.38607	−	5.86484i	−0.206452	−	0.357586i	−0.950594	+	0.310435i	$0.899525\pi$
$270$		0			0
$271$	7.23822	+	4.17899i	0.439691	+	0.253856i	0.703466	−	0.710729i	$-0.251635\pi$
$271$	7.23822	+	4.17899i	0.439691	+	0.253856i	−0.263776	+	0.964584i	$0.584968\pi$
$272$	−3.35863	+	5.81732i	−0.203647	+	0.352727i
$273$		0			0
$274$	1.65655	+	2.86923i	0.100076	+	0.173336i
$275$			0.226333i			0.0136484i
$276$		0			0
$277$	−16.2123			−0.974105			−0.487053	−	0.873373i	$-0.661928\pi$
$277$	−16.2123			−0.974105			−0.487053	+	0.873373i	$0.661928\pi$
$278$	−1.73608	+	3.00698i	−0.104123	+	0.180346i
$279$		0			0
$280$	−5.35745	−	2.78339i	−0.320169	−	0.166339i
$281$	25.3352	+	14.6273i	1.51137	+	0.872590i	0.999912	+	0.0132818i	$0.00422786\pi$
$281$	25.3352	+	14.6273i	1.51137	+	0.872590i	0.511458	+	0.859308i	$0.329105\pi$
$282$		0			0
$283$	1.24230	+	0.717242i	0.0738470	+	0.0426356i	0.536469	−	0.843920i	$-0.319758\pi$
$283$	1.24230	+	0.717242i	0.0738470	+	0.0426356i	−0.462622	+	0.886556i	$0.653091\pi$
$284$	−0.202223	−	0.116753i	−0.0119997	−	0.00692803i
$285$		0			0
$286$	6.46469	+	3.73239i	0.382265	+	0.220701i
$287$	12.9786	−	0.577211i	0.766104	−	0.0340717i
$288$		0			0
$289$	−14.0608	+	24.3541i	−0.827108	+	1.43259i
$290$	−4.21408			−0.247459
$291$		0			0
$292$		−	6.80432i		−	0.398193i
$293$	−10.8260	−	18.7511i	−0.632459	−	1.09545i	−0.987047	−	0.160429i	$-0.948712\pi$
$293$	−10.8260	−	18.7511i	−0.632459	−	1.09545i	0.354588	−	0.935023i	$-0.384621\pi$
$294$		0			0
$295$	2.21575	−	3.83779i	0.129006	−	0.223444i
$296$	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
$301$	10.6538	+	16.6933i	0.614077	+	0.962184i
$302$	4.62450	−	2.66995i	0.266110	−	0.153639i
$303$		0			0
$304$			2.86351i			0.164233i
$305$	−2.63137	+	1.51922i	−0.150672	+	0.0869904i
$306$		0			0
$307$		−	13.4732i		−	0.768957i	−0.923134	−	0.384479i	$-0.874381\pi$
$307$		−	13.4732i		−	0.768957i	0.923134	−	0.384479i	$-0.125619\pi$
$308$	2.43773	−	1.55578i	0.138902	−	0.0886491i
$309$		0			0
$310$	−4.61324			−0.262014
$311$	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	−0.950504	−	0.310712i	$-0.899433\pi$
$313$	−20.4636	+	11.8147i	−1.15667	+	0.667805i	−0.206167	+	0.978517i	$0.566099\pi$
$314$	17.6673			0.997023
$315$		0			0
$316$	7.27248			0.409109
$317$	0.760093	−	0.438840i	0.0426911	−	0.0246477i	−0.478503	−	0.878086i	$-0.658820\pi$
$317$	0.760093	−	0.438840i	0.0426911	−	0.0246477i	0.521194	+	0.853438i	$0.325487\pi$
$318$		0			0
$319$	1.00927	−	1.74811i	0.0565083	−	0.0978753i
$320$	2.28190			0.127562
$321$		0			0
$322$	10.3239	−	0.459146i	0.575329	−	0.0255872i
$323$			19.2349i			1.07026i
$324$		0			0
$325$	−1.22471	+	0.707086i	−0.0679346	+	0.0392221i
$326$			15.8983i			0.880525i
$327$		0			0
$328$	−4.25245	+	2.45515i	−0.234802	+	0.135563i
$329$	−17.9826	+	0.799756i	−0.991411	+	0.0440920i
$330$		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
$335$	5.81791	−	10.0769i	0.317866	−	0.550561i
$336$		0			0
$337$	0.757605	+	1.31221i	0.0412694	+	0.0714807i	0.885922	−	0.463834i	$-0.153526\pi$
$337$	0.757605	+	1.31221i	0.0412694	+	0.0714807i	−0.844653	+	0.535314i	$0.820193\pi$
$338$			33.6415i			1.82985i
$339$		0			0
$340$	15.3281			0.831285
$341$	1.10487	−	1.91369i	0.0598319	−	0.103632i
$342$		0			0
$343$	−18.3559	+	2.46207i	−0.991124	+	0.132939i
$344$	−6.48214	−	3.74246i	−0.349494	−	0.201780i
$345$		0			0
$346$	13.1681	+	7.60258i	0.707919	+	0.408717i
$347$	−31.2622	−	18.0492i	−1.67824	−	0.968934i	−0.962781	−	0.270281i	$-0.912883\pi$
$347$	−31.2622	−	18.0492i	−1.67824	−	0.968934i	−0.715461	−	0.698652i	$-0.753783\pi$
$348$		0			0
$349$	16.7962	+	9.69727i	0.899078	+	0.519083i	0.876901	−	0.480671i	$-0.159607\pi$
$349$	16.7962	+	9.69727i	0.899078	+	0.519083i	0.0221769	+	0.999754i	$0.492940\pi$
$350$	0.0243412	+	0.547313i	0.00130109	+	0.0292551i
$351$		0			0
$352$	−0.546514	+	0.946590i	−0.0291293	+	0.0504534i
$353$	−4.03818			−0.214931			−0.107465	−	0.994209i	$-0.534273\pi$
$353$	−4.03818			−0.214931			−0.107465	+	0.994209i	$0.534273\pi$
$354$		0			0
$355$			0.532839i			0.0282801i
$356$	8.99707	+	15.5834i	0.476844	+	0.825918i
$357$		0			0
$358$	−2.02986	+	3.51582i	−0.107281	+	0.185817i
$359$	21.2649	+	12.2773i	1.12232	+	0.647970i	0.941991	−	0.335637i	$-0.108952\pi$
$359$	21.2649	+	12.2773i	1.12232	+	0.647970i	0.180326	+	0.983607i	$0.442285\pi$
$360$		0			0
$361$	−5.40016	−	9.35335i	−0.284219	−	0.492282i
$362$	1.84226	+	3.19089i	0.0968272	+	0.167710i
$363$		0			0
$364$	16.0342	+	8.33035i	0.840420	+	0.436629i
$365$	−13.4466	+	7.76339i	−0.703827	+	0.406354i
$366$		0			0
$367$			7.25277i			0.378592i	0.981920	+	0.189296i	$0.0606205\pi$
$367$			7.25277i			0.378592i	−0.981920	+	0.189296i	$0.939379\pi$
$368$	−3.38264	+	1.95297i	−0.176332	+	0.101805i
$369$		0			0
$370$		−	16.3347i		−	0.849203i
$371$	−0.0301428	−	0.677763i	−0.00156494	−	0.0351877i
$372$		0			0
$373$	−29.7842			−1.54217			−0.771083	−	0.636735i	$-0.780285\pi$
$373$	−29.7842			−1.54217			−0.771083	+	0.636735i	$0.780285\pi$
$374$	−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
$383$	32.4903			1.66018			0.830088	−	0.557632i	$-0.188290\pi$
$383$	32.4903			1.66018			0.830088	+	0.557632i	$0.188290\pi$
$384$		0			0
$385$	−5.85584	−	3.04232i	−0.298441	−	0.155051i
$386$			9.28662i			0.472677i
$387$		0			0
$388$	4.13903	−	2.38967i	0.210127	−	0.121317i
$389$		−	2.08210i		−	0.105567i	−0.998606	−	0.0527834i	$-0.983191\pi$
$389$		−	2.08210i		−	0.105567i	0.998606	−	0.0527834i	$-0.0168093\pi$
$390$		0			0
$391$	−22.7221	+	13.1186i	−1.14910	+	0.663435i
$392$	5.72754	−	4.02434i	0.289284	−	0.203260i
$393$		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	0.851472	−	0.524400i	$-0.175710\pi$
$397$	16.3994	+	9.46822i	0.823064	+	0.475196i	−0.0284077	+	0.999596i	$0.509044\pi$
$398$	8.03191	−	13.9117i	0.402603	−	0.697329i
$399$		0			0
$400$	−0.103535	−	0.179327i	−0.00517674	−	0.00896637i
$401$			3.87654i			0.193585i	0.995305	+	0.0967926i	$0.0308584\pi$
$401$			3.87654i			0.193585i	−0.995305	+	0.0967926i	$0.969142\pi$
$402$		0			0
$403$	13.8069			0.687769
$404$	5.22981	−	9.05829i	0.260193	−	0.450667i
$405$		0			0
$406$	2.25260	−	4.33578i	0.111794	−	0.215181i
$407$	6.77606	+	3.91216i	0.335877	+	0.193919i
$408$		0			0
$409$	14.0286	+	8.09940i	0.693669	+	0.400490i	0.804985	−	0.593295i	$-0.202173\pi$
$409$	14.0286	+	8.09940i	0.693669	+	0.400490i	−0.111316	+	0.993785i	$0.535507\pi$
$410$	9.70367	+	5.60242i	0.479230	+	0.276684i
$411$		0			0
$412$	−11.0398	−	6.37383i	−0.543892	−	0.314016i
$413$	2.76421	+	4.33119i	0.136018	+	0.213124i
$414$		0			0
$415$	6.64838	−	11.5153i	0.326356	−	0.565266i
$416$	−6.82946			−0.334842
$417$		0			0
$418$			3.12989i			0.153088i
$419$	−1.63790	−	2.83692i	−0.0800165	−	0.138593i	0.823240	−	0.567693i	$-0.192164\pi$
$419$	−1.63790	−	2.83692i	−0.0800165	−	0.138593i	−0.903257	+	0.429100i	$0.858831\pi$
$420$		0			0
$421$	−0.844823	+	1.46328i	−0.0411741	+	0.0713157i	−0.885878	−	0.463918i	$-0.846443\pi$
$421$	−0.844823	+	1.46328i	−0.0411741	+	0.0713157i	0.844704	+	0.535234i	$0.179777\pi$
$422$	−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
$427$	−0.156524	−	3.51945i	−0.00757473	−	0.170318i
$428$	8.25865	−	4.76813i	0.399197	−	0.230476i
$429$		0			0
$430$			17.0799i			0.823664i
$431$	0.0157083	−	0.00906921i	0.000756644	−	0.000436848i	−0.499622	−	0.866244i	$-0.666528\pi$
$431$	0.0157083	−	0.00906921i	0.000756644	−	0.000436848i	0.500378	+	0.865807i	$0.333194\pi$
$432$		0			0
$433$			5.36964i			0.258048i	0.991641	+	0.129024i	$0.0411845\pi$
$433$			5.36964i			0.258048i	−0.991641	+	0.129024i	$0.958815\pi$
$434$	2.46596	−	4.74646i	0.118370	−	0.227838i
$435$		0			0
$436$	−5.76503			−0.276095
$437$	−5.59233	+	9.68621i	−0.267518	+	0.463354i
$438$		0			0
$439$	−18.9141	+	10.9201i	−0.902720	+	0.521186i	−0.878082	−	0.478511i	$-0.841177\pi$
$439$	−18.9141	+	10.9201i	−0.902720	+	0.521186i	−0.0246384	+	0.999696i	$0.507843\pi$
$440$	2.49418			0.118905
$441$		0			0
$442$	−45.8753			−2.18206
$443$	−1.81806	+	1.04966i	−0.0863785	+	0.0498707i	−0.542567	−	0.840012i	$-0.682548\pi$
$443$	−1.81806	+	1.04966i	−0.0863785	+	0.0498707i	0.456189	+	0.889883i	$0.349214\pi$
$444$		0			0
$445$	20.5304	−	35.5597i	0.973235	−	1.68569i
$446$	3.69551			0.174988
$447$		0			0
$448$	−1.21977	+	2.34780i	−0.0576286	+	0.110923i
$449$		−	27.1356i		−	1.28061i	−0.768122	−	0.640303i	$-0.778809\pi$
$449$		−	27.1356i		−	1.28061i	0.768122	−	0.640303i	$-0.221191\pi$
$450$		0			0
$451$	−4.64805	+	2.68355i	−0.218868	+	0.126364i
$452$		−	11.9318i		−	0.561227i
$453$		0			0
$454$	3.99322	−	2.30549i	0.187411	−	0.108202i
$455$	−1.83193	−	41.1910i	−0.0858822	−	1.93107i
$456$		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
$461$	4.67153	−	8.09133i	0.217575	−	0.376851i	−0.736491	−	0.676447i	$-0.763519\pi$
$461$	4.67153	−	8.09133i	0.217575	−	0.376851i	0.954066	+	0.299596i	$0.0968520\pi$
$462$		0			0
$463$	−12.7281	−	22.0458i	−0.591526	−	1.02455i	−0.994027	−	0.109134i	$-0.965192\pi$
$463$	−12.7281	−	22.0458i	−0.591526	−	1.02455i	0.402501	−	0.915420i	$-0.368141\pi$
$464$			1.84674i			0.0857329i
$465$		0			0
$466$	7.13153			0.330362
$467$	−10.3199	+	17.8746i	−0.477547	+	0.827136i	−0.999669	−	0.0257351i	$-0.991807\pi$
$467$	−10.3199	+	17.8746i	−0.477547	+	0.827136i	0.522122	+	0.852871i	$0.325141\pi$
$468$		0			0
$469$	7.25803	+	11.3724i	0.335145	+	0.525131i
$470$	−13.4449	−	7.76244i	−0.620169	−	0.358055i
$471$		0			0
$472$	−1.68184	−	0.971009i	−0.0774128	−	0.0446943i
$473$	−7.08516	−	4.09062i	−0.325776	−	0.188087i
$474$		0			0
$475$	−0.513506	−	0.296473i	−0.0235613	−	0.0136031i
$476$	−8.19350	+	15.7708i	−0.375548	+	0.722853i
$477$		0			0
$478$	7.86462	−	13.6219i	0.359720	−	0.623053i
$479$	−6.14884			−0.280948			−0.140474	−	0.990084i	$-0.544863\pi$
$479$	−6.14884			−0.280948			−0.140474	+	0.990084i	$0.544863\pi$
$480$		0			0
$481$			48.8879i			2.22910i
$482$	0.804201	+	1.39292i	0.0366303	+	0.0634456i
$483$		0			0
$484$	4.90265	−	8.49163i	0.222848	−	0.385983i
$485$	−9.44486	−	5.45299i	−0.428869	−	0.247608i
$486$		0			0
$487$	−9.86365	−	17.0843i	−0.446965	−	0.774166i	0.551222	−	0.834359i	$-0.314162\pi$
$487$	−9.86365	−	17.0843i	−0.446965	−	0.774166i	−0.998187	+	0.0601930i	$0.980828\pi$
$488$	0.665771	+	1.15315i	0.0301380	+	0.0522006i
$489$		0			0
$490$	−14.4877	−	6.72711i	−0.654486	−	0.303900i
$491$	−3.42935	+	1.97994i	−0.154764	+	0.0893533i	−0.575382	−	0.817885i	$-0.695147\pi$
$491$	−3.42935	+	1.97994i	−0.154764	+	0.0893533i	0.420618	+	0.907238i	$0.361813\pi$
$492$		0			0
$493$			12.4051i			0.558696i
$494$	−16.9362	+	9.77810i	−0.761994	+	0.439938i
$495$		0			0
$496$			2.02166i			0.0907754i
$497$	−0.548227	−	0.284824i	−0.0245913	−	0.0127761i
$498$		0			0
$499$	−36.8183			−1.64822			−0.824108	−	0.566433i	$-0.808323\pi$
$499$	−36.8183			−1.64822			−0.824108	+	0.566433i	$0.808323\pi$
$500$	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
$509$	15.0906			0.668877			0.334438	−	0.942418i	$-0.391453\pi$
$509$	15.0906			0.668877			0.334438	+	0.942418i	$0.391453\pi$
$510$		0			0
$511$	−0.799855	−	17.9848i	−0.0353835	−	0.795599i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	15.1326	−	8.73678i	0.667468	−	0.385363i
$515$			29.0889i			1.28181i
$516$		0			0
$517$	6.44011	−	3.71820i	0.283236	−	0.163526i
$518$	16.8065	+	8.73158i	0.738435	+	0.383643i
$519$		0			0
$520$	7.79207	+	13.4963i	0.341705	+	0.591850i
$521$	−12.4908	−	21.6347i	−0.547231	−	0.947832i	−0.998463	−	0.0554255i	$-0.982348\pi$
$521$	−12.4908	−	21.6347i	−0.547231	−	0.947832i	0.451232	−	0.892407i	$-0.350985\pi$
$522$		0			0
$523$	21.6818	+	12.5180i	0.948077	+	0.547372i	0.892483	−	0.451081i	$-0.148961\pi$
$523$	21.6818	+	12.5180i	0.948077	+	0.547372i	0.0555939	+	0.998453i	$0.482295\pi$
$524$	−0.989677	+	1.71417i	−0.0432342	+	0.0748839i
$525$		0			0
$526$	13.8072	+	23.9148i	0.602023	+	1.04273i
$527$			13.5801i			0.591556i
$528$		0			0
$529$	7.74371			0.336683
$530$	0.292567	−	0.506740i	0.0127083	−	0.0220114i
$531$		0			0
$532$	0.336608	+	7.56865i	0.0145938	+	0.328143i
$533$	−29.0419	−	16.7674i	−1.25795	−	0.726275i
$534$		0			0
$535$	−18.8454	−	10.8804i	−0.814759	−	0.470401i
$536$	−4.41602	−	2.54959i	−0.190743	−	0.110126i
$537$		0			0
$538$	5.86484	+	3.38607i	0.252851	+	0.145984i
$539$	6.26036	−	4.39871i	0.269653	−	0.189466i
$540$		0			0
$541$	7.23042	−	12.5235i	0.310860	−	0.538426i	−0.667689	−	0.744441i	$-0.732716\pi$
$541$	7.23042	−	12.5235i	0.310860	−	0.538426i	0.978549	+	0.206015i	$0.0660496\pi$
$542$	−8.35798			−0.359006
$543$		0			0
$544$		−	6.71727i		−	0.288000i
$545$	6.57761	+	11.3928i	0.281754	+	0.488012i
$546$		0			0
$547$	16.9160	−	29.2994i	0.723277	−	1.25275i	−0.236402	−	0.971655i	$-0.575968\pi$
$547$	16.9160	−	29.2994i	0.723277	−	1.25275i	0.959679	−	0.281098i	$-0.0906985\pi$
$548$	−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
$553$	19.2222	−	0.854888i	0.817410	−	0.0363535i
$554$	14.0403	−	8.10617i	0.596515	−	0.344398i
$555$		0			0
$556$		−	3.47216i		−	0.147252i
$557$	−5.09456	+	2.94134i	−0.215863	+	0.124629i	−0.604033	−	0.796959i	$-0.706441\pi$
$557$	−5.09456	+	2.94134i	−0.215863	+	0.124629i	0.388170	+	0.921588i	$0.373107\pi$
$558$		0			0
$559$		−	51.1180i		−	2.16206i
$560$	6.03138	−	0.268240i	0.254872	−	0.0113352i
$561$		0			0
$562$	−29.2545			−1.23403
$563$	−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	−0.893580	−	0.448905i	$-0.851814\pi$
$569$	−22.6993	+	13.1055i	−0.951606	+	0.549410i	−0.0580267	+	0.998315i	$0.518481\pi$
$570$		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	$0.986586\pi$
$572$	−7.46479			−0.312118
$573$		0			0
$574$	−10.9512	+	6.98919i	−0.457095	+	0.291723i
$575$		−	0.808799i		−	0.0337292i
$576$		0			0
$577$	28.0540	−	16.1970i	1.16790	−	0.674288i	0.214717	−	0.976676i	$-0.431117\pi$
$577$	28.0540	−	16.1970i	1.16790	−	0.674288i	0.953185	+	0.302388i	$0.0977839\pi$
$578$		−	28.1217i		−	1.16971i
$579$		0			0
$580$	3.64950	−	2.10704i	0.151537	−	0.0874901i
$581$	8.29407	+	12.9958i	0.344096	+	0.539157i
$582$		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
$587$	−4.76851	+	8.25931i	−0.196818	+	0.340898i	−0.947495	−	0.319771i	$-0.896394\pi$
$587$	−4.76851	+	8.25931i	−0.196818	+	0.340898i	0.750677	+	0.660669i	$0.229727\pi$
$588$		0			0
$589$	2.89453	+	5.01347i	0.119267	+	0.206576i
$590$			4.43149i			0.182442i
$591$		0			0
$592$	−7.15840			−0.294208
$593$	−1.89409	+	3.28065i	−0.0777808	+	0.134720i	−0.902292	−	0.431125i	$-0.858117\pi$
$593$	−1.89409	+	3.28065i	−0.0777808	+	0.134720i	0.824511	+	0.565845i	$0.191450\pi$
$594$		0			0
$595$	40.5144	−	1.80184i	1.66093	−	0.0738681i
$596$	−11.5534	−	6.67036i	−0.473246	−	0.273229i
$597$		0			0
$598$	−23.1016	−	13.3377i	−0.944693	−	0.545419i
$599$	−31.2971	−	18.0694i	−1.27876	−	0.738295i	−0.302143	−	0.953263i	$-0.597702\pi$
$599$	−31.2971	−	18.0694i	−1.27876	−	0.738295i	−0.976621	+	0.214968i	$0.931035\pi$
$600$		0			0
$601$	13.8275	+	7.98332i	0.564036	+	0.325646i	0.754764	−	0.655997i	$-0.227751\pi$
$601$	13.8275	+	7.98332i	0.564036	+	0.325646i	−0.190728	+	0.981643i	$0.561085\pi$
$602$	−17.5731	−	9.12987i	−0.716227	−	0.372106i
$603$		0			0
$604$	−2.66995	+	4.62450i	−0.108639	+	0.188168i
$605$	−22.3747			−0.909661
$606$		0			0
$607$		−	22.6540i		−	0.919498i	−0.888049	−	0.459749i	$-0.847939\pi$
$607$		−	22.6540i		−	0.919498i	0.888049	−	0.459749i	$-0.152061\pi$
$608$	−1.43175	−	2.47987i	−0.0580653	−	0.100572i
$609$		0			0
$610$	1.51922	−	2.63137i	0.0615115	−	0.106541i
$611$	40.2391	+	23.2321i	1.62790	+	0.939868i
$612$		0			0
$613$	−1.84758	−	3.20011i	−0.0746232	−	0.129251i	0.826299	−	0.563231i	$-0.190442\pi$
$613$	−1.84758	−	3.20011i	−0.0746232	−	0.129251i	−0.900922	+	0.433980i	$0.857109\pi$
$614$	6.73661	+	11.6682i	0.271868	+	0.470888i
$615$		0			0
$616$	−1.33324	+	2.56621i	−0.0537178	+	0.103396i
$617$	−22.5187	+	13.0011i	−0.906567	+	0.523407i	−0.879325	−	0.476222i	$-0.842006\pi$
$617$	−22.5187	+	13.0011i	−0.906567	+	0.523407i	−0.0272418	+	0.999629i	$0.508672\pi$
$618$		0			0
$619$		−	23.7321i		−	0.953873i	−0.878938	−	0.476937i	$-0.841747\pi$
$619$		−	23.7321i		−	0.953873i	0.878938	−	0.476937i	$-0.158253\pi$
$620$	3.99518	−	2.30662i	0.160450	−	0.0926360i
$621$		0			0
$622$			28.7338i			1.15212i
$623$	25.6123	+	40.1314i	1.02614	+	1.60783i
$624$		0			0
$625$	−25.9925			−1.03970
$626$	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
$635$	24.9031			0.988249
$636$		0			0
$637$	43.3599	+	20.1334i	1.71798	+	0.797715i
$638$			2.01854i			0.0799148i
$639$		0			0
$640$	−1.97618	+	1.14095i	−0.0781155	+	0.0451000i
$641$		−	8.40006i		−	0.331782i	−0.986144	−	0.165891i	$-0.946950\pi$
$641$		−	8.40006i		−	0.331782i	0.986144	−	0.165891i	$-0.0530500\pi$
$642$		0			0
$643$	0.237974	−	0.137394i	0.00938478	−	0.00541831i	−0.495300	−	0.868722i	$-0.664942\pi$
$643$	0.237974	−	0.137394i	0.00938478	−	0.00541831i	0.504685	+	0.863304i	$0.331609\pi$
$644$	−8.71120	+	5.55959i	−0.343269	+	0.219079i
$645$		0			0
$646$	−9.61747	−	16.6580i	−0.378394	−	0.655398i
$647$	17.0508	+	29.5328i	0.670335	+	1.16105i	0.977809	+	0.209498i	$0.0671829\pi$
$647$	17.0508	+	29.5328i	0.670335	+	1.16105i	−0.307474	+	0.951556i	$0.599484\pi$
$648$		0			0
$649$	−1.83830	−	1.06134i	−0.0721594	−	0.0416612i
$650$	0.707086	−	1.22471i	0.0277342	−	0.0480370i
$651$		0			0
$652$	−7.94915	−	13.7683i	−0.311313	−	0.539209i
$653$		−	1.71306i		−	0.0670373i	−0.999438	−	0.0335187i	$-0.989329\pi$
$653$		−	1.71306i		−	0.0670373i	0.999438	−	0.0335187i	$-0.0106713\pi$
$654$		0			0
$655$	4.51669			0.176482
$656$	2.45515	−	4.25245i	0.0958576	−	0.166030i
$657$		0			0
$658$	15.1735	−	9.68389i	0.591524	−	0.377517i
$659$	−30.0556	−	17.3526i	−1.17080	−	0.675961i	−0.216930	−	0.976187i	$-0.569604\pi$
$659$	−30.0556	−	17.3526i	−1.17080	−	0.675961i	−0.953868	+	0.300226i	$0.902938\pi$
$660$		0			0
$661$	−33.2075	−	19.1724i	−1.29162	−	0.745718i	−0.312681	−	0.949858i	$-0.601227\pi$
$661$	−33.2075	−	19.1724i	−1.29162	−	0.745718i	−0.978942	+	0.204140i	$0.934560\pi$
$662$	−17.4790	−	10.0915i	−0.679341	−	0.392218i
$663$		0			0
$664$	−5.04638	−	2.91353i	−0.195838	−	0.113067i
$665$	14.5730	−	9.30065i	0.565116	−	0.360664i
$666$		0			0
$667$	−3.60662	+	6.24686i	−0.139649	+	0.241879i
$668$	5.71756			0.221219
$669$		0			0
$670$			11.6358i			0.449531i
$671$	0.727706	+	1.26042i	0.0280928	+	0.0486581i
$672$		0			0
$673$	−8.33538	+	14.4373i	−0.321305	+	0.556517i	−0.980758	−	0.195229i	$-0.937455\pi$
$673$	−8.33538	+	14.4373i	−0.321305	+	0.556517i	0.659452	+	0.751746i	$0.270788\pi$
$674$	−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
$679$	10.6591	−	6.80278i	0.409060	−	0.261067i
$680$	−13.2746	+	7.66407i	−0.509056	+	0.293903i
$681$		0			0
$682$			2.20974i			0.0846151i
$683$	6.62003	−	3.82208i	0.253308	−	0.146248i	−0.367970	−	0.929838i	$-0.619947\pi$
$683$	6.62003	−	3.82208i	0.253308	−	0.146248i	0.621278	+	0.783590i	$0.286614\pi$
$684$		0			0
$685$			7.56016i			0.288859i
$686$	14.6656	−	11.3102i	0.559936	−	0.431824i
$687$		0			0
$688$	7.48493			0.285360
$689$	−0.875617	+	1.51661i	−0.0333583	+	0.0577783i
$690$		0			0
$691$	9.10461	−	5.25655i	0.346356	−	0.199969i	−0.316723	−	0.948518i	$-0.602583\pi$
$691$	9.10461	−	5.25655i	0.346356	−	0.199969i	0.663079	+	0.748549i	$0.269249\pi$
$692$	−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
$698$	−19.3945			−0.734094
$699$		0			0
$700$	−0.294737	−	0.461817i	−0.0111400	−	0.0174550i
$701$		−	15.7336i		−	0.594250i	−0.954839	−	0.297125i	$-0.903972\pi$
$701$		−	15.7336i		−	0.594250i	0.954839	−	0.297125i	$-0.0960277\pi$
$702$		0			0
$703$	−17.7519	+	10.2491i	−0.669526	+	0.386551i
$704$		−	1.09303i		−	0.0411950i
$705$		0			0
$706$	3.49717	−	2.01909i	0.131618	−	0.0759895i
$707$	12.7583	−	24.5571i	0.479825	−	0.923565i
$708$		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
$713$	−3.94824	+	6.83855i	−0.147863	+	0.256106i
$714$		0			0
$715$	8.51695	+	14.7518i	0.318516	+	0.551686i
$716$		−	4.05972i		−	0.151719i
$717$		0			0
$718$	−24.5546			−0.916368
$719$	20.5644	−	35.6186i	0.766924	−	1.32835i	−0.172299	−	0.985045i	$-0.555120\pi$
$719$	20.5644	−	35.6186i	0.766924	−	1.32835i	0.939223	−	0.343307i	$-0.111547\pi$
$720$		0			0
$721$	−29.9290	−	15.5492i	−1.11461	−	0.579082i
$722$	9.35335	+	5.40016i	0.348096	+	0.200973i
$723$		0			0
$724$	−3.19089	−	1.84226i	−0.118589	−	0.0684671i
$725$	−0.331172	−	0.191202i	−0.0122994	−	0.00710106i
$726$		0			0
$727$	33.6212	+	19.4112i	1.24694	+	0.719921i	0.970498	−	0.241109i	$-0.0775112\pi$
$727$	33.6212	+	19.4112i	1.24694	+	0.719921i	0.276442	+	0.961031i	$0.410845\pi$
$728$	−18.0512	+	0.802809i	−0.669022	+	0.0297541i
$729$		0			0
$730$	7.76339	−	13.4466i	0.287336	−	0.497681i
$731$	50.2783			1.85961
$732$		0			0
$733$			26.0226i			0.961166i	0.876949	+	0.480583i	$0.159575\pi$
$733$			26.0226i			0.961166i	−0.876949	+	0.480583i	$0.840425\pi$
$734$	−3.62639	−	6.28109i	−0.133852	−	0.231839i
$735$		0			0
$736$	1.95297	−	3.38264i	0.0719873	−	0.124686i
$737$	−4.82683	−	2.78677i	−0.177799	−	0.102652i
$738$		0			0
$739$	−3.70004	−	6.40866i	−0.136108	−	0.235746i	0.789912	−	0.613220i	$-0.210126\pi$
$739$	−3.70004	−	6.40866i	−0.136108	−	0.235746i	−0.926020	+	0.377474i	$0.876793\pi$
$740$	8.16737	+	14.1463i	0.300239	+	0.520028i
$741$		0			0
$742$	0.364986	+	0.571889i	0.0133991	+	0.0209947i
$743$	24.3241	−	14.0435i	0.892366	−	0.515208i	0.0176504	−	0.999844i	$-0.494381\pi$
$743$	24.3241	−	14.0435i	0.892366	−	0.515208i	0.874716	+	0.484636i	$0.161048\pi$
$744$		0			0
$745$			30.4422i			1.11532i
$746$	25.7939	−	14.8921i	0.944380	−	0.545238i
$747$		0			0
$748$		−	7.34216i		−	0.268456i
$749$	21.2683	−	13.5737i	0.777125	−	0.495971i
$750$		0			0
$751$	42.3793			1.54644			0.773221	−	0.634136i	$-0.218644\pi$
$751$	42.3793			1.54644			0.773221	+	0.634136i	$0.218644\pi$
$752$	−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
$761$	34.9645			1.26746			0.633732	−	0.773553i	$-0.281522\pi$
$761$	34.9645			1.26746			0.633732	+	0.773553i	$0.281522\pi$
$762$		0			0
$763$	−15.2378	+	0.677684i	−0.551644	+	0.0245338i
$764$			25.7989i			0.933370i
$765$		0			0
$766$	−28.1374	+	16.2451i	−1.01665	+	0.586961i
$767$		−	13.2629i		−	0.478897i
$768$		0			0
$769$	−18.9307	+	10.9296i	−0.682658	+	0.394133i	−0.800856	−	0.598857i	$-0.795622\pi$
$769$	−18.9307	+	10.9296i	−0.682658	+	0.394133i	0.118198	+	0.992990i	$0.462288\pi$
$770$	6.59247	−	0.293193i	0.237576	−	0.0105660i
$771$		0			0
$772$	−4.64331	−	8.04245i	−0.167116	−	0.289454i
$773$	10.6368	+	18.4235i	0.382579	+	0.662646i	0.991430	−	0.130638i	$-0.0417026\pi$
$773$	10.6368	+	18.4235i	0.382579	+	0.662646i	−0.608851	+	0.793285i	$0.708369\pi$
$774$		0			0
$775$	−0.362540	−	0.209312i	−0.0130228	−	0.00751872i
$776$	−2.38967	+	4.13903i	−0.0857842	+	0.148583i
$777$		0			0
$778$	1.04105	+	1.80316i	0.0373235	+	0.0646463i
$779$		−	14.0607i		−	0.503777i
$780$		0			0
$781$	0.255229			0.00913282
$782$	13.1186	−	22.7221i	0.469120	−	0.812539i
$783$		0			0
$784$	−2.94803	+	6.34895i	−0.105287	+	0.226748i
$785$	34.9138	+	20.1575i	1.24613	+	0.719452i
$786$		0			0
$787$	40.7238	+	23.5119i	1.45165	+	0.838108i	0.998575	−	0.0533671i	$-0.0169954\pi$
$787$	40.7238	+	23.5119i	1.45165	+	0.838108i	0.453070	+	0.891475i	$0.350329\pi$
$788$	5.07696	+	2.93119i	0.180859	+	0.104419i
$789$		0			0
$790$	14.3718	+	8.29754i	0.511325	+	0.295213i
$791$	−1.40260	−	31.5375i	−0.0498707	−	1.12134i
$792$		0			0
$793$	−4.54685	+	7.87538i	−0.161463	+	0.279663i
$794$	−18.9364			−0.672029
$795$		0			0
$796$			16.0638i			0.569367i
$797$	14.5203	+	25.1499i	0.514336	+	0.890856i	0.999862	+	0.0166334i	$0.00529483\pi$
$797$	14.5203	+	25.1499i	0.514336	+	0.890856i	−0.485526	+	0.874222i	$0.661372\pi$
$798$		0			0
$799$	−22.8504	+	39.5781i	−0.808390	+	1.40017i
$800$	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
$805$	20.9258	+	10.8717i	0.737538	+	0.383178i
$806$	−11.9571	+	6.90343i	−0.421171	+	0.243163i
$807$		0			0
$808$			10.4596i			0.367968i
$809$	47.5777	−	27.4690i	1.67274	−	0.965759i	0.706650	−	0.707563i	$-0.250205\pi$
$809$	47.5777	−	27.4690i	1.67274	−	0.965759i	0.966093	−	0.258195i	$-0.0831279\pi$
$810$		0			0
$811$			34.0190i			1.19457i	0.802030	+	0.597284i	$0.203754\pi$
$811$			34.0190i			1.19457i	−0.802030	+	0.597284i	$0.796246\pi$
$812$	0.217086	+	4.88120i	0.00761824	+	0.171296i
$813$		0			0
$814$	−7.82433			−0.274242
$815$	−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	−0.374187	−	0.927353i	$-0.622078\pi$
$821$	6.92921	−	4.00058i	0.241831	−	0.139621i	0.616018	+	0.787732i	$0.288745\pi$
$822$		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	$0.205737\pi$
$824$	12.7477			0.444086
$825$		0			0
$826$	−4.55947	−	2.36881i	−0.158644	−	0.0824215i
$827$			37.4952i			1.30384i	0.758290	+	0.651918i	$0.226035\pi$
$827$			37.4952i			1.30384i	−0.758290	+	0.651918i	$0.773965\pi$
$828$		0			0
$829$	−2.96310	+	1.71074i	−0.102913	+	0.0594166i	−0.550573	−	0.834787i	$-0.685591\pi$
$829$	−2.96310	+	1.71074i	−0.102913	+	0.0594166i	0.447660	+	0.894204i	$0.352257\pi$
$830$			13.2968i			0.461538i
$831$		0			0
$832$	5.91448	−	3.41473i	0.205048	−	0.118384i
$833$	−19.8027	+	42.6476i	−0.686122	+	1.47765i
$834$		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
$839$	4.87530	−	8.44428i	0.168314	−	0.291529i	−0.769513	−	0.638631i	$-0.779501\pi$
$839$	4.87530	−	8.44428i	0.168314	−	0.291529i	0.937827	+	0.347102i	$0.112834\pi$
$840$		0			0
$841$	−12.7948	−	22.1612i	−0.441199	−	0.764179i
$842$		−	1.68965i		−	0.0582290i
$843$		0			0
$844$	24.7482			0.851867
$845$	−38.3832	+	66.4817i	−1.32042	+	2.28704i
$846$		0			0
$847$	11.9602	−	23.0209i	0.410956	−	0.791006i
$848$	−0.222069	−	0.128212i	−0.00762589	−	0.00440281i
$849$		0			0
$850$	1.20459	+	0.695470i	0.0413171	+	0.0238544i
$851$	−24.2142	−	13.9801i	−0.830053	−	0.479232i
$852$		0			0
$853$	21.2846	+	12.2887i	0.728771	+	0.420756i	0.817972	−	0.575258i	$-0.195098\pi$
$853$	21.2846	+	12.2887i	0.728771	+	0.420756i	−0.0892016	+	0.996014i	$0.528432\pi$
$854$	1.89528	+	2.96967i	0.0648551	+	0.101620i
$855$		0			0
$856$	−4.76813	+	8.25865i	−0.162971	+	0.282275i
$857$	29.9367			1.02262			0.511309	−	0.859397i	$-0.329161\pi$
$857$	29.9367			1.02262			0.511309	+	0.859397i	$0.329161\pi$
$858$		0			0
$859$		−	53.8556i		−	1.83753i	−0.394805	−	0.918765i	$-0.629188\pi$
$859$		−	53.8556i		−	1.83753i	0.394805	−	0.918765i	$-0.370812\pi$
$860$	−8.53993	−	14.7916i	−0.291209	−	0.504389i
$861$		0			0
$862$	−0.00906921	+	0.0157083i	−0.000308899	+	0.000535028i
$863$	−42.6599	−	24.6297i	−1.45216	−	0.838404i	−0.453555	−	0.891228i	$-0.649844\pi$
$863$	−42.6599	−	24.6297i	−1.45216	−	0.838404i	−0.998604	+	0.0528239i	$0.983178\pi$
$864$		0			0
$865$	17.3483	+	30.0482i	0.589861	+	1.02167i
$866$	−2.68482	−	4.65025i	−0.0912339	−	0.158022i
$867$		0			0
$868$	0.237649	+	5.34354i	0.00806632	+	0.181372i
$869$	−6.88406	+	3.97451i	−0.233526	+	0.134826i
$870$		0			0
$871$		−	34.8246i		−	1.17999i
$872$	4.99266	−	2.88251i	0.169073	−	0.0976142i
$873$		0			0
$874$		−	11.1847i		−	0.378327i
$875$	13.3406	−	25.6779i	0.450994	−	0.868071i
$876$		0			0
$877$	19.6076			0.662103			0.331051	−	0.943613i	$-0.392597\pi$
$877$	19.6076			0.662103			0.331051	+	0.943613i	$0.392597\pi$
$878$	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
$887$	−5.87359			−0.197216			−0.0986079	−	0.995126i	$-0.531439\pi$
$887$	−5.87359			−0.197216			−0.0986079	+	0.995126i	$0.531439\pi$
$888$		0			0
$889$	−13.3117	+	25.6223i	−0.446460	+	0.859344i
$890$			41.0608i			1.37636i
$891$		0			0
$892$	−3.20041	+	1.84776i	−0.107158	+	0.0618675i
$893$			19.4818i			0.651935i
$894$		0			0
$895$	−8.02276	+	4.63194i	−0.268171	+	0.154829i
$896$	−0.117551	−	2.64314i	−0.00392710	−	0.0883011i
$897$		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
$902$	2.68355	−	4.64805i	0.0893525	−	0.154763i
$903$		0			0
$904$	5.96592	+	10.3333i	0.198424	+	0.343680i
$905$			8.40772i			0.279482i
$906$		0			0
$907$	−49.2610			−1.63568			−0.817842	−	0.575443i	$-0.804830\pi$
$907$	−49.2610			−1.63568			−0.817842	+	0.575443i	$0.804830\pi$
$908$	−2.30549	+	3.99322i	−0.0765102	+	0.132520i
$909$		0			0
$910$	22.1820	+	34.7565i	0.735327	+	1.15217i
$911$	−14.0032	−	8.08474i	−0.463946	−	0.267859i	0.249756	−	0.968309i	$-0.419650\pi$
$911$	−14.0032	−	8.08474i	−0.463946	−	0.267859i	−0.713702	+	0.700450i	$0.752983\pi$
$912$		0			0
$913$	−5.51584	−	3.18457i	−0.182548	−	0.105394i
$914$	7.30229	+	4.21598i	0.241538	+	0.139452i
$915$		0			0
$916$	−13.8220	−	7.98016i	−0.456693	−	0.263672i
$917$	−2.41435	+	4.64713i	−0.0797289	+	0.153462i
$918$		0			0
$919$	−26.5159	+	45.9269i	−0.874680	+	1.51499i	−0.0175762	+	0.999846i	$0.505595\pi$
$919$	−26.5159	+	45.9269i	−0.874680	+	1.51499i	−0.857104	+	0.515144i	$0.827738\pi$
$920$	−8.91294			−0.293851
$921$		0			0
$922$			9.34306i			0.307697i
$923$	0.797361	+	1.38107i	0.0262455	+	0.0454585i
$924$		0			0
$925$	0.741142	−	1.28370i	0.0243686	−	0.0422077i
$926$	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
$931$	1.77940	+	19.9654i	0.0583176	+	0.654340i
$932$	−6.17609	+	3.56577i	−0.202305	+	0.116801i
$933$		0			0
$934$		−	20.6398i		−	0.675354i
$935$	−14.5095	+	8.37704i	−0.474510	+	0.273958i
$936$		0			0
$937$		−	27.1986i		−	0.888540i	−0.895893	−	0.444270i	$-0.853463\pi$
$937$		−	27.1986i		−	0.888540i	0.895893	−	0.444270i	$-0.146537\pi$
$938$	−11.9719	−	6.21981i	−0.390895	−	0.203084i
$939$		0			0
$940$	15.5249			0.506366
$941$	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	−0.732646	−	0.680609i	$-0.761715\pi$
$947$	−15.6804	+	9.05308i	−0.509545	+	0.294186i	0.223102	+	0.974795i	$0.428382\pi$
$948$		0			0
$949$	−23.2349	+	40.2440i	−0.754237	+	1.30638i
$950$	0.592945			0.0192377
$951$		0			0
$952$	−0.789621	−	17.7547i	−0.0255918	−	0.575432i
$953$		−	31.8552i		−	1.03189i	−0.856621	−	0.515946i	$-0.827441\pi$
$953$		−	31.8552i		−	1.03189i	0.856621	−	0.515946i	$-0.172559\pi$
$954$		0			0
$955$	50.9833	−	29.4352i	1.64978	−	0.952501i
$956$			15.7292i			0.508720i
$957$		0			0
$958$	5.32505	−	3.07442i	0.172045	−	0.0993300i
$959$	−7.77849	−	4.04121i	−0.251181	−	0.130497i
$960$		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
$965$	−10.5956	+	18.3521i	−0.341084	+	0.590774i
$966$		0			0
$967$	1.32305	+	2.29159i	0.0425464	+	0.0736925i	0.886514	−	0.462701i	$-0.153120\pi$
$967$	1.32305	+	2.29159i	0.0425464	+	0.0736925i	−0.843968	+	0.536393i	$0.819786\pi$
$968$			9.80529i			0.315154i
$969$		0			0
$970$	10.9060			0.350170
$971$	−17.9023	+	31.0077i	−0.574513	+	0.995086i	0.421581	+	0.906791i	$0.361475\pi$
$971$	−17.9023	+	31.0077i	−0.574513	+	0.995086i	−0.996094	+	0.0882950i	$0.971858\pi$
$972$		0			0
$973$	−0.408155	−	9.17739i	−0.0130849	−	0.294214i
$974$	17.0843	+	9.86365i	0.547418	+	0.316052i
$975$		0			0
$976$	−1.15315	−	0.665771i	−0.0369114	−	0.0213108i
$977$	−3.83398	−	2.21355i	−0.122660	−	0.0708178i	0.437415	−	0.899260i	$-0.355894\pi$
$977$	−3.83398	−	2.21355i	−0.122660	−	0.0708178i	−0.560075	+	0.828442i	$0.689228\pi$
$978$		0			0
$979$	−17.0331	−	9.83405i	−0.544379	−	0.314298i
$980$	15.9102	−	1.41799i	0.508234	−	0.0452960i
$981$		0			0
$982$	1.97994	−	3.42935i	0.0631823	−	0.109435i
$983$	17.8127			0.568137			0.284068	−	0.958804i	$-0.408316\pi$
$983$	17.8127			0.568137			0.284068	+	0.958804i	$0.408316\pi$
$984$		0			0
$985$		−	13.3774i		−	0.426238i
$986$	−6.20253	−	10.7431i	−0.197529	−	0.342130i
$987$		0			0
$988$	9.77810	−	16.9362i	0.311083	−	0.538811i
$989$	25.3188	+	14.6178i	0.805091	+	0.464819i
$990$		0			0
$991$	7.62877	+	13.2134i	0.242336	+	0.419738i	0.961379	−	0.275227i	$-0.0887531\pi$
$991$	7.62877	+	13.2134i	0.242336	+	0.419738i	−0.719043	+	0.694965i	$0.755420\pi$
$992$	−1.01083	−	1.75081i	−0.0320940	−	0.0555884i
$993$		0			0
$994$	0.617190	−	0.0274489i	0.0195761	−	0.000870627i
$995$	31.7451	−	18.3280i	1.00639	−	0.581037i
$996$		0			0
$997$		−	41.2999i		−	1.30798i	−0.756502	−	0.653991i	$-0.773093\pi$
$997$		−	41.2999i		−	1.30798i	0.756502	−	0.653991i	$-0.226907\pi$
$998$	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	378.2.t.a.89.1		16
3.2	odd	2		126.2.t.a.47.5	yes	16
4.3	odd	2		3024.2.df.c.1601.2		16
7.2	even	3		2646.2.m.a.1763.8		16
7.3	odd	6		378.2.l.a.143.1		16
7.4	even	3		2646.2.l.a.521.4		16
7.5	odd	6		2646.2.m.b.1763.5		16
7.6	odd	2		2646.2.t.b.1979.4		16
9.2	odd	6		1134.2.k.b.971.1		16
9.4	even	3		126.2.l.a.5.1	✓	16
9.5	odd	6		378.2.l.a.341.5		16
9.7	even	3		1134.2.k.a.971.8		16
12.11	even	2		1008.2.df.c.929.8		16
21.2	odd	6		882.2.m.a.587.3		16
21.5	even	6		882.2.m.b.587.2		16
21.11	odd	6		882.2.l.b.227.8		16
21.17	even	6		126.2.l.a.101.5	yes	16
21.20	even	2		882.2.t.a.803.8		16
28.3	even	6		3024.2.ca.c.2033.2		16
36.23	even	6		3024.2.ca.c.2609.2		16
36.31	odd	6		1008.2.ca.c.257.6		16
63.4	even	3		882.2.t.a.815.8		16
63.5	even	6		2646.2.m.a.881.8		16
63.13	odd	6		882.2.l.b.509.4		16
63.23	odd	6		2646.2.m.b.881.5		16
63.31	odd	6		126.2.t.a.59.5	yes	16
63.32	odd	6		2646.2.t.b.2285.4		16
63.38	even	6		1134.2.k.a.647.8		16
63.40	odd	6		882.2.m.a.293.3		16
63.41	even	6		2646.2.l.a.1097.8		16
63.52	odd	6		1134.2.k.b.647.1		16
63.58	even	3		882.2.m.b.293.2		16
63.59	even	6	inner	378.2.t.a.17.1		16
84.59	odd	6		1008.2.ca.c.353.6		16
252.31	even	6		1008.2.df.c.689.8		16
252.59	odd	6		3024.2.df.c.17.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.1	✓	16	9.4	even	3
126.2.l.a.101.5	yes	16	21.17	even	6
126.2.t.a.47.5	yes	16	3.2	odd	2
126.2.t.a.59.5	yes	16	63.31	odd	6
378.2.l.a.143.1		16	7.3	odd	6
378.2.l.a.341.5		16	9.5	odd	6
378.2.t.a.17.1		16	63.59	even	6	inner
378.2.t.a.89.1		16	1.1	even	1	trivial
882.2.l.b.227.8		16	21.11	odd	6
882.2.l.b.509.4		16	63.13	odd	6
882.2.m.a.293.3		16	63.40	odd	6
882.2.m.a.587.3		16	21.2	odd	6
882.2.m.b.293.2		16	63.58	even	3
882.2.m.b.587.2		16	21.5	even	6
882.2.t.a.803.8		16	21.20	even	2
882.2.t.a.815.8		16	63.4	even	3
1008.2.ca.c.257.6		16	36.31	odd	6
1008.2.ca.c.353.6		16	84.59	odd	6
1008.2.df.c.689.8		16	252.31	even	6
1008.2.df.c.929.8		16	12.11	even	2
1134.2.k.a.647.8		16	63.38	even	6
1134.2.k.a.971.8		16	9.7	even	3
1134.2.k.b.647.1		16	63.52	odd	6
1134.2.k.b.971.1		16	9.2	odd	6
2646.2.l.a.521.4		16	7.4	even	3
2646.2.l.a.1097.8		16	63.41	even	6
2646.2.m.a.881.8		16	63.5	even	6
2646.2.m.a.1763.8		16	7.2	even	3
2646.2.m.b.881.5		16	63.23	odd	6
2646.2.m.b.1763.5		16	7.5	odd	6
2646.2.t.b.1979.4		16	7.6	odd	2
2646.2.t.b.2285.4		16	63.32	odd	6
3024.2.ca.c.2033.2		16	28.3	even	6
3024.2.ca.c.2609.2		16	36.23	even	6
3024.2.df.c.17.2		16	252.59	odd	6
3024.2.df.c.1601.2		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -2.28190 q^{5} +(1.21977 - 2.34780i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -2.28190 q^{5} +(1.21977 - 2.34780i) q^{7} +1.00000i q^{8} +(1.97618 - 1.14095i) q^{10} +1.09303i q^{11} +(-5.91448 + 3.41473i) q^{13} +(0.117551 + 2.64314i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.35863 - 5.81732i) q^{17} +(-2.47987 - 1.43175i) q^{19} +(-1.14095 + 1.97618i) q^{20} +(-0.546514 - 0.946590i) q^{22} -3.90593i q^{23} +0.207069 q^{25} +(3.41473 - 5.91448i) q^{26} +(-1.42337 - 2.23025i) q^{28} +(-1.59933 - 0.923371i) q^{29} +(-1.75081 - 1.01083i) q^{31} +(0.866025 + 0.500000i) q^{32} +(5.81732 + 3.35863i) q^{34} +(-2.78339 + 5.35745i) q^{35} +(3.57920 - 6.19935i) q^{37} +2.86351 q^{38} -2.28190i q^{40} +(2.45515 + 4.25245i) q^{41} +(-3.74246 + 6.48214i) q^{43} +(0.946590 + 0.546514i) q^{44} +(1.95297 + 3.38264i) q^{46} +(-3.40174 - 5.89199i) q^{47} +(-4.02434 - 5.72754i) q^{49} +(-0.179327 + 0.103535i) q^{50} +6.82946i q^{52} +(0.222069 - 0.128212i) q^{53} -2.49418i q^{55} +(2.34780 + 1.21977i) q^{56} +1.84674 q^{58} +(-0.971009 + 1.68184i) q^{59} +(1.15315 - 0.665771i) q^{61} +2.02166 q^{62} -1.00000 q^{64} +(13.4963 - 7.79207i) q^{65} +(-2.54959 + 4.41602i) q^{67} -6.71727 q^{68} +(-0.268240 - 6.03138i) q^{70} -0.233507i q^{71} +(5.89272 - 3.40216i) q^{73} +7.15840i q^{74} +(-2.47987 + 1.43175i) q^{76} +(2.56621 + 1.33324i) q^{77} +(3.63624 + 6.29816i) q^{79} +(1.14095 + 1.97618i) q^{80} +(-4.25245 - 2.45515i) q^{82} +(-2.91353 + 5.04638i) q^{83} +(7.66407 + 13.2746i) q^{85} -7.48493i q^{86} -1.09303 q^{88} +(-8.99707 + 15.5834i) q^{89} +(0.802809 + 18.0512i) q^{91} +(-3.38264 - 1.95297i) q^{92} +(5.89199 + 3.40174i) q^{94} +(5.65882 + 3.26712i) q^{95} +(4.13903 + 2.38967i) q^{97} +(6.34895 + 2.94803i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47} + 10 q^{49} + 12 q^{50} - 36 q^{53} - 12 q^{58} - 30 q^{59} - 60 q^{61} + 36 q^{62} - 16 q^{64} - 42 q^{65} + 14 q^{67} - 36 q^{68} + 18 q^{77} - 16 q^{79} - 12 q^{85} - 24 q^{89} - 12 q^{91} - 6 q^{92} + 66 q^{95} - 6 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

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